java codility training Genomic-range-query - java

The task is:
A non-empty zero-indexed string S is given. String S consists of N characters from the set of upper-case English letters A, C, G, T.
This string actually represents a DNA sequence, and the upper-case letters represent single nucleotides.
You are also given non-empty zero-indexed arrays P and Q consisting of M integers. These arrays represent queries about minimal nucleotides. We represent the letters of string S as integers 1, 2, 3, 4 in arrays P and Q, where A = 1, C = 2, G = 3, T = 4, and we assume that A < C < G < T.
Query K requires you to find the minimal nucleotide from the range (P[K], Q[K]), 0 ≤ P[i] ≤ Q[i] < N.
For example, consider string S = GACACCATA and arrays P, Q such that:
P[0] = 0 Q[0] = 8
P[1] = 0 Q[1] = 2
P[2] = 4 Q[2] = 5
P[3] = 7 Q[3] = 7
The minimal nucleotides from these ranges are as follows:
(0, 8) is A identified by 1,
(0, 2) is A identified by 1,
(4, 5) is C identified by 2,
(7, 7) is T identified by 4.
Write a function:
class Solution { public int[] solution(String S, int[] P, int[] Q); }
that, given a non-empty zero-indexed string S consisting of N characters and two non-empty zero-indexed arrays P and Q consisting of M integers, returns an array consisting of M characters specifying the consecutive answers to all queries.
The sequence should be returned as:
a Results structure (in C), or
a vector of integers (in C++), or
a Results record (in Pascal), or
an array of integers (in any other programming language).
For example, given the string S = GACACCATA and arrays P, Q such that:
P[0] = 0 Q[0] = 8
P[1] = 0 Q[1] = 2
P[2] = 4 Q[2] = 5
P[3] = 7 Q[3] = 7
the function should return the values [1, 1, 2, 4], as explained above.
Assume that:
N is an integer within the range [1..100,000];
M is an integer within the range [1..50,000];
each element of array P, Q is an integer within the range [0..N − 1];
P[i] ≤ Q[i];
string S consists only of upper-case English letters A, C, G, T.
Complexity:
expected worst-case time complexity is O(N+M);
expected worst-case space complexity is O(N),
beyond input storage
(not counting the storage required for input arguments).
Elements of input arrays can be modified.
My solution is:
class Solution {
public int[] solution(String S, int[] P, int[] Q) {
final char c[] = S.toCharArray();
final int answer[] = new int[P.length];
int tempAnswer;
char tempC;
for (int iii = 0; iii < P.length; iii++) {
tempAnswer = 4;
for (int zzz = P[iii]; zzz <= Q[iii]; zzz++) {
tempC = c[zzz];
if (tempC == 'A') {
tempAnswer = 1;
break;
} else if (tempC == 'C') {
if (tempAnswer > 2) {
tempAnswer = 2;
}
} else if (tempC == 'G') {
if (tempAnswer > 3) {
tempAnswer = 3;
}
}
}
answer[iii] = tempAnswer;
}
return answer;
}
}
It is not optimal, I believe it's supposed to be done within one loop, any hint how can I achieve it?
You can check quality of your solution here https://codility.com/train/ test name is Genomic-range-query.

Here is the solution that got 100 out of 100 in codility.com. Please read about prefix sums to understand the solution:
public static int[] solveGenomicRange(String S, int[] P, int[] Q) {
//used jagged array to hold the prefix sums of each A, C and G genoms
//we don't need to get prefix sums of T, you will see why.
int[][] genoms = new int[3][S.length()+1];
//if the char is found in the index i, then we set it to be 1 else they are 0
//3 short values are needed for this reason
short a, c, g;
for (int i=0; i<S.length(); i++) {
a = 0; c = 0; g = 0;
if ('A' == (S.charAt(i))) {
a=1;
}
if ('C' == (S.charAt(i))) {
c=1;
}
if ('G' == (S.charAt(i))) {
g=1;
}
//here we calculate prefix sums. To learn what's prefix sums look at here https://codility.com/media/train/3-PrefixSums.pdf
genoms[0][i+1] = genoms[0][i] + a;
genoms[1][i+1] = genoms[1][i] + c;
genoms[2][i+1] = genoms[2][i] + g;
}
int[] result = new int[P.length];
//here we go through the provided P[] and Q[] arrays as intervals
for (int i=0; i<P.length; i++) {
int fromIndex = P[i];
//we need to add 1 to Q[i],
//because our genoms[0][0], genoms[1][0] and genoms[2][0]
//have 0 values by default, look above genoms[0][i+1] = genoms[0][i] + a;
int toIndex = Q[i]+1;
if (genoms[0][toIndex] - genoms[0][fromIndex] > 0) {
result[i] = 1;
} else if (genoms[1][toIndex] - genoms[1][fromIndex] > 0) {
result[i] = 2;
} else if (genoms[2][toIndex] - genoms[2][fromIndex] > 0) {
result[i] = 3;
} else {
result[i] = 4;
}
}
return result;
}

Simple, elegant, domain specific, 100/100 solution in JS with comments!
function solution(S, P, Q) {
var N = S.length, M = P.length;
// dictionary to map nucleotide to impact factor
var impact = {A : 1, C : 2, G : 3, T : 4};
// nucleotide total count in DNA
var currCounter = {A : 0, C : 0, G : 0, T : 0};
// how many times nucleotide repeats at the moment we reach S[i]
var counters = [];
// result
var minImpact = [];
var i;
// count nucleotides
for(i = 0; i <= N; i++) {
counters.push({A: currCounter.A, C: currCounter.C, G: currCounter.G});
currCounter[S[i]]++;
}
// for every query
for(i = 0; i < M; i++) {
var from = P[i], to = Q[i] + 1;
// compare count of A at the start of query with count at the end of equry
// if counter was changed then query contains A
if(counters[to].A - counters[from].A > 0) {
minImpact.push(impact.A);
}
// same things for C and others nucleotides with higher impact factor
else if(counters[to].C - counters[from].C > 0) {
minImpact.push(impact.C);
}
else if(counters[to].G - counters[from].G > 0) {
minImpact.push(impact.G);
}
else { // one of the counters MUST be changed, so its T
minImpact.push(impact.T);
}
}
return minImpact;
}

Java, 100/100, but with no cumulative/prefix sums! I stashed the last occurrence index of lower 3 nucelotides in a array "map". Later I check if the last index is between P-Q. If so it returns the nuclotide, if not found, it's the top one (T):
class Solution {
int[][] lastOccurrencesMap;
public int[] solution(String S, int[] P, int[] Q) {
int N = S.length();
int M = P.length;
int[] result = new int[M];
lastOccurrencesMap = new int[3][N];
int lastA = -1;
int lastC = -1;
int lastG = -1;
for (int i = 0; i < N; i++) {
char c = S.charAt(i);
if (c == 'A') {
lastA = i;
} else if (c == 'C') {
lastC = i;
} else if (c == 'G') {
lastG = i;
}
lastOccurrencesMap[0][i] = lastA;
lastOccurrencesMap[1][i] = lastC;
lastOccurrencesMap[2][i] = lastG;
}
for (int i = 0; i < M; i++) {
int startIndex = P[i];
int endIndex = Q[i];
int minimum = 4;
for (int n = 0; n < 3; n++) {
int lastOccurence = getLastNucleotideOccurrence(startIndex, endIndex, n);
if (lastOccurence != 0) {
minimum = n + 1;
break;
}
}
result[i] = minimum;
}
return result;
}
int getLastNucleotideOccurrence(int startIndex, int endIndex, int nucleotideIndex) {
int[] lastOccurrences = lastOccurrencesMap[nucleotideIndex];
int endValueLastOccurenceIndex = lastOccurrences[endIndex];
if (endValueLastOccurenceIndex >= startIndex) {
return nucleotideIndex + 1;
} else {
return 0;
}
}
}

Here is the solution, supposing someone is still interested.
class Solution {
public int[] solution(String S, int[] P, int[] Q) {
int[] answer = new int[P.length];
char[] chars = S.toCharArray();
int[][] cumulativeAnswers = new int[4][chars.length + 1];
for (int iii = 0; iii < chars.length; iii++) {
if (iii > 0) {
for (int zzz = 0; zzz < 4; zzz++) {
cumulativeAnswers[zzz][iii + 1] = cumulativeAnswers[zzz][iii];
}
}
switch (chars[iii]) {
case 'A':
cumulativeAnswers[0][iii + 1]++;
break;
case 'C':
cumulativeAnswers[1][iii + 1]++;
break;
case 'G':
cumulativeAnswers[2][iii + 1]++;
break;
case 'T':
cumulativeAnswers[3][iii + 1]++;
break;
}
}
for (int iii = 0; iii < P.length; iii++) {
for (int zzz = 0; zzz < 4; zzz++) {
if ((cumulativeAnswers[zzz][Q[iii] + 1] - cumulativeAnswers[zzz][P[iii]]) > 0) {
answer[iii] = zzz + 1;
break;
}
}
}
return answer;
}
}

In case anyone cares about C:
#include <string.h>
struct Results solution(char *S, int P[], int Q[], int M) {
int i, a, b, N, *pA, *pC, *pG;
struct Results result;
result.A = malloc(sizeof(int) * M);
result.M = M;
// calculate prefix sums
N = strlen(S);
pA = malloc(sizeof(int) * N);
pC = malloc(sizeof(int) * N);
pG = malloc(sizeof(int) * N);
pA[0] = S[0] == 'A' ? 1 : 0;
pC[0] = S[0] == 'C' ? 1 : 0;
pG[0] = S[0] == 'G' ? 1 : 0;
for (i = 1; i < N; i++) {
pA[i] = pA[i - 1] + (S[i] == 'A' ? 1 : 0);
pC[i] = pC[i - 1] + (S[i] == 'C' ? 1 : 0);
pG[i] = pG[i - 1] + (S[i] == 'G' ? 1 : 0);
}
for (i = 0; i < M; i++) {
a = P[i] - 1;
b = Q[i];
if ((pA[b] - pA[a]) > 0) {
result.A[i] = 1;
} else if ((pC[b] - pC[a]) > 0) {
result.A[i] = 2;
} else if ((pG[b] - pG[a]) > 0) {
result.A[i] = 3;
} else {
result.A[i] = 4;
}
}
return result;
}

Here is my solution Using Segment Tree O(n)+O(log n)+O(M) time
public class DNAseq {
public static void main(String[] args) {
String S="CAGCCTA";
int[] P={2, 5, 0};
int[] Q={4, 5, 6};
int [] results=solution(S,P,Q);
System.out.println(results[0]);
}
static class segmentNode{
int l;
int r;
int min;
segmentNode left;
segmentNode right;
}
public static segmentNode buildTree(int[] arr,int l,int r){
if(l==r){
segmentNode n=new segmentNode();
n.l=l;
n.r=r;
n.min=arr[l];
return n;
}
int mid=l+(r-l)/2;
segmentNode le=buildTree(arr,l,mid);
segmentNode re=buildTree(arr,mid+1,r);
segmentNode root=new segmentNode();
root.left=le;
root.right=re;
root.l=le.l;
root.r=re.r;
root.min=Math.min(le.min,re.min);
return root;
}
public static int getMin(segmentNode root,int l,int r){
if(root.l>r || root.r<l){
return Integer.MAX_VALUE;
}
if(root.l>=l&& root.r<=r) {
return root.min;
}
return Math.min(getMin(root.left,l,r),getMin(root.right,l,r));
}
public static int[] solution(String S, int[] P, int[] Q) {
int[] arr=new int[S.length()];
for(int i=0;i<S.length();i++){
switch (S.charAt(i)) {
case 'A':
arr[i]=1;
break;
case 'C':
arr[i]=2;
break;
case 'G':
arr[i]=3;
break;
case 'T':
arr[i]=4;
break;
default:
break;
}
}
segmentNode root=buildTree(arr,0,S.length()-1);
int[] result=new int[P.length];
for(int i=0;i<P.length;i++){
result[i]=getMin(root,P[i],Q[i]);
}
return result;
} }

