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I have getting problem saving a dynamic programming problem called partition equal subset sum

I am sorry to be posting this question, but i am new to dp and I have been doing some problems to get the concept. In the problem, I am given an array and I need to tell if I can divide the array into 2 subsets such that they have the same sum.
Problem -
What I am doing -
I first calculate the sum of the array and return false if the sum is not divisible by 2. If not I go on to use to bottom-up approach of the knapsack problem solve this problem.
class Solution {
boolean[][] dp;
// using the knapsack problem that i know
public boolean canPartition(int[] nums) {
int sum = 0;
for(int num : nums){
sum += num;
}
// we have the sum;
if(sum % 2 == 1){
return false;
}
// else do other things
sum = sum / 2;
dp = new boolean[nums.length + 1][sum + 1];
// initiation of the array
for(int i = 0; i < dp.length; i++){
for(int j = 0; j < dp[0].length; j++){
if(i == 0 && j == 0){
dp[i][j] = true;
}else if(i == 0){
dp[i][j] = false;
}else if(j == 0){
dp[i][j] = true;
}
}
}
helper(nums, sum);
for(int i = 0; i < dp.length; i++){
for(int j = 0; j < dp[0].length; j++){
System.out.print(dp[i][j] + " ");
}
System.out.println();
}
return dp[nums.length][sum];
}
// i and j are the indexes that we are trying to access right now
public void helper(int[] nums, int sum){
for(int i = 1; i < nums.length; i++){
for(int j = 1; j < sum + 1; j++){
if(nums[i - 1] <= j){
dp[i][j] = dp[i][j - nums[i - 1]] || dp[i - 1][j];
}else{
dp[i][j] = dp[i - 1][j];
}
}
}
}
}
Printing my dp matrix at the end I get this -

You have missed the equality in your helper function for loop i < nums.length should be for(int i = 1; i <= nums.length; i++) . Also your array initialization shouldn't be so complex . Check the code below which works fine
class Solution {
boolean[][] dp;
// using the knapsack problem that i know
public boolean canPartition(int[] nums) {
int sum = 0;
for(int num : nums){
sum += num;
}
// we have the sum;
if(sum % 2 == 1){
return false;
}
// else do other things
sum = sum / 2;
dp = new boolean[nums.length + 1][sum + 1];
// initiation of the array
for(int i = 0; i<dp.length; i++)
dp[i][0]=true; // clean initialization
for(int i = 1; i <= nums.length; i++){ // added i==nums.length
for(int j = 1; j <=sum ; j++){
dp[i][j] = dp[i - 1][j]; // changed
if(nums[i - 1] <= j){
dp[i][j]=dp[i-1][j-nums[i-1]]||dp[i-1][j];
}
}
}
return dp[nums.length][sum];
}
}

SPOJ Prime Generator, getting TLE, but approached with the best I could. (JAVA)