Here is a C# solution, the basic idea is pretty much the same as the other answers, but it may be cleaner:
using System;
class Solution
{
public int[] solution(string S, int[] P, int[] Q)
{
int N = S.Length;
int M = P.Length;
char[] chars = {'A','C','G','T'};
//Calculate accumulates
int[,] accum = new int[3, N+1];
for (int i = 0; i <= 2; i++)
{
for (int j = 0; j < N; j++)
{
if(S[j] == chars[i]) accum[i, j+1] = accum[i, j] + 1;
else accum[i, j+1] = accum[i, j];
}
}
//Get minimal nucleotides for the given ranges
int diff;
int[] minimums = new int[M];
for (int i = 0; i < M; i++)
{
minimums[i] = 4;
for (int j = 0; j <= 2; j++)
{
diff = accum[j, Q[i]+1] - accum[j, P[i]];
if (diff > 0)
{
minimums[i] = j+1;
break;
}
}
}
return minimums;
}
}

Here is my solution. Got %100 . Of course I needed to first check and study a little bit prefix sums.
public int[] solution(String S, int[] P, int[] Q){
int[] result = new int[P.length];
int[] factor1 = new int[S.length()];
int[] factor2 = new int[S.length()];
int[] factor3 = new int[S.length()];
int[] factor4 = new int[S.length()];
int factor1Sum = 0;
int factor2Sum = 0;
int factor3Sum = 0;
int factor4Sum = 0;
for(int i=0; i<S.length(); i++){
switch (S.charAt(i)) {
case 'A':
factor1Sum++;
break;
case 'C':
factor2Sum++;
break;
case 'G':
factor3Sum++;
break;
case 'T':
factor4Sum++;
break;
default:
break;
}
factor1[i] = factor1Sum;
factor2[i] = factor2Sum;
factor3[i] = factor3Sum;
factor4[i] = factor4Sum;
}
for(int i=0; i<P.length; i++){
int start = P[i];
int end = Q[i];
if(start == 0){
if(factor1[end] > 0){
result[i] = 1;
}else if(factor2[end] > 0){
result[i] = 2;
}else if(factor3[end] > 0){
result[i] = 3;
}else{
result[i] = 4;
}
}else{
if(factor1[end] > factor1[start-1]){
result[i] = 1;
}else if(factor2[end] > factor2[start-1]){
result[i] = 2;
}else if(factor3[end] > factor3[start-1]){
result[i] = 3;
}else{
result[i] = 4;
}
}
}
return result;
}

If someone is still interested in this exercise, I share my Python solution (100/100 in Codility)
def solution(S, P, Q):
count = []
for i in range(3):
count.append([0]*(len(S)+1))
for index, i in enumerate(S):
count[0][index+1] = count[0][index] + ( i =='A')
count[1][index+1] = count[1][index] + ( i =='C')
count[2][index+1] = count[2][index] + ( i =='G')
result = []
for i in range(len(P)):
start = P[i]
end = Q[i]+1
if count[0][end] - count[0][start]:
result.append(1)
elif count[1][end] - count[1][start]:
result.append(2)
elif count[2][end] - count[2][start]:
result.append(3)
else:
result.append(4)
return result

This is my JavaScript solution that got 100% across the board on Codility:
function solution(S, P, Q) {
let total = [];
let min;
for (let i = 0; i < P.length; i++) {
const substring = S.slice(P[i], Q[i] + 1);
if (substring.includes('A')) {
min = 1;
} else if (substring.includes('C')) {
min = 2;
} else if (substring.includes('G')) {
min = 3;
} else if (substring.includes('T')) {
min = 4;
}
total.push(min);
}
return total;
}

import java.util.Arrays;
import java.util.HashMap;
class Solution {
static HashMap<Character, Integer > characterMapping = new HashMap<Character, Integer>(){{
put('A',1);
put('C',2);
put('G',3);
put('T',4);
}};
public static int minimum(int[] arr) {
if (arr.length ==1) return arr[0];
int smallestIndex = 0;
for (int index = 0; index<arr.length; index++) {
if (arr[index]<arr[smallestIndex]) smallestIndex=index;
}
return arr[smallestIndex];
}
public int[] solution(String S, int[] P, int[] Q) {
final char[] characterInput = S.toCharArray();
final int[] integerInput = new int[characterInput.length];
for(int counter=0; counter < characterInput.length; counter++) {
integerInput[counter] = characterMapping.get(characterInput[counter]);
}
int[] result = new int[P.length];
//assuming P and Q have the same length
for(int index =0; index<P.length; index++) {
if (P[index]==Q[index]) {
result[index] = integerInput[P[index]];
break;
}
final int[] subArray = Arrays.copyOfRange(integerInput, P[index], Q[index]+1);
final int minimumValue = minimum(subArray);
result[index]= minimumValue;
}
return result;
}
}

Here's 100% Scala solution:
def solution(S: String, P: Array[Int], Q: Array[Int]): Array[Int] = {
val resp = for(ind <- 0 to P.length-1) yield {
val sub= S.substring(P(ind),Q(ind)+1)
var factor = 4
if(sub.contains("A")) {factor=1}
else{
if(sub.contains("C")) {factor=2}
else{
if(sub.contains("G")) {factor=3}
}
}
factor
}
return resp.toArray
}
And performance: https://codility.com/demo/results/trainingEUR4XP-425/

Hope this helps.
public int[] solution(String S, int[] P, int[] K) {
// write your code in Java SE 8
char[] sc = S.toCharArray();
int[] A = new int[sc.length];
int[] G = new int[sc.length];
int[] C = new int[sc.length];
int prevA =-1,prevG=-1,prevC=-1;
for(int i=0;i<sc.length;i++){
if(sc[i]=='A')
prevA=i;
else if(sc[i] == 'G')
prevG=i;
else if(sc[i] =='C')
prevC=i;
A[i] = prevA;
G[i] = prevG;
C[i] = prevC;
//System.out.println(A[i]+ " "+G[i]+" "+C[i]);
}
int[] result = new int[P.length];
for(int i=0;i<P.length;i++){
//System.out.println(A[P[i]]+ " "+A[K[i]]+" "+C[P[i]]+" "+C[K[i]]+" "+P[i]+" "+K[i]);
if(A[K[i]] >=P[i] && A[K[i]] <=K[i]){
result[i] =1;
}
else if(C[K[i]] >=P[i] && C[K[i]] <=K[i]){
result[i] =2;
}else if(G[K[i]] >=P[i] && G[K[i]] <=K[i]){
result[i] =3;
}
else{
result[i]=4;
}
}
return result;
}

Python Solution with explanation
The idea is to hold an auxiliary array per nucleotide X, with position i (ignoring zero) is how many times X has occurred as of now. And so if we need the number of occurrences of X from position f to position t, we could take the following equation:
aux(t) - aux(f)
Time complexity is:
O(N+M)
def solution(S, P, Q):
n = len(S)
m = len(P)
aux = [[0 for i in range(n+1)] for i in [0,1,2]]
for i,c in enumerate(S):
aux[0][i+1] = aux[0][i] + ( c == 'A' )
aux[1][i+1] = aux[1][i] + ( c == 'C' )
aux[2][i+1] = aux[2][i] + ( c == 'G' )
result = []
for i in range(m):
fromIndex , toIndex = P[i] , Q[i] +1
if aux[0][toIndex] - aux[0][fromIndex] > 0:
r = 1
elif aux[1][toIndex] - aux[1][fromIndex] > 0:
r = 2
elif aux[2][toIndex] - aux[2][fromIndex] > 0:
r = 3
else:
r = 4
result.append(r)
return result

This is a Swift 4 solution to the same problem. It is based on #codebusta's solution above:
public func solution(_ S : inout String, _ P : inout [Int], _ Q : inout [Int]) -> [Int] {
var impacts = [Int]()
var prefixSum = [[Int]]()
for _ in 0..<3 {
let array = Array(repeating: 0, count: S.count + 1)
prefixSum.append(array)
}
for (index, character) in S.enumerated() {
var a = 0
var c = 0
var g = 0
switch character {
case "A":
a = 1
case "C":
c = 1
case "G":
g = 1
default:
break
}
prefixSum[0][index + 1] = prefixSum[0][index] + a
prefixSum[1][index + 1] = prefixSum[1][index] + c
prefixSum[2][index + 1] = prefixSum[2][index] + g
}
for tuple in zip(P, Q) {
if prefixSum[0][tuple.1 + 1] - prefixSum[0][tuple.0] > 0 {
impacts.append(1)
}
else if prefixSum[1][tuple.1 + 1] - prefixSum[1][tuple.0] > 0 {
impacts.append(2)
}
else if prefixSum[2][tuple.1 + 1] - prefixSum[2][tuple.0] > 0 {
impacts.append(3)
}
else {
impacts.append(4)
}
}
return impacts
}

Here is python solution with little explanation hope it helps some one.
Python codility 100%
def solution(S, P, Q):
"""
https://app.codility.com/demo/results/training8QBVFJ-EQB/
100%
Idea is consider solution as single dimensional array and use concept of prefix some ie.
stores the value in array for p,c and g based on frequency
array stores the frequency of p,c and g for all positions
Example -
# [0, 0, 1, 1, 1, 1, 1, 2] - prefix some of A - represents the max occurrence of A as 2 in array
# [0, 1, 1, 1, 2, 3, 3, 3] - prefix some of C - represents the max occurrence of A as 3 in array
# [0, 0, 0, 1, 1, 1, 1, 1] - prefix some of G - represents the max occurrence of A as 1 in array
# To find the query answers we can just use prefix some and find the distance between position
S = CAGCCTA
P[0] = 2 Q[0] = 4
P[1] = 5 Q[1] = 5
P[2] = 0 Q[2] = 6
Given a non-empty zero-indexed string S consisting of N characters and two non-empty zero-indexed arrays P and Q consisting
of M integers, returns an array consisting of M integers specifying the consecutive answers to all queries.
The part of the DNA between positions 2 and 4 contains nucleotide G and C (twice), whose impact factors are 3 and 2 respectively, so the answer is 2.
The part between positions 5 and 5 contains a single nucleotide T, whose impact factor is 4, so the answer is 4.
The part between positions 0 and 6 (the whole string) contains all nucleotide, in particular nucleotide A whose impact factor is 1, so the answer is 1.
N is an integer within the range [1..100,000];
M is an integer within the range [1..50,000];
each element of arrays P, Q is an integer within the range [0..N − 1];
P[K] ≤ Q[K], where 0 ≤ K < M;
string S consists only of upper-case English letters A, C, G, T.
Ref - https://github.com/ghanan94/codility-lesson-solutions/blob/master/Lesson%2005%20-%20Prefix%20Sums/PrefixSums.pdf
:return: return the values [2, 4, 1]
"""
# two d array - column size is 3 for a,c,g - not taking size 4 since that will be part of else ie. don`t need to calculate
# row size is the length of DNA sequence
prefix_sum_two_d_array = [[0 for i in range(len(S) + 1)] for j in range(3)]
# find the prefix some of all nucleotide in given sequence
for i, nucleotide in enumerate(S):
# store prefix some of each
# nucleotide == 'A -> 1 if true 0 if false
# [0, 0, 1, 1, 1, 1, 1, 2] - prefix some of A - represents the max occurrence of A as 2 in array
prefix_sum_two_d_array[0][i + 1] = prefix_sum_two_d_array[0][i] + (nucleotide == 'A')
# store prefix some of c
# [0, 1, 1, 1, 2, 3, 3, 3] - prefix some of C - represents the max occurrence of A as 3 in array
prefix_sum_two_d_array[1][i + 1] = prefix_sum_two_d_array[1][i] + (nucleotide == 'C')
# store prefix some of g
# [0, 0, 0, 1, 1, 1, 1, 1] - prefix some of G - represents the max occurrence of A as 1 in array
prefix_sum_two_d_array[2][i + 1] = prefix_sum_two_d_array[2][i] + (nucleotide == 'G')
#print(prefix_sum_two_d_array)
# now to find the query answers we can just use prefix some and find the distance between position
query_answers = []
for position in range(len(P)):
# for each query of p
# find the start index from p
start_index = P[position]
# find the end index from Q
end_index = Q[position] + 1
# find the value from prefix some array - just subtract end index and start index to find the value
if prefix_sum_two_d_array[0][end_index] - prefix_sum_two_d_array[0][start_index]:
query_answers.append(1)
elif prefix_sum_two_d_array[1][end_index] - prefix_sum_two_d_array[1][start_index]:
query_answers.append(2)
elif prefix_sum_two_d_array[2][end_index] - prefix_sum_two_d_array[2][start_index]:
query_answers.append(3)
else:
query_answers.append(4)
return query_answers
result = solution("CAGCCTA", [2, 5, 0], [4, 5, 6])
print("Sol " + str(result))
# Sol [2, 4, 1]

My 100% JavaScript solution with O(N + M) time complexity and no use of advanced built-in methods such as .includes, .substring, etc:
function solution(S, P, Q) {
// initialize prefix sums for A, C, G (you don't need T)
const A = [0];
const C = [0];
const G = [0];
// calculate prefix sums for A, C, G
for (let i = 0, len = S.length; i < len; i++) {
A.push(A[i] + Number("A" === S[i]));
C.push(C[i] + Number("C" === S[i]));
G.push(G[i] + Number("G" === S[i]));
}
// calculate the result using prefix sums
const result = [];
for (let i = 0, len = P.length; i < len; i++) {
const from = P[i];
const to = Q[i] + 1;
if (A[to] - A[from] > 0) {
result.push(1);
} else if (C[to] - C[from] > 0) {
result.push(2);
} else if (G[to] - G[from] > 0) {
result.push(3);
} else {
result.push(4); // this is why you don't need T
}
}
return result;
}

pshemek's solution constrains itself to the space complexity (O(N)) - even with the 2-d array and the answer array because a constant (4) is used for the 2-d array. That solution also fits in with the computational complexity - whereas mine is O (N^2) - though the actual computational complexity is much lower because it skips over entire ranges that include minimal values.
I gave it a try - but mine ends up using more space - but makes more intuitive sense to me (C#):
public static int[] solution(String S, int[] P, int[] Q)
{
const int MinValue = 1;
Dictionary<char, int> stringValueTable = new Dictionary<char,int>(){ {'A', 1}, {'C', 2}, {'G', 3}, {'T', 4} };
char[] inputArray = S.ToCharArray();
int[,] minRangeTable = new int[S.Length, S.Length]; // The meaning of this table is [x, y] where x is the start index and y is the end index and the value is the min range - if 0 then it is the min range (whatever that is)
for (int startIndex = 0; startIndex < S.Length; ++startIndex)
{
int currentMinValue = 4;
int minValueIndex = -1;
for (int endIndex = startIndex; (endIndex < S.Length) && (minValueIndex == -1); ++endIndex)
{
int currentValue = stringValueTable[inputArray[endIndex]];
if (currentValue < currentMinValue)
{
currentMinValue = currentValue;
if (currentMinValue == MinValue) // We can stop iterating - because anything with this index in its range will always be minimal
minValueIndex = endIndex;
else
minRangeTable[startIndex, endIndex] = currentValue;
}
else
minRangeTable[startIndex, endIndex] = currentValue;
}
if (minValueIndex != -1) // Skip over this index - since it is minimal
startIndex = minValueIndex; // We would have a "+ 1" here - but the "auto-increment" in the for statement will get us past this index
}
int[] result = new int[P.Length];
for (int outputIndex = 0; outputIndex < result.Length; ++outputIndex)
{
result[outputIndex] = minRangeTable[P[outputIndex], Q[outputIndex]];
if (result[outputIndex] == 0) // We could avoid this if we initialized our 2-d array with 1's
result[outputIndex] = 1;
}
return result;
}
In pshemek's answer - the "trick" in the second loop is simply that once you've determined you've found a range with the minimal value - you don't need to continue iterating. Not sure if that helps.

The php 100/100 solution:
function solution($S, $P, $Q) {
$S = str_split($S);
$len = count($S);
$lep = count($P);
$arr = array();
$result = array();
$clone = array_fill(0, 4, 0);
for($i = 0; $i < $len; $i++){
$arr[$i] = $clone;
switch($S[$i]){
case 'A':
$arr[$i][0] = 1;
break;
case 'C':
$arr[$i][1] = 1;
break;
case 'G':
$arr[$i][2] = 1;
break;
default:
$arr[$i][3] = 1;
break;
}
}
for($i = 1; $i < $len; $i++){
for($j = 0; $j < 4; $j++){
$arr[$i][$j] += $arr[$i - 1][$j];
}
}
for($i = 0; $i < $lep; $i++){
$x = $P[$i];
$y = $Q[$i];
for($a = 0; $a < 4; $a++){
$sub = 0;
if($x - 1 >= 0){
$sub = $arr[$x - 1][$a];
}
if($arr[$y][$a] - $sub > 0){
$result[$i] = $a + 1;
break;
}
}
}
return $result;
}

This program has got score 100 and performance wise has got an edge over other java codes listed above!
The code can be found here.
public class GenomicRange {
final int Index_A=0, Index_C=1, Index_G=2, Index_T=3;
final int A=1, C=2, G=3, T=4;
public static void main(String[] args) {
GenomicRange gen = new GenomicRange();
int[] M = gen.solution( "GACACCATA", new int[] { 0,0,4,7 } , new int[] { 8,2,5,7 } );
System.out.println(Arrays.toString(M));
}
public int[] solution(String S, int[] P, int[] Q) {
int[] M = new int[P.length];
char[] charArr = S.toCharArray();
int[][] occCount = new int[3][S.length()+1];
int charInd = getChar(charArr[0]);
if(charInd!=3) {
occCount[charInd][1]++;
}
for(int sInd=1; sInd<S.length(); sInd++) {
charInd = getChar(charArr[sInd]);
if(charInd!=3)
occCount[charInd][sInd+1]++;
occCount[Index_A][sInd+1]+=occCount[Index_A][sInd];
occCount[Index_C][sInd+1]+=occCount[Index_C][sInd];
occCount[Index_G][sInd+1]+=occCount[Index_G][sInd];
}
for(int i=0;i<P.length;i++) {
int a,c,g;
if(Q[i]+1>=occCount[0].length) continue;
a = occCount[Index_A][Q[i]+1] - occCount[Index_A][P[i]];
c = occCount[Index_C][Q[i]+1] - occCount[Index_C][P[i]];
g = occCount[Index_G][Q[i]+1] - occCount[Index_G][P[i]];
M[i] = a>0? A : c>0 ? C : g>0 ? G : T;
}
return M;
}
private int getChar(char c) {
return ((c=='A') ? Index_A : ((c=='C') ? Index_C : ((c=='G') ? Index_G : Index_T)));
}
}

Here's a simple javascript solution which got 100%.
function solution(S, P, Q) {
var A = [];
var C = [];
var G = [];
var T = [];
var result = [];
var i = 0;
S.split('').forEach(function(a) {
if (a === 'A') {
A.push(i);
} else if (a === 'C') {
C.push(i);
} else if (a === 'G') {
G.push(i);
} else {
T.push(i);
}
i++;
});
function hasNucl(typeArray, start, end) {
return typeArray.some(function(a) {
return a >= P[j] && a <= Q[j];
});
}
for(var j=0; j<P.length; j++) {
if (hasNucl(A, P[j], P[j])) {
result.push(1)
} else if (hasNucl(C, P[j], P[j])) {
result.push(2);
} else if (hasNucl(G, P[j], P[j])) {
result.push(3);
} else {
result.push(4);
}
}
return result;
}

perl 100/100 solution:
sub solution {
my ($S, $P, $Q)=#_; my #P=#$P; my #Q=#$Q;
my #_A = (0), #_C = (0), #_G = (0), #ret =();
foreach (split //, $S)
{
push #_A, $_A[-1] + ($_ eq 'A' ? 1 : 0);
push #_C, $_C[-1] + ($_ eq 'C' ? 1 : 0);
push #_G, $_G[-1] + ($_ eq 'G' ? 1 : 0);
}
foreach my $i (0..$#P)
{
my $from_index = $P[$i];
my $to_index = $Q[$i] + 1;
if ( $_A[$to_index] - $_A[$from_index] > 0 )
{
push #ret, 1;
next;
}
if ( $_C[$to_index] - $_C[$from_index] > 0 )
{
push #ret, 2;
next;
}
if ( $_G[$to_index] - $_G[$from_index] > 0 )
{
push #ret, 3;
next;
}
push #ret, 4
}
return #ret;
}

Java 100/100
class Solution {
public int[] solution(String S, int[] P, int[] Q) {
int qSize = Q.length;
int[] answers = new int[qSize];
char[] sequence = S.toCharArray();
int[][] occCount = new int[3][sequence.length+1];
int[] geneImpactMap = new int['G'+1];
geneImpactMap['A'] = 0;
geneImpactMap['C'] = 1;
geneImpactMap['G'] = 2;
if(sequence[0] != 'T') {
occCount[geneImpactMap[sequence[0]]][0]++;
}
for(int i = 0; i < sequence.length; i++) {
occCount[0][i+1] = occCount[0][i];
occCount[1][i+1] = occCount[1][i];
occCount[2][i+1] = occCount[2][i];
if(sequence[i] != 'T') {
occCount[geneImpactMap[sequence[i]]][i+1]++;
}
}
for(int j = 0; j < qSize; j++) {
for(int k = 0; k < 3; k++) {
if(occCount[k][Q[j]+1] - occCount[k][P[j]] > 0) {
answers[j] = k+1;
break;
}
answers[j] = 4;
}
}
return answers;
}
}

In ruby (100/100)
def interval_sum x,y,p
p[y+1] - p[x]
end
def solution(s,p,q)
#Hash of arrays with prefix sums
p_sums = {}
respuesta = []
%w(A C G T).each do |letter|
p_sums[letter] = Array.new s.size+1, 0
end
(0...s.size).each do |count|
%w(A C G T).each do |letter|
p_sums[letter][count+1] = p_sums[letter][count]
end if count > 0
case s[count]
when 'A'
p_sums['A'][count+1] += 1
when 'C'
p_sums['C'][count+1] += 1
when 'G'
p_sums['G'][count+1] += 1
when 'T'
p_sums['T'][count+1] += 1
end
end
(0...p.size).each do |count|
x = p[count]
y = q[count]
if interval_sum(x, y, p_sums['A']) > 0 then
respuesta << 1
next
end
if interval_sum(x, y, p_sums['C']) > 0 then
respuesta << 2
next
end
if interval_sum(x, y, p_sums['G']) > 0 then
respuesta << 3
next
end
if interval_sum(x, y, p_sums['T']) > 0 then
respuesta << 4
next
end
end
respuesta
end

simple php 100/100 solution
function solution($S, $P, $Q) {
$result = array();
for ($i = 0; $i < count($P); $i++) {
$from = $P[$i];
$to = $Q[$i];
$length = $from >= $to ? $from - $to + 1 : $to - $from + 1;
$new = substr($S, $from, $length);
if (strpos($new, 'A') !== false) {
$result[$i] = 1;
} else {
if (strpos($new, 'C') !== false) {
$result[$i] = 2;
} else {
if (strpos($new, 'G') !== false) {
$result[$i] = 3;
} else {
$result[$i] = 4;
}
}
}
}
return $result;
}