The problem is to generate prime in between two interval, detail problem is given in this link. SPOJ Prime Generator.
Let me explain the magic numbers and the algorithm I followed.
I have used modified Sieve Eratosthenes algorithm (modified in sense because I used the basic idea.) for implementation.
Starting number of interval, m and End number of the interval n are <= 10^9 and the difference is <=10^5 (1 <= m <= n <= 1000000000, n-m<=100000)
There is no even prime number except 2, so I considered max m and n (10^9)/2
and sqrt(max number) is around 32000 (considering both odd and even), finally 32000/2= 16,000 is the size of odd numbers list input_aray.
Finally total number range is divided into 3 regiions.
m and n both >= 32000 in this case the size of the input_aray is (n-m+1)/2 from 16001 index of array, numbers between m and n is stored (only odd numbers).
m and n <32000 in this case size of input_aray is upto n/2.
m <32000 and n>32000 in this case size of input_aray is (n-32000+1)/2.
Boolean array bol of same size as input_aray is kept to track which number is visited so that two number can't be considered twice.
for (int j = 1; j < 16001; j++) {
int flag = input_aray[j];
This loop choose n index from input_aray and check if there is any number in this array that is divisible, if so then same index of bol is initialized into false.
for (int k = j + flag; k <= 16000; k = k + flag)
This loop check for prime numbers upto 32000.
for (int k = 16001; k < input_aray.length; k++)
This one checks in between ** m and n** (when m&n >=32000)
*This is the fastest approach I could implement, but still get Time Limit Exceed. What could be the probable cause?
public static void main(String args[]){
Scanner take= new Scanner(System.in);
ArrayList<String> arrayList= new ArrayList<>();
int m,n;
int temp= take.nextInt();
take.nextLine();
if(temp>=0 && temp<=10){
for(int i=0;i<temp;i++) {
String temp1 = take.nextLine();
arrayList.add(temp1);
}
}
for(int i=0;i<arrayList.size();i++){
String[] temp_aray= arrayList.get(i).split(" ");
m= Integer.parseInt(temp_aray[0]);
n= Integer.parseInt(temp_aray[1]);
if(m>0 && n>0 && m<=10E8 && n<=10E8 && n-m<= 10E4 ) {
if (m >= 32000 && n >= 32000) {
//m & n > 32000
int start;
int[] input_aray = new int[16001 + ((n - m + 1) / 2) + 1];
boolean[] bol = new boolean[16001 + ((n - m + 1) / 2) + 1];
Arrays.fill(bol, true);
input_aray[0] = 2;
input_aray[1] = 3;
for (int j = 2; j < 16001; j++) {
input_aray[j] = input_aray[j - 1] + 2;
}
if (m % 2 == 0) {
start = m + 1;
} else {
start = m;
}
for (int j = 16001; j < input_aray.length; j++) {
input_aray[j] = start;
start += 2;
}
for (int j = 1; j < 16001; j++) {
int flag = input_aray[j];
for (int k = j + flag; k <= 16000; k = k + flag) {
if (input_aray[k] % flag == 0 && bol[k] == true) {
bol[k] = false;
}
}
for (int k = 16001; k < input_aray.length; k++) {
if (input_aray[k] % flag == 0) {
bol[k] = false;
}
}
}
int num = 1;
for (int j = 16001; j < bol.length; j++) {
if (bol[j] == true) {
System.out.println(input_aray[j]);
num++;
}
}
System.out.println();
}
if(m<32000 && n< 32000){
int[] input_aray = new int[(n/2)+1];
boolean[] bol = new boolean[(n/2)+1];
Arrays.fill(bol, true);
input_aray[0] = 2;
input_aray[1] = 3;
for (int j = 2; j < input_aray.length; j++) {
input_aray[j] = input_aray[j - 1] + 2;
}
for (int j = 1; j < Math.sqrt(n); j++) {
int flag = input_aray[j];
for (int k = j + flag; k<input_aray.length; k = k + flag) {
if (input_aray[k] % flag == 0 && bol[k] == true) {
bol[k] = false;
}
}
}
int num = 1;
for (int j = 0; j < bol.length; j++) {
if (bol[j] == true && input_aray[j] >=m && input_aray[j]<=n) {
System.out.println(input_aray[j]);
num++;
}
}
System.out.println();
}
if(m<32000 && n>32000){
int start;
int[] input_aray = new int[16001 + ((n - 32000 + 1) / 2) + 1];
boolean[] bol = new boolean[16001 + ((n - 32000 + 1) / 2) + 1];
Arrays.fill(bol, true);
input_aray[0] = 2;
input_aray[1] = 3;
for (int j = 2; j < 16001; j++) {
input_aray[j] = input_aray[j - 1] + 2;
}
start=32001;
for (int j = 16001; j < input_aray.length; j++) {
input_aray[j] = start;
start += 2;
}
for (int j = 1; j < 16001; j++) {
int flag = input_aray[j];
for (int k = j + flag; k <= 16000; k = k + flag) {
if (input_aray[k] % flag == 0 && bol[k] == true) {
bol[k] = false;
}
}
for (int k = 16001; k < input_aray.length; k++) {
if (input_aray[k] % flag == 0) {
bol[k] = false;
}
}
}
int num = 1;
for (int j = 0; j < bol.length; j++) {
if (bol[j] == true && input_aray[j]>=m && input_aray[j]<=n) {
System.out.println(input_aray[j]);
num++;
}
}
System.out.println();
}
}
}
}

Count the minimum number of jumps required for a frog to get to the other side of a river

I work with a Codility problem provided below,
The Fibonacci sequence is defined using the following recursive formula:
F(0) = 0
F(1) = 1
F(M) = F(M - 1) + F(M - 2) if M >= 2
A small frog wants to get to the other side of a river. The frog is initially located at one bank of the river (position −1) and wants to get to the other bank (position N). The frog can jump over any distance F(K), where F(K) is the K-th Fibonacci number. Luckily, there are many leaves on the river, and the frog can jump between the leaves, but only in the direction of the bank at position N.
The leaves on the river are represented in an array A consisting of N integers. Consecutive elements of array A represent consecutive positions from 0 to N − 1 on the river. Array A contains only 0s and/or 1s:
0 represents a position without a leaf;
1 represents a position containing a leaf.
The goal is to count the minimum number of jumps in which the frog can get to the other side of the river (from position −1 to position N). The frog can jump between positions −1 and N (the banks of the river) and every position containing a leaf.
For example, consider array A such that:
A[0] = 0
A[1] = 0
A[2] = 0
A[3] = 1
A[4] = 1
A[5] = 0
A[6] = 1
A[7] = 0
A[8] = 0
A[9] = 0
A[10] = 0
The frog can make three jumps of length F(5) = 5, F(3) = 2 and F(5) = 5.
Write a function:
class Solution { public int solution(int[] A); }
that, given an array A consisting of N integers, returns the minimum number of jumps by which the frog can get to the other side of the river. If the frog cannot reach the other side of the river, the function should return −1.
For example, given:
A[0] = 0
A[1] = 0
A[2] = 0
A[3] = 1
A[4] = 1
A[5] = 0
A[6] = 1
A[7] = 0
A[8] = 0
A[9] = 0
A[10] = 0
the function should return 3, as explained above.
Assume that:
N is an integer within the range [0..100,000];
each element of array A is an integer that can have one of the following values: 0, 1.
Complexity:
expected worst-case time complexity is O(N*log(N));
expected worst-case space complexity is O(N) (not counting the storage required for input arguments).
I wrote the following solution,
class Solution {
private class Jump {
int position;
int number;
public int getPosition() {
return position;
}
public int getNumber() {
return number;
}
public Jump(int pos, int number) {
this.position = pos;
this.number = number;
}
}
public int solution(int[] A) {
int N = A.length;
List<Integer> fibs = getFibonacciNumbers(N + 1);
Stack<Jump> jumps = new Stack<>();
jumps.push(new Jump(-1, 0));
boolean[] visited = new boolean[N];
while (!jumps.isEmpty()) {
Jump jump = jumps.pop();
int position = jump.getPosition();
int number = jump.getNumber();
for (int fib : fibs) {
if (position + fib > N) {
break;
} else if (position + fib == N) {
return number + 1;
} else if (!visited[position + fib] && A[position + fib] == 1) {
visited[position + fib] = true;
jumps.add(new Jump(position + fib, number + 1));
}
}
}
return -1;
}
private List<Integer> getFibonacciNumbers(int N) {
List<Integer> list = new ArrayList<>();
for (int i = 0; i < 2; i++) {
list.add(i);
}
int i = 2;
while (list.get(list.size() - 1) <= N) {
list.add(i, (list.get(i - 1) + list.get(i - 2)));
i++;
}
for (i = 0; i < 2; i++) {
list.remove(i);
}
return list;
}
public static void main(String[] args) {
int[] A = new int[11];
A[0] = 0;
A[1] = 0;
A[2] = 0;
A[3] = 1;
A[4] = 1;
A[5] = 0;
A[6] = 1;
A[7] = 0;
A[8] = 0;
A[9] = 0;
A[10] = 0;
System.out.println(solution(A));
}
}
However, while the correctness seems good, the performance is not high enough. Is there a bug in the code and how do I improve the performance?