Here's my Java (100/100) Solution:
class Solution {
private ImpactFactorHolder[] mHolder;
private static final int A=0,C=1,G=2,T=3;
public int[] solution(String S, int[] P, int[] Q) {
mHolder = createImpactHolderArray(S);
int queriesLength = P.length;
int[] result = new int[queriesLength];
for (int i = 0; i < queriesLength; ++i ) {
int value = 0;
if( P[i] == Q[i]) {
value = lookupValueForIndex(S.charAt(P[i])) + 1;
} else {
value = calculateMinImpactFactor(P[i], Q[i]);
}
result[i] = value;
}
return result;
}
public int calculateMinImpactFactor(int P, int Q) {
int minImpactFactor = 3;
for (int nucleotide = A; nucleotide <= T; ++nucleotide ) {
int qValue = mHolder[nucleotide].mOcurrencesSum[Q];
int pValue = mHolder[nucleotide].mOcurrencesSum[P];
// handling special cases when the less value is assigned on the P index
if( P-1 >= 0 ) {
pValue = mHolder[nucleotide].mOcurrencesSum[P-1] == 0 ? 0 : pValue;
} else if ( P == 0 ) {
pValue = mHolder[nucleotide].mOcurrencesSum[P] == 1 ? 0 : pValue;
}
if ( qValue - pValue > 0) {
minImpactFactor = nucleotide;
break;
}
}
return minImpactFactor + 1;
}
public int lookupValueForIndex(char nucleotide) {
int value = 0;
switch (nucleotide) {
case 'A' :
value = A;
break;
case 'C' :
value = C;
break;
case 'G':
value = G;
break;
case 'T':
value = T;
break;
default:
break;
}
return value;
}
public ImpactFactorHolder[] createImpactHolderArray(String S) {
int length = S.length();
ImpactFactorHolder[] holder = new ImpactFactorHolder[4];
holder[A] = new ImpactFactorHolder(1,'A', length);
holder[C] = new ImpactFactorHolder(2,'C', length);
holder[G] = new ImpactFactorHolder(3,'G', length);
holder[T] = new ImpactFactorHolder(4,'T', length);
int i =0;
for(char c : S.toCharArray()) {
int nucleotide = lookupValueForIndex(c);
++holder[nucleotide].mAcum;
holder[nucleotide].mOcurrencesSum[i] = holder[nucleotide].mAcum;
holder[A].mOcurrencesSum[i] = holder[A].mAcum;
holder[C].mOcurrencesSum[i] = holder[C].mAcum;
holder[G].mOcurrencesSum[i] = holder[G].mAcum;
holder[T].mOcurrencesSum[i] = holder[T].mAcum;
++i;
}
return holder;
}
private static class ImpactFactorHolder {
public ImpactFactorHolder(int impactFactor, char nucleotide, int length) {
mImpactFactor = impactFactor;
mNucleotide = nucleotide;
mOcurrencesSum = new int[length];
mAcum = 0;
}
int mImpactFactor;
char mNucleotide;
int[] mOcurrencesSum;
int mAcum;
}
}
Link: https://codility.com/demo/results/demoJFB5EV-EG8/
I'm looking forward to implement a Segment Tree similar to #Abhishek Kumar solution

My C++ solution
vector<int> solution(string &S, vector<int> &P, vector<int> &Q) {
vector<int> impactCount_A(S.size()+1, 0);
vector<int> impactCount_C(S.size()+1, 0);
vector<int> impactCount_G(S.size()+1, 0);
int lastTotal_A = 0;
int lastTotal_C = 0;
int lastTotal_G = 0;
for (int i = (signed)S.size()-1; i >= 0; --i) {
switch(S[i]) {
case 'A':
++lastTotal_A;
break;
case 'C':
++lastTotal_C;
break;
case 'G':
++lastTotal_G;
break;
};
impactCount_A[i] = lastTotal_A;
impactCount_C[i] = lastTotal_C;
impactCount_G[i] = lastTotal_G;
}
vector<int> results(P.size(), 0);
for (int i = 0; i < P.size(); ++i) {
int pIndex = P[i];
int qIndex = Q[i];
int numA = impactCount_A[pIndex]-impactCount_A[qIndex+1];
int numC = impactCount_C[pIndex]-impactCount_C[qIndex+1];
int numG = impactCount_G[pIndex]-impactCount_G[qIndex+1];
if (numA > 0) {
results[i] = 1;
}
else if (numC > 0) {
results[i] = 2;
}
else if (numG > 0) {
results[i] = 3;
}
else {
results[i] = 4;
}
}
return results;
}

/* 100/100 solution C++.
Using prefix sums. Firstly converting chars to integer in nuc variable. Then in a bi-dimensional vector we account the occurrence in S of each nucleoside x in it's respective prefix_sum[s][x]. After we just have to find out the lower nucluoside that occurred in each interval K.
*/
.
vector solution(string &S, vector &P, vector &Q) {
int n=S.size();
int m=P.size();
vector<vector<int> > prefix_sum(n+1,vector<int>(4,0));
int nuc;
//prefix occurrence sum
for (int s=0;s<n; s++) {
nuc = S.at(s) == 'A' ? 1 : (S.at(s) == 'C' ? 2 : (S.at(s) == 'G' ? 3 : 4) );
for (int u=0;u<4;u++) {
prefix_sum[s+1][u] = prefix_sum[s][u] + ((u+1)==nuc?1:0);
}
}
//find minimal impact factor in each interval K
int lower_impact_factor;
for (int k=0;k<m;k++) {
lower_impact_factor=4;
for (int u=2;u>=0;u--) {
if (prefix_sum[Q[k]+1][u] - prefix_sum[P[k]][u] != 0)
lower_impact_factor = u+1;
}
P[k]=lower_impact_factor;
}
return P;
}

static public int[] solution(String S, int[] P, int[] Q) {
// write your code in Java SE 8
int A[] = new int[S.length() + 1], C[] = new int[S.length() + 1], G[] = new int[S.length() + 1];
int last_a = 0, last_c = 0, last_g = 0;
int results[] = new int[P.length];
int p = 0, q = 0;
for (int i = S.length() - 1; i >= 0; i -= 1) {
switch (S.charAt(i)) {
case 'A': {
last_a += 1;
break;
}
case 'C': {
last_c += 1;
break;
}
case 'G': {
last_g += 1;
break;
}
}
A[i] = last_a;
G[i] = last_g;
C[i] = last_c;
}
for (int i = 0; i < P.length; i++) {
p = P[i];
q = Q[i];
if (A[p] - A[q + 1] > 0) {
results[i] = 1;
} else if (C[p] - C[q + 1] > 0) {
results[i] = 2;
} else if (G[p] - G[q + 1] > 0) {
results[i] = 3;
} else {
results[i] = 4;
}
}
return results;
}

scala solution 100/100
import scala.annotation.switch
import scala.collection.mutable
object Solution {
def solution(s: String, p: Array[Int], q: Array[Int]): Array[Int] = {
val n = s.length
def arr = mutable.ArrayBuffer.fill(n + 1)(0L)
val a = arr
val c = arr
val g = arr
val t = arr
for (i <- 1 to n) {
def inc(z: mutable.ArrayBuffer[Long]): Unit = z(i) = z(i - 1) + 1L
def shift(z: mutable.ArrayBuffer[Long]): Unit = z(i) = z(i - 1)
val char = s(i - 1)
(char: #switch) match {
case 'A' => inc(a); shift(c); shift(g); shift(t);
case 'C' => shift(a); inc(c); shift(g); shift(t);
case 'G' => shift(a); shift(c); inc(g); shift(t);
case 'T' => shift(a); shift(c); shift(g); inc(t);
}
}
val r = mutable.ArrayBuffer.fill(p.length)(0)
for (i <- p.indices) {
val start = p(i)
val end = q(i) + 1
r(i) =
if (a(start) != a(end)) 1
else if (c(start) != c(end)) 2
else if (g(start) != g(end)) 3
else if (t(start) != t(end)) 4
else 0
}
r.toArray
}
}

Related

How to change `List` to `List of tuple` in java

I am using the below function to converting the sublists of list to 0 and the rest elements to 1 however i am trying to change the data structure to list of tuple.
for example the function provide for the input [1,2,3,5,10] to [0,0,0,1,1]. how can i convert this data structure to get the following output like this: [(0,1),(0,2),(0,3),(1,5),(1,10)] ? Or maybe to another similar data-structure if possible? like list of two element arrays
public static void main(String[] args) {
int[] arr = { 1, 8, 1, 9, 10 };
// assume arr.length >= 2
boolean asc = arr[1] - arr[0] == 1;
for (int i = 1; i < arr.length - 1; i++) {
if (arr[i + 1] - arr[i] == 1) {
arr[i] = 0;
asc = true;
} else {
if (asc) {
asc = false;
arr[i] = 0;
}
else {
arr[i] = 1;
}
}
}
arr[arr.length - 1] = asc ? 0 : 1;
for (int i = 0; i < arr.length; i++) {
System.out.println(arr[i]);
}
}
You can create a class Tuple to hold your values
public class Tuple {
int first;
boolean second;
public Tuple(int first, boolean second) {
this.first = first;
this.second = second;
}
#Override
public String toString() {
return String.format("(%d, %b)", first, second);
}
}
And then slightly change your code to use it
final int[] arr = { 1, 8, 1, 9, 10 };
Tuple[] result = new Tuple[arr.length];
boolean asc = arr[1] - arr[0] == 1;
result[0] = new Tuple(arr[0], asc);
for (int i = 1; i < arr.length - 1; i++) {
if (arr[i + 1] - arr[i] == 1) {
asc = true;
} else {
if (asc) {
asc = false;
}
}
result[i] = new Tuple(arr[i], asc);
}
result[arr.length - 1] = new Tuple(arr[arr.length - 1], asc);
for (int i = 0; i < arr.length; i++) {
System.out.println(result[i]);
}
This outputs
(1, false)
(8, false)
(1, false)
(9, true)
(10, true)
Note that if/else inside the for loops probably can be improved but since it wasn't essential to the answer I haven't done so myself

java solution to bridge building not returning right answer

I am having issues with my code it is returning 1 when it should be returning 2. The pairs I have are: new CityPairs(6, 2), new CityPairs( 4, 3 ), new CityPairs( 2, 6) , new CityPairs( 1, 5 ). Which it should return 2 bridges but is returning 1. Below is my code.
class CityPairs {
int north, south;
public CityPairs(int north, int south){
this.north = north;
this.south = south;
}
}
class CityPairsDriver {
// function to find the maximum number
// of bridges that can be built
static int maxBridges(CityPairs values[], int n) {
int lis[] = new int[n];
for (int i = 0; i < n; i++)
lis[i] = 1;
Arrays.sort(values, new Comparator<CityPairs>() {
#Override
public int compare(CityPairs a, CityPairs b) {
if (a.south == b.south)
if (a.north < b.north)
return -1;
else
return 1;
else {
if (a.south < b.south)
return 1;
else
return 1;
}
}
});
// logic of longest increasing subsequence
// applied on the northern coordinates
for (int i = 1; i < n; i++)
for (int j = 0; j < i; j++)
if (values[i].north >= values[j].north && lis[i] < 1 + lis[j])
lis[i] = 1 + lis[j];
int max = lis[0];
for (int i = 1; i < n; i++)
if (max < lis[i])
max = lis[i];
// required number of bridges
// that can be built
return max;
}
// Driver program to test above
public static void main(String args[]) {
CityPairs values[] = { new CityPairs(6, 2), new CityPairs( 4, 3 ), new CityPairs( 2, 6) , new CityPairs( 1, 5 ) };
int n = 4;
System.out.println("Maximum number of bridges = " + maxBridges(values, n));
}
}
I based my answer off of this:
https://www.geeksforgeeks.org/dynamic-programming-building-bridges/
you have 3 return that return the same value i think you need to change the last one
so your problem is in the compare function

sum of two arrays element wise?

There is a problem in which two random integer arrays are given, in which numbers from 0 to 9 are present at every index (i.e. single digit integer is present at every index of both given arrays). I need to find the sum of the numbers represented by the input arrays and put the result in another array.
I believe everything is fine with my code as I execute it almost 50 to 60 times for different arrays. But when I submit it in my school's online judge it accepted only 4 test cases and rejected the other two. I can't figure out in which case it will give wrong output. Need a little help guys.
HERE IS MY CODE
public static int[] sumOfTwoArrays(int[] arr1, int[] arr2){
int size1 = arr1.length;
int size2 = arr2.length;
int carry = 0,sum,s,r;
if(size1 == size2) {
int arr3[] = new int[size1+1];
for(int i=arr1.length-1;i>=-1;i--) {
if(i==-1) {
arr3[i+1] = carry;
//System.out.println(i+1+" "+arr3[i+1]);
} else {
sum = arr1[i] + arr2[i];
if(sum>9) {
s =sum;
r = s % 10;
arr3[i+1] = carry + r;
carry = 1;
//System.out.println(i+" "+arr3[i]);
} else {
if(sum==9 && carry==1) {
s =sum+carry;
r = s % 10;
arr3[i+1] = r;
} else {
arr3[i+1] = sum+carry;
carry=0;
}
//System.out.println(i+" "+arr3[i]);
}
}
}
return arr3;
} else if (size1>size2) {
int arr3[] = new int[size1+1];
int diff = arr1.length - arr2.length;
for(int i=arr1.length-1;i>=-1;i--) {
if(i==-1) {
arr3[i+1] = carry;
} else {
if(i>=diff) {
sum = arr1[i] + arr2[i-diff];
if(sum>9) {
s =sum;
r = s % 10;
arr3[i+1] = carry + r;
carry = 1;
} else {
if(sum==9 && carry==1) {
s =sum+carry;
r = s % 10;
arr3[i+1] = r;
} else {
arr3[i+1] = sum+carry;
carry=0;
}
}
} // end of diff i
else {
arr3[i+1] = arr1[i];
carry = 0;
}
}
}
return arr3;
} else {
int arr3[] = new int[size2+1];
int diff = arr2.length - arr1.length;
for(int i=arr2.length-1;i>=-1;i--) {
if(i==-1) {
arr3[i+1] = carry;
} else {
if(i>=diff) {
sum = arr2[i] + arr1[i-diff];
if(sum>9) {
s =sum;
r = s % 10;
arr3[i+1] = carry + r;
carry = 1;
} else {
if(sum==9 && carry==1) {
s =sum+carry;
r = s % 10;
arr3[i+1] = r;
} else {
arr3[i+1] = sum+carry;
carry=0;
}
}
} // end of diff i
else {
arr3[i+1] = arr2[i];
carry = 0;
}
}
}
return arr3;
}
}
Sample input:
int[] arr1 = {8,5,3,9,6};
int[] arr2 = {3,3,3,3,3};
Sample output:
{1,1,8,7,2,9}
Sample input:
int[] arr1 = {8,5,3,9,6};
int[] arr2 = {1,0,5};
Sample output:
{0,8,5,5,0,1}
Well, I have this algorith based on Eran solution (was working to fixe the bug he since corrected), I will shared it since I use less arrays.
public static int[] sum(int[] arr1, int[] arr2){
int carry = 0;
int sum = 0;
int len1 = arr1.length;
int len2 = arr2.length;
int len = Math.max(len1, len2);
int arr3[] = new int[len + 1];
for (int i = 1; i <= len; i++) {
sum =
(len1 - i >= 0 ? arr1[len1-i] : 0)
+ (len2 - i >= 0 ? arr2[len2-i] : 0)
+ carry;
arr3[len-i+1] = sum%10;
carry = sum/10;
}
arr3[0] = carry;
return arr3;
}
The usage of ternary operator is still readable so I find this a good solution.
For a short explanation, we read the arrays from the end, using i to read from right to left but based on the length of the arrays. The ternary operation is used in case of different array size.
EDIT :
Your algorithm doesn't manage correctly the carry value with different sized array.
185 + 16 gives 101.
Simply because you set the values like :
arr3[i+1] = arr1[i];
So you forgot the carry that could occurs in the last operation.
This code is way more complicated than it has to be, which increases the chances of it containing bugs hard to detect.
You don't have to implement the algorithm 3 times (based of whether the first array is smaller, larger or equal to the second array). You can implement it once for two equal sized arrays whose size is Math.max(arr1.length,arr2.length).
That would eliminate 2/3 of your code.
int len = Math.max(arr1.length,arr2.length);
int[] arr11 = new int[len];
int[] arr22 = new int[len];
int arr3[] = new int[len+1];
for(int i=len-1;i>=-1;i--) {
if (i>=len-arr1.length)
arr11[i]=arr1[i-(len-arr1.length)];
if (i>=len-arr2.length)
arr22[i]=arr2[i-(len-arr2.length)];
// now you can use arr11[i] and arr22[i] instead of arr1[i] and arr2[i]
...
}
Besides, instead of sum = arr1[i] + arr2[i]; I suggest you add the carry immediately - sum = arr11[i] + arr22[i] + carry;. Now you only have to check once whether sum > 9.
if(i==-1) {
arr3[i+1] = carry;
} else {
sum = arr11[i] + arr22[i] + carry;
if(sum>9) {
arr3[i+1] = sum % 10;
carry = 1;
} else {
arr3[i+1] = sum;
carry = 0;
}
}
Combining the two snippets, you'll get :
int carry = 0;
int sum = 0;
int len = Math.max(arr1.length,arr2.length);
int[] arr11 = new int[len];
int[] arr22 = new int[len];
int arr3[] = new int[len+1];
for(int i=len-1;i>=-1;i--) {
if(i==-1) {
arr3[i+1] = carry;
} else {
if (i>=len-arr1.length)
arr11[i]=arr1[i-(len-arr1.length)];
if (i>=len-arr2.length)
arr22[i]=arr2[i-(len-arr2.length)];
sum = arr11[i] + arr22[i] + carry;
if(sum>9) {
arr3[i+1] = sum % 10;
carry = 1;
} else {
arr3[i+1] = sum;
carry = 0;
}
}
}
return arr3;
EDIT :
I had a small bug. I was adding 0s in the least significant digits of the smaller array (which are the high indices) instead of the most significant bits (the low indices), which made the result wrong if the arrays had different lengths. I fixed it, though now the part that copies the elements from the original arrays to arr11 and arr22 is less readable.
If that leading 0 in your second sample output is not necessary, you can also use a different approach by transforming the input beforehand, e.g. with a function as follows:
static Integer toNumber(int[] arr) {
return Integer.valueOf(Arrays.stream(arr)
.mapToObj(Integer::toString)
.collect(Collectors.joining()));
}
That way you can just sum up your arrays as if they would be normal integers:
Integer sum = toNumber(arr1) + toNumber(arr2);
Transforming that back to an array can be done as follows:
int[] sumArray = sum.toString().chars()
.map(operand -> Character.digit(operand, 10))
.toArray();
But you don't have that leading 0 now in your output. That code uses Java 8, but the same is also writable without streams (but untested):
static Integer toNumber(int[] arr) {
StringBuilder integerStrBuilder = new StringBuilder();
for (int i = 0; i < arr.length; i++) {
integerStrBuilder.append(Integer.toString(arr[i]));
}
return Integer.valueOf(integerStrBuilder.toString());
}
and for the array:
char[] characters = sum.toString().toCharArray();
int[] sumArray = new int[characters.length];
for (int j = 0; j < characters.length; j++) {
sumArray[j] = Characters.digit(characters[j], 10);
}
int[] firstArray = {1,8,8,8, 8};
int[] secondArray = {1,8,9};
String diffstring1 = "", diffstring2 = "";
for (int i = 0; i < firstArray.length; i++) {
diffstring1 = diffstring1 + String.valueOf(firstArray[i]);
}
for (int i = 0; i < secondArray.length; i++) {
diffstring2 = diffstring2 + String.valueOf(secondArray[i]);
}
int diff = Integer.parseInt(diffstring1) + Integer.parseInt(diffstring2);
String diifffinal = String.valueOf(diff);
int[] third = new int[diifffinal.length()];
for (int j = 0; j < diifffinal.length(); j++) {
char abc = diifffinal.charAt(j);
third[j] = Character.getNumericValue(abc);
Log.d(TAG, "onCreate:---> " + third[j]);
}
It kinda works
int[] arr1 = {1, 2, 3, 4, 5, 6}, arr2 = {3, 5, 2, 9, 0};
int[] output = new int[Math.max(arr1.length, arr2.length)];
int num1 = 0, num2 = 0;
for (int value : arr1) {
num1 = (num1 * 10) + value;
}
for (int i : arr2) {
num2 = (num2 * 10) + i;
}
int result = (num1 + num2), k = output.length - 1;
while(result > 0){
output[k] = (result % 10);
result = result / 10;
k--;
}
if(k>0){
output[k] = 0;
k--;
}
for(int value: output){
System.out.print(value + " ");
}
}