Got 100% with simple BFS:
public class Jump {
int pos;
int move;
public Jump(int pos, int move) {
this.pos = pos;
this.move = move;
}
}
public int solution(int[] A) {
int n = A.length;
List < Integer > fibs = fibArray(n + 1);
Queue < Jump > positions = new LinkedList < Jump > ();
boolean[] visited = new boolean[n + 1];
if (A.length <= 2)
return 1;
for (int i = 0; i < fibs.size(); i++) {
int initPos = fibs.get(i) - 1;
if (A[initPos] == 0)
continue;
positions.add(new Jump(initPos, 1));
visited[initPos] = true;
}
while (!positions.isEmpty()) {
Jump jump = positions.remove();
for (int j = fibs.size() - 1; j >= 0; j--) {
int nextPos = jump.pos + fibs.get(j);
if (nextPos == n)
return jump.move + 1;
else if (nextPos < n && A[nextPos] == 1 && !visited[nextPos]) {
positions.add(new Jump(nextPos, jump.move + 1));
visited[nextPos] = true;
}
}
}
return -1;
}
private List < Integer > fibArray(int n) {
List < Integer > fibs = new ArrayList < > ();
fibs.add(1);
fibs.add(2);
while (fibs.get(fibs.size() - 1) + fibs.get(fibs.size() - 2) <= n) {
fibs.add(fibs.get(fibs.size() - 1) + fibs.get(fibs.size() - 2));
}
return fibs;
}

You can apply knapsack algorithms to solve this problem.
In my solution I precomputed fibonacci numbers. And applied knapsack algorithm to solve it. It contains duplicate code, did not have much time to refactor it. Online ide with the same code is in repl
import java.util.*;
class Main {
public static int solution(int[] A) {
int N = A.length;
int inf=1000000;
int[] fibs={1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025};
int[] moves = new int[N+1];
for(int i=0; i<=N; i++){
moves[i]=inf;
}
for(int i=0; i<fibs.length; i++){
if(fibs[i]-1<N && A[fibs[i]-1]==1){
moves[ fibs[i]-1 ] = 1;
}
if(fibs[i]-1==N){
moves[N] = 1;
}
}
for(int i=0; i<N; i++){
if(A[i]==1)
for(int j=0; j<fibs.length; j++){
if(i-fibs[j]>=0 && moves[i-fibs[j]]!=inf && moves[i]>moves[i-fibs[j]]+1){
moves[i]=moves[i-fibs[j]]+1;
}
}
System.out.println(i + " => " + moves[i]);
}
for(int i=N; i<=N; i++){
for(int j=0; j<fibs.length; j++){
if(i-fibs[j]>=0 && moves[i-fibs[j]]!=inf && moves[i]>moves[i-fibs[j]]+1){
moves[i]=moves[i-fibs[j]]+1;
}
}
System.out.println(i + " => " + moves[i]);
}
if(moves[N]==inf) return -1;
return moves[N];
}
public static void main(String[] args) {
int[] A = new int[4];
A[0] = 0;
A[1] = 0;
A[2] = 0;
A[3] = 0;
System.out.println(solution(A));
}
}

Javascript 100%
function solution(A) {
function fibonacciUntilNumber(n) {
const fib = [0,1];
while (true) {
let newFib = fib[fib.length - 1] + fib[fib.length - 2];
if (newFib > n) {
break;
}
fib.push(newFib);
}
return fib.slice(2);
}
A.push(1);
const fibSet = fibonacciUntilNumber(A.length);
if (fibSet.includes(A.length)) return 1;
const reachable = Array.from({length: A.length}, () => -1);
fibSet.forEach(jump => {
if (A[jump - 1] === 1) {
reachable[jump - 1] = 1;
}
})
for (let index = 0; index < A.length; index++) {
if (A[index] === 0 || reachable[index] > 0) {
continue;
}
let minValue = 100005;
for (let jump of fibSet) {
let previousIndex = index - jump;
if (previousIndex < 0) {
break;
}
if (reachable[previousIndex] > 0 && minValue > reachable[previousIndex]) {
minValue = reachable[previousIndex];
}
}
if (minValue !== 100005) {
reachable[index] = minValue + 1;
}
}
return reachable[A.length - 1];
}