A better algorithm to find the next palindrome of a number string

Firstly here is the problem:
A positive integer is called a palindrome if its representation in the decimal system is the same when read from left to right and from right to left. For a given positive integer K of not more than 1000000 digits, write the value of the smallest palindrome larger than K to output. Numbers are always displayed without leading zeros.
Input: The first line contains integer t, the number of test cases. Integers K are given in the next t lines.
Output: For each K, output the smallest palindrome larger than K.
Example
Input:
2
808
2133
Output:
818
2222
Secondly here is my code:
// I know it is bad practice to not cater for erroneous input,
// however for the purpose of the execise it is omitted
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.lang.Exception;
import java.math.BigInteger;
public class Main
{
public static void main(String [] args){
try{
Main instance = new Main(); // create an instance to access non-static
// variables
// Use java.util.Scanner to scan the get the input and initialise the
// variable
Scanner sc=null;
BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
String input = "";
int numberOfTests = 0;
String k; // declare any other variables here
if((input = r.readLine()) != null){
sc = new Scanner(input);
numberOfTests = sc.nextInt();
}
for (int i = 0; i < numberOfTests; i++){
if((input = r.readLine()) != null){
sc = new Scanner(input);
k=sc.next(); // initialise the remainder of the variables sc.next()
instance.palindrome(k);
} //if
}// for
}// try
catch (Exception e)
{
e.printStackTrace();
}
}// main
public void palindrome(String number){
StringBuffer theNumber = new StringBuffer(number);
int length = theNumber.length();
int left, right, leftPos, rightPos;
// if incresing a value to more than 9 the value to left (offset) need incrementing
int offset, offsetPos;
boolean offsetUpdated;
// To update the string with new values
String insert;
boolean hasAltered = false;
for(int i = 0; i < length/2; i++){
leftPos = i;
rightPos = (length-1) - i;
offsetPos = rightPos -1; offsetUpdated = false;
// set values at opposite indices and offset
left = Integer.parseInt(String.valueOf(theNumber.charAt(leftPos)));
right = Integer.parseInt(String.valueOf(theNumber.charAt(rightPos)));
offset = Integer.parseInt(String.valueOf(theNumber.charAt(offsetPos)));
if(left != right){
// if r > l then offest needs updating
if(right > left){
// update and replace
right = left;
insert = Integer.toString(right);
theNumber.replace(rightPos, rightPos + 1, insert);
offset++; if (offset == 10) offset = 0;
insert = Integer.toString(offset);
theNumber.replace(offsetPos, offsetPos + 1, insert);
offsetUpdated = true;
// then we need to update the value to left again
while (offset == 0 && offsetUpdated){
offsetPos--;
offset =
Integer.parseInt(String.valueOf(theNumber.charAt(offsetPos)));
offset++; if (offset == 10) offset = 0;
// replace
insert = Integer.toString(offset);
theNumber.replace(offsetPos, offsetPos + 1, insert);
}
// finally incase right and offset are the two middle values
left = Integer.parseInt(String.valueOf(theNumber.charAt(leftPos)));
if (right != left){
right = left;
insert = Integer.toString(right);
theNumber.replace(rightPos, rightPos + 1, insert);
}
}// if r > l
else
// update and replace
right = left;
insert = Integer.toString(right);
theNumber.replace(rightPos, rightPos + 1, insert);
}// if l != r
}// for i
System.out.println(theNumber.toString());
}// palindrome
}
Finally my explaination and question.
My code compares either end and then moves in
if left and right are not equal
if right is greater than left
(increasing right past 9 should increase the digit
to its left i.e 09 ---- > 10) and continue to do
so if require as for 89999, increasing the right
most 9 makes the value 90000
before updating my string we check that the right
and left are equal, because in the middle e.g 78849887
we set the 9 --> 4 and increase 4 --> 5, so we must cater for this.
The problem is from spoj.pl an online judge system. My code works for all the test can provide but when I submit it, I get a time limit exceeded error and my answer is not accepted.
Does anyone have any suggestions as to how I can improve my algorithm. While writing this question i thought that instead of my while (offset == 0 && offsetUpdated) loop i could use a boolean to to make sure i increment the offset on my next [i] iteration. Confirmation of my chang or any suggestion would be appreciated, also let me know if i need to make my question clearer.
This seems like a lot of code. Have you tried a very naive approach yet? Checking whether something is a palindrome is actually very simple.
private boolean isPalindrome(int possiblePalindrome) {
String stringRepresentation = String.valueOf(possiblePalindrome);
if ( stringRepresentation.equals(stringRepresentation.reverse()) ) {
return true;
}
}
Now that might not be the most performant code, but it gives you a really simple starting point:
private int nextLargestPalindrome(int fromNumber) {
for ( int i = fromNumber + 1; ; i++ ) {
if ( isPalindrome( i ) ) {
return i;
}
}
}
Now if that isn't fast enough you can use it as a reference implementation and work on decreasing the algorithmic complexity.
There should actually be a constant-time (well it is linear on the number of digits of the input) way to find the next largest palindrome. I will give an algorithm that assumes the number is an even number of digits long (but can be extended to an odd number of digits).
Find the decimal representation of the input number ("2133").
Split it into the left half and right half ("21", "33");
Compare the last digit in the left half and the first digit in the right half.
a. If the right is greater than the left, increment the left and stop. ("22")
b. If the right is less than the left, stop.
c. If the right is equal to the left, repeat step 3 with the second-last digit in the left and the second digit in the right (and so on).
Take the left half and append the left half reversed. That's your next largest palindrome. ("2222")
Applied to a more complicated number:
1. 1234567887654322
2. 12345678 87654322
3. 12345678 87654322
^ ^ equal
3. 12345678 87654322
^ ^ equal
3. 12345678 87654322
^ ^ equal
3. 12345678 87654322
^ ^ equal
3. 12345678 87654322
^ ^ equal
3. 12345678 87654322
^ ^ equal
3. 12345678 87654322
^ ^ equal
3. 12345678 87654322
^ ^ greater than, so increment the left
3. 12345679
4. 1234567997654321 answer
This seems a bit similar to the algorithm you described, but it starts at the inner digits and moves to the outer.
There is no reason to fiddle with individual digits when the only needed operation is one simple addition. The following code is based on Raks' answer.
The code stresses simplicity over execution speed, intentionally.
import static org.junit.Assert.assertEquals;
import java.math.BigInteger;
import org.junit.Test;
public class NextPalindromeTest {
public static String nextPalindrome(String num) {
int len = num.length();
String left = num.substring(0, len / 2);
String middle = num.substring(len / 2, len - len / 2);
String right = num.substring(len - len / 2);
if (right.compareTo(reverse(left)) < 0)
return left + middle + reverse(left);
String next = new BigInteger(left + middle).add(BigInteger.ONE).toString();
return next.substring(0, left.length() + middle.length())
+ reverse(next).substring(middle.length());
}
private static String reverse(String s) {
return new StringBuilder(s).reverse().toString();
}
#Test
public void testNextPalindrome() {
assertEquals("5", nextPalindrome("4"));
assertEquals("11", nextPalindrome("9"));
assertEquals("22", nextPalindrome("15"));
assertEquals("101", nextPalindrome("99"));
assertEquals("151", nextPalindrome("149"));
assertEquals("123454321", nextPalindrome("123450000"));
assertEquals("123464321", nextPalindrome("123454322"));
}
}
Well I have constant order solution(atleast of order k, where k is number of digits in the number)
Lets take some examples
suppose n=17208
divide the number into two parts from middle
and reversibly write the most significant part onto the less significant one.
ie, 17271
if the so generated number is greater than your n it is your palindrome, if not just increase the center number(pivot) ie, you get 17371
other examples
n=17286
palidrome-attempt=17271(since it is less than n increment the pivot, 2 in this case)
so palidrome=17371
n=5684
palidrome1=5665
palidrome=5775
n=458322
palindrome=458854
now suppose n = 1219901
palidrome1=1219121
incrementing the pivot makes my number smaller here
so increment the number adjacent pivot too
1220221
and this logic could be extended
public class NextPalindrome
{
int rev, temp;
int printNextPalindrome(int n)
{
int num = n;
for (int i = num+1; i >= num; i++)
{
temp = i;
rev = 0;
while (temp != 0)
{
int remainder = temp % 10;
rev = rev * 10 + remainder;
temp = temp / 10;
}
if (rev == i)
{
break;
}
}
return rev;
}
public static void main(String args[])
{
NextPalindrome np = new NextPalindrome();
int nxtpalin = np.printNextPalindrome(11);
System.out.println(nxtpalin);
}
}
Here is my code in java. Whole idea is from here.
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
System.out.println("Enter number of tests: ");
int t = sc.nextInt();
for (int i = 0; i < t; i++) {
System.out.println("Enter number: ");
String numberToProcess = sc.next(); // ne proveravam dal su brojevi
nextSmallestPalindrom(numberToProcess);
}
}