Python 100% answer.
For me the easiest solution was to locate all leaves within one fib jump of -1. Then consider each of these leaves to be index[0] and find all jumps from there.
Each generation or jump is recorded in a set until a generation contains len(A) or no more jumps can be found.
def gen_fib(n):
fn = [0,1]
i = 2
s = 2
while s < n:
s = fn[i-2] + fn[i-1]
fn.append(s)
i+=1
return fn
def new_paths(A, n, last_pos, fn):
"""
Given an array A of len n.
From index last_pos which numbers in fn jump to a leaf?
returns list: set of indexes with leaves.
"""
paths = []
for f in fn:
new_pos = last_pos + f
if new_pos == n or (new_pos < n and A[new_pos]):
paths.append(new_pos)
return path
def solution(A):
n = len(A)
if n < 3:
return 1
# A.append(1) # mark final jump
fn = sorted(gen_fib(100000)[2:]) # Fib numbers with 0, 1, 1, 2.. clipped to just 1, 2..
# print(fn)
paths = set([-1]) # locate all the leaves that are one fib jump from the start position.
jump = 1
while True:
# Considering each of the previous jump positions - How many leaves from there are one fib jump away
paths = set([idx for pos in paths for idx in new_paths(A, n, pos, fn)])
# no new jumps means game over!
if not paths:
break
# If there was a result in the new jumps record that
if n in paths:
return jump
jump += 1
return -1
https://app.codility.com/demo/results/training4GQV8Y-9ES/
https://github.com/niall-oc/things/blob/master/codility/fib_frog.py

Got 100%- solution in C.
typedef struct state {
int pos;
int step;
}state;
int solution(int A[], int N) {
int f1 = 0;
int f2 = 1;
int count = 2;
// precalculating count of maximum possible fibonacci numbers to allocate array in next loop. since this is C language we do not have flexible dynamic structure as in C++
while(1)
{
int f3 = f2 + f1;
if(f3 > N)
break;
f1 = f2;
f2 = f3;
++count;
}
int fib[count+1];
fib[0] = 0;
fib[1] = 1;
int i = 2;
// calculating fibonacci numbers in array
while(1)
{
fib[i] = fib[i-1] + fib[i-2];
if(fib[i] > N)
break;
++i;
}
// reversing the fibonacci numbers because we need to create minumum jump counts with bigger jumps
for(int j = 0, k = count; j < count/2; j++,k--)
{
int t = fib[j];
fib[j] = fib[k];
fib[k] = t;
}
state q[N];
int front = 0 ;
int rear = 0;
q[0].pos = -1;
q[0].step = 0;
int que_s = 1;
while(que_s > 0)
{
state s = q[front];
front++;
que_s--;
for(int i = 0; i <= count; i++)
{
int nextpo = s.pos + fib[i];
if(nextpo == N)
{
return s.step+1;
}
else if(nextpo > N || nextpo < 0 || A[nextpo] == 0){
continue;
}
else
{
q[++rear].pos = nextpo;
q[rear].step = s.step + 1;
que_s++;
A[nextpo] = 0;
}
}
}
return -1;
}

//100% on codility Dynamic Programming Solution. https://app.codility.com/demo/results/training7WSQJW-WTX/
class Solution {
public int solution(int[] A) {
int n = A.length + 1;
int dp[] = new int[n];
for(int i=0;i<n;i++) {
dp[i] = -1;
}
int f[] = new int[100005];
f[0] = 1;
f[1] = 1;
for(int i=2;i<100005;i++) {
f[i] = f[i - 1] + f[i - 2];
}
for(int i=-1;i<n;i++) {
if(i == -1 || dp[i] > 0) {
for(int j=0;i+f[j] <n;j++) {
if(i + f[j] == n -1 || A[i+f[j]] == 1) {
if(i == -1) {
dp[i + f[j]] = 1;
} else if(dp[i + f[j]] == -1) {
dp[i + f[j]] = dp[i] + 1;
} else {
dp[i + f[j]] = Math.min(dp[i + f[j]], dp[i] + 1);
}
}
}
}
}
return dp[n - 1];
}
}

Ruby 100% solution
def solution(a)
f = 2.step.inject([1,2]) {|acc,e| acc[e] = acc[e-1] + acc[e-2]; break(acc) if acc[e] > a.size + 1;acc }.reverse
mins = []
(a.size + 1).times do |i|
next mins[i] = -1 if i < a.size && a[i] == 0
mins[i] = f.inject(nil) do |min, j|
k = i - j
next min if k < -1
break 1 if k == -1
next min if mins[k] < 0
[mins[k] + 1, min || Float::INFINITY].min
end || -1
end
mins[a.size]
end

I have translated the previous C solution to Java and find the performance is improved.
import java.util.*;
class Solution {
private static class State {
int pos;
int step;
public State(int pos, int step) {
this.pos = pos;
this.step = step;
}
}
public static int solution(int A[]) {
int N = A.length;
int f1 = 0;
int f2 = 1;
int count = 2;
while (true) {
int f3 = f2 + f1;
if (f3 > N) {
break;
}
f1 = f2;
f2 = f3;
++count;
}
int[] fib = new int[count + 1];
fib[0] = 0;
fib[1] = 1;
int i = 2;
while (true) {
fib[i] = fib[i - 1] + fib[i - 2];
if (fib[i] > N) {
break;
}
++i;
}
for (int j = 0, k = count; j < count / 2; j++, k--) {
int t = fib[j];
fib[j] = fib[k];
fib[k] = t;
}
State[] q = new State[N];
for (int j = 0; j < N; j++) {
q[j] = new State(-1,0);
}
int front = 0;
int rear = 0;
// q[0].pos = -1;
// q[0].step = 0;
int que_s = 1;
while (que_s > 0) {
State s = q[front];
front++;
que_s--;
for (i = 0; i <= count; i++) {
int nextpo = s.pos + fib[i];
if (nextpo == N) {
return s.step + 1;
}
//
else if (nextpo > N || nextpo < 0 || A[nextpo] == 0) {
continue;
}
//
else {
q[++rear].pos = nextpo;
q[rear].step = s.step + 1;
que_s++;
A[nextpo] = 0;
}
}
}
return -1;
}
}

JavaScript with 100%.
Inspired from here.
function solution(A) {
const createFibs = n => {
const fibs = Array(n + 2).fill(null)
fibs[1] = 1
for (let i = 2; i < n + 1; i++) {
fibs[i] = fibs[i - 1] + fibs[i - 2]
}
return fibs
}
const createJumps = (A, fibs) => {
const jumps = Array(A.length + 1).fill(null)
let prev = null
for (i = 2; i < fibs.length; i++) {
const j = -1 + fibs[i]
if (j > A.length) break
if (j === A.length || A[j] === 1) {
jumps[j] = 1
if (prev === null) prev = j
}
}
if (prev === null) {
jumps[A.length] = -1
return jumps
}
while (prev < A.length) {
for (let i = 2; i < fibs.length; i++) {
const j = prev + fibs[i]
if (j > A.length) break
if (j === A.length || A[j] === 1) {
const x = jumps[prev] + 1
const y = jumps[j]
jumps[j] = y === null ? x : Math.min(y, x)
}
}
prev++
while (prev < A.length) {
if (jumps[prev] !== null) break
prev++
}
}
if (jumps[A.length] === null) jumps[A.length] = -1
return jumps
}
const fibs = createFibs(26)
const jumps = createJumps(A, fibs)
return jumps[A.length]
}
const A = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]
console.log(A)
const s = solution(A)
console.log(s)

You should use a QUEUE AND NOT A STACK. This is a form of breadth-first search and your code needs to visit nodes that were added first to the queue to get the minimum distance.
A stack uses the last-in, first-out mechanism to remove items while a queue uses the first-in, first-out mechanism.
I copied and pasted your exact code but used a queue instead of a stack and I got 100% on codility.

100% C++ solution
More answers in my github
Inspired from here
Solution1 : Bottom-Top, using Dynamic programming algorithm (storing calculated values in an array)
vector<int> getFibonacciArrayMax(int MaxNum) {
if (MaxNum == 0)
return vector<int>(1, 0);
vector<int> fib(2, 0);
fib[1] = 1;
for (int i = 2; fib[fib.size()-1] + fib[fib.size() - 2] <= MaxNum; i++)
fib.push_back(fib[i - 1] + fib[i - 2]);
return fib;
}
int solution(vector<int>& A) {
int N = A.size();
A.push_back(1);
N++;
vector<int> f = getFibonacciArrayMax(N);
const int oo = 1'000'000;
vector<int> moves(N, oo);
for (auto i : f)
if (i - 1 >= 0 && A[i-1])
moves[i-1] = 1;
for (int pos = 0; pos < N; pos++) {
if (A[pos] == 0)
continue;
for (int i = f.size()-1; i >= 0; i--) {
if (pos + f[i] < N && A[pos + f[i]]) {
moves[pos + f[i]] = min(moves[pos]+1, moves[pos + f[i]]);
}
}
}
if (moves[N - 1] != oo) {
return moves[N - 1];
}
return -1;
}
Solution2: Top-Bottom using set container:
#include <set>
int solution2(vector<int>& A) {
int N = A.size();
vector<int> fib = getFibonacciArrayMax(N);
set<int> positions;
positions.insert(N);
for (int jumps = 1; ; jumps++)
{
set<int> new_positions;
for (int pos : positions)
{
for (int f : fib)
{
// return jumps if we reach to the start point
if (pos - (f - 1) == 0)
return jumps;
int prev_pos = pos - f;
// we do not need to calculate bigger jumps.
if (prev_pos < 0)
break;
if (prev_pos < A.size() && A[prev_pos])
new_positions.insert(prev_pos);
}
}
if (new_positions.size() == 0)
return -1;
positions = new_positions;
}
return -1;
}

Tape-Equilibrium Codility Training program

I submitted a solution to Tape Equilibrium problem in Codility. [Codility training][1]
The problem is described as follows:
A non-empty zero-indexed array A consisting of N integers is given. Array A represents numbers on a tape.
Any integer P, such that 0 < P < N, splits this tape into two non-empty parts: A[0], A[1], ..., A[P − 1] and A[P], A[P + 1], ..., A[N − 1].
The difference between the two parts is the value of: |(A[0] + A[1] + ... + A[P − 1]) − (A[P] + A[P + 1] + ... + A[N − 1])|
In other words, it is the absolute difference between the sum of the first part and the sum of the second part.
The solution I submitted is:
class Solution {
public int solution(int[] A) {
long d = A[0] - A[A.length-1];
int l = 1;
int r = A.length -2;
while(l <= r) {
if (Math.abs(d + A[l]) < Math.abs(d - A[r])) {
d += A[l];
l++;
}
else {
d -= A[r];
r--;
}
}
return (int) Math.abs(d);
}
}
I achieved 85% accuracy but couldn't get to correct for some use case. Can someone help me to find what's wrong with this solution. Thanks