private static void nextSmallestPalindrom(String numberToProcess) {
int i, j;
int length = numberToProcess.length();
int[] numberAsIntArray = new int[length];
for (int k = 0; k < length; k++)
numberAsIntArray[k] = Integer.parseInt(String
.valueOf(numberToProcess.charAt(k)));
numberToProcess = null;
boolean all9 = true;
for (int k = 0; k < length; k++) {
if (numberAsIntArray[k] != 9) {
all9 = false;
break;
}
}
// case 1, sve 9ke
if (all9) {
whenAll9(length);
return;
}
int mid = length / 2;
if (length % 2 == 0) {
i = mid - 1;
j = mid;
} else {
i = mid - 1;
j = mid + 1;
}
while (i >= 0 && numberAsIntArray[i] == numberAsIntArray[j]) {
i--;
j++;
}
// case 2 already polindrom
if (i == -1) {
if (length % 2 == 0) {
i = mid - 1;
j = mid;
} else {
i = mid;
j = i;
}
addOneToMiddleWithCarry(numberAsIntArray, i, j, true);
} else {
// case 3 not polindrom
if (numberAsIntArray[i] > numberAsIntArray[j]) { // 3.1)
while (i >= 0) {
numberAsIntArray[j] = numberAsIntArray[i];
i--;
j++;
}
for (int k = 0; k < numberAsIntArray.length; k++)
System.out.print(numberAsIntArray[k]);
System.out.println();
} else { // 3.2 like case 2
if (length % 2 == 0) {
i = mid - 1;
j = mid;
} else {
i = mid;
j = i;
}
addOneToMiddleWithCarry(numberAsIntArray, i, j, false);
}
}
}
private static void whenAll9(int length) {
for (int i = 0; i <= length; i++) {
if (i == 0 || i == length)
System.out.print('1');
else
System.out.print('0');
}
}
private static void addOneToMiddleWithCarry(int[] numberAsIntArray, int i,
int j, boolean palindrom) {
numberAsIntArray[i]++;
numberAsIntArray[j] = numberAsIntArray[i];
while (numberAsIntArray[i] == 10) {
numberAsIntArray[i] = 0;
numberAsIntArray[j] = numberAsIntArray[i];
i--;
j++;
numberAsIntArray[i]++;
numberAsIntArray[j] = numberAsIntArray[i];
}
if (!palindrom)
while (i >= 0) {
numberAsIntArray[j] = numberAsIntArray[i];
i--;
j++;
}
for (int k = 0; k < numberAsIntArray.length; k++)
System.out.print(numberAsIntArray[k]);
System.out.println();
}
}
Try this
public static String genNextPalin(String base){
//check if it is 1 digit
if(base.length()==1){
if(Integer.parseInt(base)==9)
return "11";
else
return (Integer.parseInt(base)+1)+"";
}
boolean check = true;
//check if it is all 9s
for(char a: base.toCharArray()){
if(a!='9')
check = false;
}
if(check){
String num = "1";
for(int i=0; i<base.length()-1; i++)
num+="0";
num+="1";
return num;
}
boolean isBasePalin = isPalindrome(base);
int mid = base.length()/2;
if(isBasePalin){
//if base is palin and it is odd increase mid and return
if(base.length()%2==1){
BigInteger leftHalf = new BigInteger(base.substring(0,mid+1));
String newLeftHalf = leftHalf.add(BigInteger.ONE).toString();
String newPalin = genPalin2(newLeftHalf.substring(0,mid),newLeftHalf.charAt(mid));
return newPalin;
}
else{
BigInteger leftHalf = new BigInteger(base.substring(0,mid));
String newLeftHalf = leftHalf.add(BigInteger.ONE).toString();
String newPalin = genPalin(newLeftHalf.substring(0,mid));
return newPalin;
}
}
else{
if(base.length()%2==1){
BigInteger leftHalf = new BigInteger(base.substring(0,mid));
BigInteger rightHalf = new BigInteger(reverse(base.substring(mid+1,base.length())));
//check if leftHalf is greater than right half
if(leftHalf.compareTo(rightHalf)==1){
String newPalin = genPalin2(base.substring(0,mid),base.charAt(mid));
return newPalin;
}
else{
BigInteger leftHalfMid = new BigInteger(base.substring(0,mid+1));
String newLeftHalfMid = leftHalfMid.add(BigInteger.ONE).toString();
String newPalin = genPalin2(newLeftHalfMid.substring(0,mid),newLeftHalfMid.charAt(mid));
return newPalin;
}
}
else{
BigInteger leftHalf = new BigInteger(base.substring(0,mid));
BigInteger rightHalf = new BigInteger(reverse(base.substring(mid,base.length())));
//check if leftHalf is greater than right half
if(leftHalf.compareTo(rightHalf)==1){
return genPalin(base.substring(0,mid));
}
else{
BigInteger leftHalfMid = new BigInteger(base.substring(0,mid));
String newLeftHalfMid = leftHalfMid.add(BigInteger.ONE).toString();
return genPalin(newLeftHalfMid);
}
}
}
}
public static String genPalin(String base){
return base + new StringBuffer(base).reverse().toString();
}
public static String genPalin2(String base, char middle){
return base + middle +new StringBuffer(base).reverse().toString();
}
public static String reverse(String in){
return new StringBuffer(in).reverse().toString();
}
static boolean isPalindrome(String str) {
int n = str.length();
for( int i = 0; i < n/2; i++ )
if (str.charAt(i) != str.charAt(n-i-1))
return false;
return true;
}
HI Here is another simple algorithm using python,
def is_palindrome(n):
if len(n) <= 1:
return False
else:
m = len(n)/2
for i in range(m):
j = i + 1
if n[i] != n[-j]:
return False
return True
def next_palindrome(n):
if not n:
return False
else:
if is_palindrome(n) is True:
return n
else:
return next_palindrome(str(int(n)+1))
print next_palindrome('1000010')
I have written comments to clarify what each step is doing in this python code.
One thing that need to be taken into consideration is that input can be very large that we can not simply perform integer operations on it. So taking input as string and then manipulating it would be much easier.
tests = int(input())
results = []
for i in range(0, tests):
pal = input().strip()
palen = len(pal)
mid = int(palen/2)
if palen % 2 != 0:
if mid == 0: # if the number is of single digit e.g. next palindrome for 5 is 6
ipal = int(pal)
if ipal < 9:
results.append(int(pal) + 1)
else:
results.append(11) # for 9 next palindrome will be 11
else:
pal = list(pal)
pl = l = mid - 1
pr = r = mid + 1
flag = 'n' # represents left and right half of input string are same
while pl >= 0:
if pal[pl] > pal[pr]:
flag = 'r' # 123483489 in this case pal[pl] = 4 and pal[pr] = 3 so we just need to copy left half in right half
break # 123484321 will be the answer
elif pal[pl] < pal[pr]:
flag = 'm' # 123487489 in this case pal[pl] = 4 and pal[pr] = 9 so copying left half in right half will make number smaller
break # in this case we need to take left half increment by 1 and the copy in right half 123494321 will be the anwere
else:
pl = pl -1
pr = pr + 1
if flag == 'm' or flag == 'n': # increment left half by one and copy in right half
if pal[mid] != '9': # if mid element is < 9 the we can simply increment the mid number only and copy left in right half
pal[mid] = str(int(pal[mid]) + 1)
while r < palen:
pal[r] = pal[l]
r = r + 1
l = l - 1
results.append(''.join(pal))
else: # if mid element is 9 this will effect entire left half because of carry
pal[mid] = '0' # we need to take care of large inputs so we can not just directly add 1 in left half
pl = l
while pal[l] == '9':
pal[l] = '0'
l = l - 1
if l >= 0:
pal[l] = str(int(pal[l]) + 1)
while r < palen:
pal[r] = pal[pl]
r = r + 1
pl = pl - 1
if l < 0:
pal[0] = '1'
pal[palen - 1] = '01'
results.append(''.join(pal))
else:
while r < palen: # when flag is 'r'
pal[r] = pal[l]
r = r + 1
l = l - 1
results.append(''.join(pal))
else: # even length almost similar concept here with flags having similar significance as in case of odd length input
pal = list(pal)
pr = r = mid
pl = l = mid - 1
flag = 'n'
while pl >= 0:
if pal[pl] > pal[pr]:
flag = 'r'
break
elif pal[pl] < pal[pr]:
flag = 'm'
break
else:
pl = pl -1
pr = pr + 1
if flag == 'r':
while r < palen:
pal[r] = pal[l]
r = r + 1
l = l - 1
results.append(''.join(pal))
else:
if pal[l] != '9':
pal[l] = str(int(pal[l]) + 1)
while r < palen:
pal[r] = pal[l]
r = r + 1
l = l - 1
results.append(''.join(pal))
else:
pal[mid] = '0'
pl = l
while pal[l] == '9':
pal[l] = '0'
l = l - 1
if l >= 0:
pal[l] = str(int(pal[l]) + 1)
while r < palen:
pal[r] = pal[pl]
r = r + 1
pl = pl - 1
if l < 0:
pal[0] = '1'
pal[palen - 1] = '01'
results.append(''.join(pal))
for xx in results:
print(xx)
We can find next palindrome easily like below.
private void findNextPalindrom(int i) {
i++;
while (!checkPalindrom(i)) {
i++;
}
Log.e(TAG, "findNextPalindrom:next palindrom is===" + i);
}
private boolean checkPalindrom(int num) {
int temp = num;
int rev = 0;
while (num > 0) {
int rem = num % 10;
rev = rev * 10 + rem;
num = num / 10;
}
return temp == rev;
}
Simple codes and test output:
class NextPalin
{
public static void main( String[] args )
{
try {
int[] a = {2, 23, 88, 234, 432, 464, 7887, 7657, 34567, 99874, 7779222, 2569981, 3346990, 229999, 2299999 };
for( int i=0; i<a.length; i++)
{
int add = findNextPalin(a[i]);
System.out.println( a[i] + " + " + add + " = " + (a[i]+add) );
}
}
catch( Exception e ){}
}
static int findNextPalin( int a ) throws Exception
{
if( a < 0 ) throw new Exception();
if( a < 10 ) return a;
int count = 0, reverse = 0, temp = a;
while( temp > 0 ){
reverse = reverse*10 + temp%10;
count++;
temp /= 10;
}
//compare 'half' value
int halfcount = count/2;
int base = (int)Math.pow(10, halfcount );
int reverseHalfValue = reverse % base;
int currentHalfValue = a % base;
if( reverseHalfValue == currentHalfValue ) return 0;
if( reverseHalfValue > currentHalfValue ) return (reverseHalfValue - currentHalfValue);
if( (((a-currentHalfValue)/base)%10) == 9 ){
//cases like 12945 or 1995
int newValue = a-currentHalfValue + base*10;
int diff = findNextPalin(newValue);
return base*10 - currentHalfValue + diff;
}
else{
return (base - currentHalfValue + reverseHalfValue );
}
}
}
$ java NextPalin
2 + 2 = 4
23 + 9 = 32
88 + 0 = 88
234 + 8 = 242
432 + 2 = 434
464 + 0 = 464
7887 + 0 = 7887
7657 + 10 = 7667
34567 + 76 = 34643
99874 + 25 = 99899
7779222 + 555 = 7779777
2569981 + 9771 = 2579752
3346990 + 443 = 3347433
229999 + 9933 = 239932
2299999 + 9033 = 2309032