The following is my 100% solution:
class Solution {
public int solution(int[] A) {
// write your code in Java SE 8
// int idx = 0;
int sumPre = A[0];
int sumPost = 0;
for (int i = 1; i < A.length; i++) {
sumPost += A[i];
}
int difMin = Math.abs(sumPost - sumPre);
int tempSub = 0;
for (int i = 1; i < A.length - 1; i++) {
sumPre += A[i];
sumPost -= A[i];
tempSub = Math.abs(sumPost - sumPre);
if (tempSub < difMin) {
difMin = tempSub;
// idx = i+1;
}
}
return difMin;
}
}
I can not find their test input, but I find a weird thing is that when "for(int i = 1; i < A.length - 1; i++) " is changed to " for(int i = 1; i < A.length; i++)", then it will trigger two wrong runs...So it still must be a border value issue.
If any one find a test input can break the validity, please share with us, thanks.
Caution: {1,-1} indeed triggered the problem, since P < N, so at least one element should be left in the right part. -> {1,-1},{} is not a valid solution according to the problem definition.
Problem solved.

C# and Linq version for 100% as of May 2021:
public int solution(int[] A)
{
int left = A[0];
int right = A.Skip(1).Aggregate((c,x)=> c+=x);
int min = Math.Abs(left-right);
for(int i=1; i < A.Length-1; i++)
{
left+=A[i];
right-=A[i];
min = Math.Min(min,Math.Abs(left-right));
}
return min;
}

I also tried and got only 83%. My solution:
class Solution {
public int solution(int[] A) {
int[] leftSums = new int[A.length];
for (int i = 0; i < leftSums.length; i++) {
leftSums[i] = 0;
}
int sum = 0;
for (int i = 0; i < A.length; i++) {
sum += A[i];
leftSums[i] = sum;
}
/*
for (int i = 0; i < leftSums.length; i++) {
if (i == 0) {
System.out.print("Left Sums Array is : [");
}
if (i == leftSums.length - 1) {
System.out.println(leftSums[i] + "]");
}
System.out.print(leftSums[i] + ", ");
}
*/
final int total = sum;
//System.out.println("Total is " + total);
int minDiff = Integer.MAX_VALUE;
int currDiff = 0;
for (int i = 0; i < leftSums.length; i++) {
currDiff = Math.abs(leftSums[i] - (total - leftSums[i]));
if (currDiff < minDiff) {
minDiff = currDiff;
}
}
return minDiff;
}
}
Below are those which failed for correctness.
double
two elements 1.280 s WRONG ANSWER
got 0 expected 2000
small
small elements 1.304 s WRONG ANSWER
got 0 expected 20
I tested myself for 2 elements and it worked for me.

I share my 100% score Java solution:
class Solution {
public int solution(int[] A) {
final int size = A.length;
long sumMin = (int)A[0];
long sumMax = 0;
for (int i = 1; i < size; i++) {
sumMax += (int)A[i];
}
int minDif = (int)Math.abs(sumMax - sumMin);
for (int i = 1; i < size; i++) {
int dif = (int)Math.abs(sumMax - sumMin);
if (dif < minDif) {
minDif = dif;
}
sumMin += A[i];
sumMax -= A[i];
}
return minDif;
}
}
The trick is that looping the array twice your complexity is 2N, which is O(N).
Addition results should be 'long' in order not to have problems with big extremes.

For %83 results, the problem is it says "splits this tape into two non-empty parts". So if you split for A[0], your first array will be empty. So you should start with A[1].

Ruby 100%
def solution(a)
left = a.inject(:+)
right = 0
a[0...-1].inject(Float::INFINITY) do |min, el|
left -=el
right += el
candidate = (right-left).abs
min < candidate ? min : candidate
end
end

You can actually do that, with one loop in C#.
Add Linq:
public int solution(int[] A)
{
// write your code in C# 6.0 with .NET 4.5 (Mono)
long sum = A.Sum(p => (long)p);
int val1 = Convert.ToInt32(A.GetValue(0));
int val2 = Convert.ToInt32(sum - val1);
int result = Math.Abs(val1 - val2);
for (int i = 1; i < A.Length-1; i++)
{
val1 += Convert.ToInt32(A.GetValue(i));
val2 -= Convert.ToInt32(A.GetValue(i));
if (result > Math.Abs(val1 - val2))
{
result = Math.Abs(val1 - val2);
}
}
return result;
}

Counterexample for user699681: A = {0, 1, 2, -5, 2},
and for Ism: A = {1, -1}.

TapeEquilibrium in C
int solution(int A[], int N) {
// write your code in C90
long int s_r=0,s_l=A[0],sum=A[0];
int i,min=11111111,r;
for(i=1;i<N;i++)
sum+=A[i];
for(i=1;i<N;i++)
{
s_r=sum-s_l;
r=(int)(s_l-s_r);
if(r<0) r=-r;
if(min>r)min=r;
if(min==0)break;
s_l=sum-s_r+A[i];
}
return min;
}

.. Or even a bit shorter to get 100%
public int solution(int[] A) {
int sumMin = A[0];
int sumMax = 0;
for (int i = 1; i < A.length; i++) {
sumMax += A[i];
}
int minDif = Math.abs(sumMin - sumMax);
for (int i = 1; i < A.length - 1; i++) {
sumMin += A[i];
sumMax -= A[i];
minDif = Math.min(minDif, Math.abs(sumMin - sumMax));
}
return minDif;
}

Here's my implementation using Java 8 IntStream to simplify the sum process...
100% Correct, 100% Performance.
import java.util.stream.IntStream;
public class TapeEquilibrium {
public static int diffIndex( int[] A ) {
long lower = 0, diff = 0, higher = IntStream.of( A ).asLongStream().sum(), minDiff = Integer.MAX_VALUE;
for(int i = 0; i < A.length-1; i++) {
lower += A[i];
higher -= A[i];
diff = Math.abs( higher - lower);
if( diff < minDiff ) {
minDiff = diff;
}
}
return (int) minDiff;
}
public static void main( String[] args ) {
int[] A = { 3, 1, 2, 4, 3 };
System.out.println( diffIndex( A ) );
}
}

here is my Solution with 100% correctness & performance
int solution(int A[], int N)
{
int sum,i;
sum=0;
for(i=0;i<N;i++)
{
sum+=A[i];
A[i]=sum;
}
int min_diff=abs(sum-A[0]*2);
for(i=0;i<N-1;i++)
{
int tmp;
tmp=abs(sum-A[i]*2);
if(tmp<min_diff)
min_diff=tmp;
}
return min_diff;
}

Try this one:
Class Solution {
public int solution(int[] A) {
int sum1 = 0;
int sum2 = 0;
int sum3 = 0;
int len = A.length;
int min = 1 ;
for(int i=0; i<len; i++){
sum2 += A[i];
}
for(int i=0; i< len-1 ; i++){
sum1 += A[i];
sum3 = sum2-sum1;
if( min > Math.abs(sum1- sum3)){
min = Math.abs( sum1 - sum3);
}
}
return min;
}
}

Here is 100% in scala.
def solution(A: Array[Int]): Int = {
//get the whole sum
val allSum = A.sum
//calculate left and right sum
var sumLeft = A(0)
var sumRight = allSum - sumLeft
//set initial diff for P=1
var minDiff = math.abs(sumLeft-sumRight) //difference
// loop for all P after the initial P position
for(p <- 1 to A.length-2){
//recalculate values
sumLeft += A(p)
sumRight -= A(p)
if(math.abs(sumLeft-sumRight) < minDiff){
// if difference is smaller then save new min diff
minDiff = math.abs(sumLeft-sumRight)
}
}
minDiff
}
Performance: https://codility.com/demo/results/trainingZNZCZN-AGC/

long sumofall = 0, leftsideSum = A[0], rightsidesum=0;
int x,LR = 0;
ArrayList listResult = new ArrayList();
for(x=0;x<A.Length;x++)
{
sumofall+= A[x];
}
for(x=1;x<A.Length;x++)
{
rightsidesum = sumofall-leftsideSum;
LR = (int)(rightsidesum - leftsideSum);
if(LR < 0)
{
LR=-LR;
}
listResult.Add(LR);
leftsideSum+=A[x];
}
listResult.Sort();
return Convert.ToInt32(listResult[0].ToString());
}

I share my 100% solution using Java 8.
public class TapeEquilibrium {
public int tapeEquilibrium(int[] A) {
final int N = A.length;
long minimalSum = (int) A[0];
int[] rightSide = Arrays.copyOfRange(A, 1, N);
long maximalSum = IntStream.of(rightSide).sum();
int minimalDifference = (int) Math.abs(maximalSum - minimalSum);
for (int i = 1; i < N; i++) {
int difference = (int) Math.abs(maximalSum - minimalSum);
minimalDifference = difference < minimalDifference ? difference : minimalDifference;
minimalSum += A[i];
maximalSum -= A[i];
}
return minimalDifference;
}
}

Here is my C# solution. Score 100%
if (A == null || A.Length == 0)
{
return 0;
}
int d1 = 0;
int d2 = A.Sum();
int p = 1;
int x = int.MaxValue;
// Replaced using A.sum();
//for (int i=0; i < A.Length; i++)
//{
// d2 += A[i];
//}
for (int j = 0; j < A.Length; j++)
{
if (j < p)
{
d1 += A[j];
}
int ad = Math.Abs(d1 - (d2 - d1));
x = Math.Min(x, ad);
if (p == A.Length -1) { break; }
p++;
}
return x;

Below is my solution which got 100% . As most of you guys did I first got the sum of the array then go through it while adding up left and right parts and then getting the absolutes of them and putting the results into a map then checking the map for the minimum value .
int totalLeft = 0;
int totalRight = 0;
int total = 0;
int result = 0;
Map<Integer, Integer> map = new HashMap<Integer, Integer>();
for (int i = 0; i < A.length; i++) {
total += A[i];
}
for (int i = 0; i < A.length - 1; i++) {
totalRight = total - (A[i] + totalLeft);
totalLeft += A[i];
result = Math.abs(totalLeft - totalRight);
map.put(i, result);
}
return Collections.min(map.values());

TapeEquilibrium in Swift 4
public func solution(_ A : inout [Int]) -> Int {
let P = 1
var splitIndex = P
var firstPartSum = A[splitIndex - 1]
var secondPartSum = Array(A[splitIndex..<A.count]).reduce(0, +)
var minimalDifference = abs(firstPartSum - secondPartSum)
if minimalDifference == 0 {
return minimalDifference
}
splitIndex += 1
while splitIndex < A.count {
firstPartSum += A[splitIndex - 1]
secondPartSum -= A[splitIndex - 1]
let dif = abs(firstPartSum - secondPartSum)
if dif == 0 {
return dif
}
if dif < minimalDifference {
minimalDifference = dif
}
splitIndex += 1
}
return minimalDifference
}