Fastest algorithm to check if a number is pandigital?

Pandigital number is a number that contains the digits 1..number length.
For example 123, 4312 and 967412385.
I have solved many Project Euler problems, but the Pandigital problems always exceed the one minute rule.
This is my pandigital function:
private boolean isPandigital(int n){
Set<Character> set= new TreeSet<Character>();
String string = n+"";
for (char c:string.toCharArray()){
if (c=='0') return false;
set.add(c);
}
return set.size()==string.length();
}
Create your own function and test it with this method
int pans=0;
for (int i=123456789;i<=123987654;i++){
if (isPandigital(i)){
pans++;
}
}
Using this loop, you should get 720 pandigital numbers. My average time was 500 millisecond.
I'm using Java, but the question is open to any language.
UPDATE
#andras answer has the best time so far, but #Sani Huttunen answer inspired me to add a new algorithm, which gets almost the same time as #andras.
C#, 17ms, if you really want a check.
class Program
{
static bool IsPandigital(int n)
{
int digits = 0; int count = 0; int tmp;
for (; n > 0; n /= 10, ++count)
{
if ((tmp = digits) == (digits |= 1 << (n - ((n / 10) * 10) - 1)))
return false;
}
return digits == (1 << count) - 1;
}
static void Main()
{
int pans = 0;
Stopwatch sw = new Stopwatch();
sw.Start();
for (int i = 123456789; i <= 123987654; i++)
{
if (IsPandigital(i))
{
pans++;
}
}
sw.Stop();
Console.WriteLine("{0}pcs, {1}ms", pans, sw.ElapsedMilliseconds);
Console.ReadKey();
}
}
For a check that is consistent with the Wikipedia definition in base 10:
const int min = 1023456789;
const int expected = 1023;
static bool IsPandigital(int n)
{
if (n >= min)
{
int digits = 0;
for (; n > 0; n /= 10)
{
digits |= 1 << (n - ((n / 10) * 10));
}
return digits == expected;
}
return false;
}
To enumerate numbers in the range you have given, generating permutations would suffice.
The following is not an answer to your question in the strict sense, since it does not implement a check. It uses a generic permutation implementation not optimized for this special case - it still generates the required 720 permutations in 13ms (line breaks might be messed up):
static partial class Permutation
{
/// <summary>
/// Generates permutations.
/// </summary>
/// <typeparam name="T">Type of items to permute.</typeparam>
/// <param name="items">Array of items. Will not be modified.</param>
/// <param name="comparer">Optional comparer to use.
/// If a <paramref name="comparer"/> is supplied,
/// permutations will be ordered according to the
/// <paramref name="comparer"/>
/// </param>
/// <returns>Permutations of input items.</returns>
public static IEnumerable<IEnumerable<T>> Permute<T>(T[] items, IComparer<T> comparer)
{
int length = items.Length;
IntPair[] transform = new IntPair[length];
if (comparer == null)
{
//No comparer. Start with an identity transform.
for (int i = 0; i < length; i++)
{
transform[i] = new IntPair(i, i);
};
}
else
{
//Figure out where we are in the sequence of all permutations
int[] initialorder = new int[length];
for (int i = 0; i < length; i++)
{
initialorder[i] = i;
}
Array.Sort(initialorder, delegate(int x, int y)
{
return comparer.Compare(items[x], items[y]);
});
for (int i = 0; i < length; i++)
{
transform[i] = new IntPair(initialorder[i], i);
}
//Handle duplicates
for (int i = 1; i < length; i++)
{
if (comparer.Compare(
items[transform[i - 1].Second],
items[transform[i].Second]) == 0)
{
transform[i].First = transform[i - 1].First;
}
}
}
yield return ApplyTransform(items, transform);
while (true)
{
//Ref: E. W. Dijkstra, A Discipline of Programming, Prentice-Hall, 1997
//Find the largest partition from the back that is in decreasing (non-icreasing) order
int decreasingpart = length - 2;
for (;decreasingpart >= 0 &&
transform[decreasingpart].First >= transform[decreasingpart + 1].First;
--decreasingpart) ;
//The whole sequence is in decreasing order, finished
if (decreasingpart < 0) yield break;
//Find the smallest element in the decreasing partition that is
//greater than (or equal to) the item in front of the decreasing partition
int greater = length - 1;
for (;greater > decreasingpart &&
transform[decreasingpart].First >= transform[greater].First;
greater--) ;
//Swap the two
Swap(ref transform[decreasingpart], ref transform[greater]);
//Reverse the decreasing partition
Array.Reverse(transform, decreasingpart + 1, length - decreasingpart - 1);
yield return ApplyTransform(items, transform);
}
}
#region Overloads
public static IEnumerable<IEnumerable<T>> Permute<T>(T[] items)
{
return Permute(items, null);
}
public static IEnumerable<IEnumerable<T>> Permute<T>(IEnumerable<T> items, IComparer<T> comparer)
{
List<T> list = new List<T>(items);
return Permute(list.ToArray(), comparer);
}
public static IEnumerable<IEnumerable<T>> Permute<T>(IEnumerable<T> items)
{
return Permute(items, null);
}
#endregion Overloads
#region Utility
public static IEnumerable<T> ApplyTransform<T>(
T[] items,
IntPair[] transform)
{
for (int i = 0; i < transform.Length; i++)
{
yield return items[transform[i].Second];
}
}
public static void Swap<T>(ref T x, ref T y)
{
T tmp = x;
x = y;
y = tmp;
}
public struct IntPair
{
public IntPair(int first, int second)
{
this.First = first;
this.Second = second;
}
public int First;
public int Second;
}
#endregion
}
class Program
{
static void Main()
{
int pans = 0;
int[] digits = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
Stopwatch sw = new Stopwatch();
sw.Start();
foreach (var p in Permutation.Permute(digits))
{
pans++;
if (pans == 720) break;
}
sw.Stop();
Console.WriteLine("{0}pcs, {1}ms", pans, sw.ElapsedMilliseconds);
Console.ReadKey();
}
}
This is my solution:
static char[][] pandigits = new char[][]{
"1".toCharArray(),
"12".toCharArray(),
"123".toCharArray(),
"1234".toCharArray(),
"12345".toCharArray(),
"123456".toCharArray(),
"1234567".toCharArray(),
"12345678".toCharArray(),
"123456789".toCharArray(),
};
private static boolean isPandigital(int i)
{
char[] c = String.valueOf(i).toCharArray();
Arrays.sort(c);
return Arrays.equals(c, pandigits[c.length-1]);
}
Runs the loop in 0.3 seconds on my (rather slow) system.
Two things you can improve:
You don't need to use a set: you can use a boolean array with 10 elements
Instead of converting to a string, use division and the modulo operation (%) to extract the digits.
Using a bit vector to keep track of which digits have been found appears to be the fastest raw method. There are two ways to improve it:
Check if the number is divisible by 9. This is a necessary condition for being pandigital, so we can exclude 88% of numbers up front.
Use multiplication and shifts instead of divisions, in case your compiler doesn't do that for you.
This gives the following, which runs the test benchmark in about 3ms on my machine. It correctly identifies the 362880 9-digit pan-digital numbers between 100000000 and 999999999.
bool IsPandigital(int n)
{
if (n != 9 * (int)((0x1c71c71dL * n) >> 32))
return false;
int flags = 0;
while (n > 0) {
int q = (int)((0x1999999aL * n) >> 32);
flags |= 1 << (n - q * 10);
n = q;
}
return flags == 0x3fe;
}
My solution involves Sums and Products.
This is in C# and runs in about 180ms on my laptop:
static int[] sums = new int[] {1, 3, 6, 10, 15, 21, 28, 36, 45};
static int[] products = new int[] {1, 2, 6, 24, 120, 720, 5040, 40320, 362880};
static void Main(string[] args)
{
var pans = 0;
for (var i = 123456789; i <= 123987654; i++)
{
var num = i.ToString();
if (Sum(num) == sums[num.Length - 1] && Product(num) == products[num.Length - 1])
pans++;
}
Console.WriteLine(pans);
}
protected static int Sum(string num)
{
int sum = 0;
foreach (char c in num)
sum += (int) (c - '0');
return sum;
}
protected static int Product(string num)
{
int prod = 1;
foreach (char c in num)
prod *= (int)(c - '0');
return prod;
}
Why find when you can make them?
from itertools import *
def generate_pandigital(length):
return (''.join for each in list(permutations('123456789',length)))
def test():
for i in range(10):
print i
generate_pandigital(i)
if __name__=='__main__':
test()
J does this nicely:
isPandigital =: 3 : 0
*./ (' ' -.~ ": 1 + i. # s) e. s =. ": y
)
isPandigital"0 (123456789 + i. 1 + 123987654 - 123456789)
But slowly. I will revise. For now, clocking at 4.8 seconds.
EDIT:
If it's just between the two set numbers, 123456789 and 123987654, then this expression:
*./"1 (1+i.9) e."1 (9#10) #: (123456789 + i. 1 + 123987654 - 123456789)
Runs in 0.23 seconds. It's about as fast, brute-force style, as it gets in J.
TheMachineCharmer is right. At least for some the problems, it's better to iterate over all the pandigitals, checking each one to see if it fits the criteria of the problem. However, I think their code is not quite right.
I'm not sure which is better SO etiquette in this case: Posting a new answer or editing theirs. In any case, here is the modified Python code which I believe to be correct, although it doesn't generate 0-to-n pandigitals.
from itertools import *
def generate_pandigital(length):
'Generate all 1-to-length pandigitals'
return (''.join(each) for each in list(permutations('123456789'[:length])))
def test():
for i in range(10):
print 'Generating all %d-digit pandigitals' % i
for (n,p) in enumerate(generate_pandigital(i)):
print n,p
if __name__=='__main__':
test()
You could add:
if (set.add(c)==false) return false;
This would short circuit a lot of your computations, since it'll return false as soon as a duplicate was found, since add() returns false in this case.
bool IsPandigital (unsigned long n) {
if (n <= 987654321) {
hash_map<int, int> m;
unsigned long count = (unsigned long)(log((double)n)/log(10.0))+1;
while (n) {
++m[n%10];
n /= 10;
}
while (m[count]==1 && --count);
return !count;
}
return false;
}
bool IsPandigital2 (unsigned long d) {
// Avoid integer overflow below if this function is passed a very long number
if (d <= 987654321) {
unsigned long sum = 0;
unsigned long prod = 1;
unsigned long n = d;
unsigned long max = (log((double)n)/log(10.0))+1;
unsigned long max_sum = max*(max+1)/2;
unsigned long max_prod = 1;
while (n) {
sum += n % 10;
prod *= (n%10);
max_prod *= max;
--max;
n /= 10;
}
return (sum == max_sum) && (prod == max_prod);
}
I have a solution for generating Pandigital numbers using StringBuffers in Java. On my laptop, my code takes a total of 5ms to run. Of this only 1ms is required for generating the permutations using StringBuffers; the remaining 4ms are required for converting this StringBuffer to an int[].
#medopal: Can you check the time this code takes on your system?
public class GenPandigits
{
/**
* The prefix that must be appended to every number, like 123.
*/
int prefix;
/**
* Length in characters of the prefix.
*/
int plen;
/**
* The digit from which to start the permutations
*/
String beg;
/**
* The length of the required Pandigital numbers.
*/
int len;
/**
* #param prefix If there is no prefix then this must be null
* #param beg If there is no prefix then this must be "1"
* #param len Length of the required numbers (excluding the prefix)
*/
public GenPandigits(String prefix, String beg, int len)
{
if (prefix == null)
{
this.prefix = 0;
this.plen = 0;
}
else
{
this.prefix = Integer.parseInt(prefix);
this.plen = prefix.length();
}
this.beg = beg;
this.len = len;
}
public StringBuffer genPermsBet()
{
StringBuffer b = new StringBuffer(beg);
for(int k=2;k<=len;k++)
{
StringBuffer rs = new StringBuffer();
int l = b.length();
int s = l/(k-1);
String is = String.valueOf(k+plen);
for(int j=0;j<k;j++)
{
rs.append(b);
for(int i=0;i<s;i++)
{
rs.insert((l+s)*j+i*k+j, is);
}
}
b = rs;
}
return b;
}
public int[] getPandigits(String buffer)
{
int[] pd = new int[buffer.length()/len];
int c= prefix;
for(int i=0;i<len;i++)
c =c *10;
for(int i=0;i<pd.length;i++)
pd[i] = Integer.parseInt(buffer.substring(i*len, (i+1)*len))+c;
return pd;
}
public static void main(String[] args)
{
GenPandigits gp = new GenPandigits("123", "4", 6);
//GenPandigits gp = new GenPandigits(null, "1", 6);
long beg = System.currentTimeMillis();
StringBuffer pansstr = gp.genPermsBet();
long end = System.currentTimeMillis();
System.out.println("Time = " + (end - beg));
int pd[] = gp.getPandigits(pansstr.toString());
long end1 = System.currentTimeMillis();
System.out.println("Time = " + (end1 - end));
}
}
This code can also be used for generating all Pandigital numbers(excluding zero). Just change the object creation call to
GenPandigits gp = new GenPandigits(null, "1", 9);
This means that there is no prefix, and the permutations must start from "1" and continue till the length of the numbers is 9.
Following are the time measurements for different lengths.
#andras: Can you try and run your code to generate the nine digit Pandigital numbers? What time does it take?
This c# implementation is about 8% faster than #andras over the range 123456789 to 123987654 but it is really difficult to see on my test box as his runs in 14ms and this one runs in 13ms.
static bool IsPandigital(int n)
{
int count = 0;
int digits = 0;
int digit;
int bit;
do
{
digit = n % 10;
if (digit == 0)
{
return false;
}
bit = 1 << digit;
if (digits == (digits |= bit))
{
return false;
}
count++;
n /= 10;
} while (n > 0);
return (1<<count)-1 == digits>>1;
}
If we average the results of 100 runs we can get a decimal point.
public void Test()
{
int pans = 0;
var sw = new Stopwatch();
sw.Start();
for (int count = 0; count < 100; count++)
{
pans = 0;
for (int i = 123456789; i <= 123987654; i++)
{
if (IsPandigital(i))
{
pans++;
}
}
}
sw.Stop();
Console.WriteLine("{0}pcs, {1}ms", pans, sw.ElapsedMilliseconds / 100m);
}
#andras implementation averages 14.4ms and this implementation averages 13.2ms
EDIT:
It seems that mod (%) is expensive in c#. If we replace the use of the mod operator with a hand coded version then this implementation averages 11ms over 100 runs.
private static bool IsPandigital(int n)
{
int count = 0;
int digits = 0;
int digit;
int bit;
do
{
digit = n - ((n / 10) * 10);
if (digit == 0)
{
return false;
}
bit = 1 << digit;
if (digits == (digits |= bit))
{
return false;
}
count++;
n /= 10;
} while (n > 0);
return (1 << count) - 1 == digits >> 1;
}
EDIT: Integrated n/=10 into the digit calculation for a small speed improvement.
private static bool IsPandigital(int n)
{
int count = 0;
int digits = 0;
int digit;
int bit;
do
{
digit = n - ((n /= 10) * 10);
if (digit == 0)
{
return false;
}
bit = 1 << digit;
if (digits == (digits |= bit))
{
return false;
}
count++;
} while (n > 0);
return (1 << count) - 1 == digits >> 1;
}
#include <cstdio>
#include <ctime>
bool isPandigital(long num)
{
int arr [] = {1,2,3,4,5,6,7,8,9}, G, count = 9;
do
{
G = num%10;
if (arr[G-1])
--count;
arr[G-1] = 0;
} while (num/=10);
return (!count);
}
int main()
{
clock_t start(clock());
int pans=0;
for (int i = 123456789;i <= 123987654; ++i)
{
if (isPandigital(i))
++pans;
}
double end((double)(clock() - start));
printf("\n\tFound %d Pandigital numbers in %lf seconds\n\n", pans, end/CLOCKS_PER_SEC);
return 0;
}
Simple implementation. Brute-forced and computes in about 140 ms
In Java
You can always just generate them, and convert the Strings to Integers, which is faster for larger numbers
public static List<String> permutation(String str) {
List<String> permutations = new LinkedList<String>();
permutation("", str, permutations);
return permutations;
}
private static void permutation(String prefix, String str, List<String> permutations) {
int n = str.length();
if (n == 0) {
permutations.add(prefix);
} else {
for (int i = 0; i < n; i++) {
permutation(prefix + str.charAt(i),
str.substring(0, i) + str.substring(i + 1, n), permutations);
}
}
}
The below code works for testing a numbers pandigitality.
For your test mine ran in around ~50ms
1-9 PanDigital
public static boolean is1To9PanDigit(int i) {
if (i < 1e8) {
return false;
}
BitSet set = new BitSet();
while (i > 0) {
int mod = i % 10;
if (mod == 0 || set.get(mod)) {
return false;
}
set.set(mod);
i /= 10;
}
return true;
}
or more general, 1 to N,
public static boolean is1ToNPanDigit(int i, int n) {
BitSet set = new BitSet();
while (i > 0) {
int mod = i % 10;
if (mod == 0 || mod > n || set.get(mod)) {
return false;
}
set.set(mod);
i /= 10;
}
return set.cardinality() == n;
}
And just for fun, 0 to 9, zero requires extra logic due to a leading zero
public static boolean is0To9PanDigit(long i) {
if (i < 1e6) {
return false;
}
BitSet set = new BitSet();
if (i <= 123456789) { // count for leading zero
set.set(0);
}
while (i > 0) {
int mod = (int) (i % 10);
if (set.get(mod)) {
return false;
}
set.set(mod);
i /= 10;
}
return true;
}
Also for setting iteration bounds:
public static int maxPanDigit(int n) {
StringBuffer sb = new StringBuffer();
for(int i = n; i > 0; i--) {
sb.append(i);
}
return Integer.parseInt(sb.toString());
}
public static int minPanDigit(int n) {
StringBuffer sb = new StringBuffer();
for(int i = 1; i <= n; i++) {
sb.append(i);
}
return Integer.parseInt(sb.toString());
}
You could easily use this code to generate a generic MtoNPanDigital number checker
I decided to use something like this:
def is_pandigital(n, zero_full=True, base=10):
"""Returns True or False if the number n is pandigital.
This function returns True for formal pandigital numbers as well as
n-pandigital
"""
r, l = 0, 0
while n:
l, r, n = l + 1, r + n % base, n / base
t = xrange(zero_full ^ 1, l + (zero_full ^ 1))
return r == sum(t) and l == len(t)
Straight forward way
boolean isPandigital(int num,int length){
for(int i=1;i<=length;i++){
if(!(num+"").contains(i+""))
return false;
}
return true;
}
OR if you are sure that the number is of the right length already
static boolean isPandigital(int num){
for(int i=1;i<=(num+"").length();i++){
if(!(num+"").contains(i+""))
return false;
}
return true;
}
I refactored Andras' answer for Swift:
extension Int {
func isPandigital() -> Bool {
let requiredBitmask = 0b1111111111;
let minimumPandigitalNumber = 1023456789;
if self >= minimumPandigitalNumber {
var resultBitmask = 0b0;
var digits = self;
while digits != 0 {
let lastDigit = digits % 10;
let binaryCodedDigit = 1 << lastDigit;
resultBitmask |= binaryCodedDigit;
// remove last digit
digits /= 10;
}
return resultBitmask == requiredBitmask;
}
return false;
}
}
1023456789.isPandigital(); // true
great answers, my 2 cents
bool IsPandigital(long long number, int n){
int arr[] = { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, amax = 0, amin;
while (number > 0){
int rem = number % 10;
arr[rem]--;
if (arr[rem] < 0)
return false;
number = number / 10;
}
for (int i = 0; i < n; i++){
if (i == 0)
amin = arr[i];
if (arr[i] > amax)
amax = arr[i];
if (arr[i] < amin)
amin = arr[i];
}
if (amax == 0 && amin == 0)
return true;
else
return false;
}

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