No one posted Javascript solution yet so here is mine with comments:
// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(A) {
// write your code in JavaScript (Node.js 8.9.4)
// Making it shorter.
let len = A.length;
// Definitely need to store, and initialise first value.
let left = new Array(len);
left[0] = A[0];
// Same as above, but initialise for last value.
let right = new Array(len);
right[len - 1] = A[len - 1];
let trackLowest = Number.MAX_SAFE_INTEGER;
// One shot calculate for both at any element (from 'outwards' 'in').
// Note there is 2 elements at least, and we already preset the first
// element, so we start and build from index 1.
for (let i = 1; i < len; ++i) {
left[i] = left[i - 1] + A[i];
right[len - 1 - i] = right[len - i] + A[len - 1 - i];
}
// Once the above is done, it's time to calculate the difference.
// If I am at index 0, then I want sum of index 0 AND left, and sum of index
// 1 and right (note not index 0 also).
// We stop before len - 1 because that's the rules and the sum of right will
// have been out of bounds if we want difference for last index, isn't it?
for (let i = 0; i < len - 1; ++i) {
let smallestDiff = Math.abs(left[i] - right[i + 1]);
if (smallestDiff < trackLowest) {
trackLowest = smallestDiff;
}
}
return trackLowest;
}
Basically sum up as you walk the loop simultaneously for the left and right side.
Once done, just get the difference, that's it. O(n) complexity.

My 100% JavaScript solution with O(N) time complexity (should be pretty self-explanatory):
function solution(A) {
let left = 0;
let right = A.reduce((sum, cur) => sum + cur, 0);
let min = Infinity;
for (let p = 0, len = A.length - 1; p < len; p++) {
left += A[p];
right -= A[p];
min = Math.min(min, Math.abs(left - right));
}
return min;
}

100% in Swift 4 for correctness & performance
Detected Time Complexity: 0(n)
var sumMin = A[0]
var sumMax = 0
for i in 1..<A.count {
sumMax += A[i]
}
var diff = abs(sumMin - sumMax)
for i in 1..<A.count-1 {
sumMin += A[i]
sumMax -= A[i]
diff = min(diff, abs(sumMin - sumMax));
}
return diff

Here mine in Java,
// got 91% because "int totalRight = (Arrays.stream(A).sum() - A[0]);" take too long to load
int totalLeft = A[0];
int totalRight = (Arrays.stream(A).sum() - A[0]);
//int afterMinus = 0;
int min = 0;
min = Math.abs(totalLeft - totalRight);
for(int i=1; i<(A.length-1); i++) {
//for(int j=A.length; j>0; j--) {
totalLeft += A[i];
totalRight -= A[i];
//System.out.println("totalLeft = "+ totalLeft);
//System.out.println("totalRight = "+ totalRight);
if(Math.abs(totalLeft - totalRight) < min) {
//System.out.println("min = "+ min);
min = Math.abs(totalLeft - totalRight);
}
}
return min;
// got 100% because change "int totalRight = (Arrays.stream(A).sum() - A[0]);" into for loop
//int totalSum = Arrays.stream(A).sum();
int totalLeft = A[0];
int totalRight = 0;
//int afterMinus = 0;
int min = 0;
for(int i=1; i<A.length; i++) {
totalRight += A[i];
}
min = Math.abs(totalLeft - totalRight);
for(int i=1; i<(A.length-1); i++) {
//for(int j=A.length; j>0; j--) {
totalLeft += A[i];
totalRight -= A[i];
//System.out.println("totalLeft = "+ totalLeft);
//System.out.println("totalRight = "+ totalRight);
if(Math.abs(totalLeft - totalRight) < min) {
//System.out.println("min = "+ min);
min = Math.abs(totalLeft - totalRight);
}
}
return min;
Well, from 91% to 100%, thanks to #sebadagostino after surfing for almost 2 hours for the logic and hints.

Traversing a 2D array matrix diagonally from bottom left to upper right

I have a 3x4 matrix represented by a 2D array:
. 0 1 2 3
0 a c f i
1 b e h k
2 d g j l
and my approach to traverse the diagonal slice was to treat each slice as a sum, like this:
a = (0+0) = 0
b,c = (0+1),(1+0) = 1
d,e,f = (0+2),(1+1),(2+0) = 2
g,h,i = (1+2),(2+1),(3+0) = 3
j, k = (2+2),(3+1) = 4
l = (3+2) = 5
However, my code right now prints it in the opposite way that I want it to, which is from upper right to bottom left.
Current Output is:
acbfedihgkjl
Desired Output is:
abcdefghijkl
for (int sum = 0; sum <= numRows + numColumns - 2; sum++) {
for (int i = 0; i < numRows; i++) {
int j = sum - i;
if ((i >= 0 && i < numRows) && (j >= 0 && j < numColumns)) {
System.out.print(array[i][j]);
}
}
}
Can somebody point me in the right direction on how to fix my code to get the output that I want?

While it isn't very pretty, I think this will do it:
int i = 0;
int j = 0;
while (true) {
System.out.println("" + array[i][j]);
--i;
++j;
if (i < 0) {
if (j == numCols)
break;
i = Math.min(j, numRows - 1);
j = Math.max(j - numCols + 2, 0);
} else if (j >= numCols) {
if (i == numRows - 2)
break;
i = numRows - 1;
j = Math.max(j + 2 - numCols + i, 0);
}
}

int i = 0;
int j = 0;
int n = 0;
int x = 3;
int y = 4;
int newSize = Math.max(x,y) * Math.max(x,y);
while(n < newSize){
if(i <= x && j <= y)
System.out.println(array[i][j]);
n++;
if(i == 0) {
i = n:
j = 0;
} else {
--i;
++j;
}
}