Develop Reference

Almost the same statements, but different value

I'm working on a classic DP question, Count Subset Sum.
The problem statement is as follows if you are not sure about the problem:
Given a set of positive numbers, find the total number of subsets whose sum is equal to a given number ‘S’.
I'm trying to work solve it with backtracking approach.
Assume the given array is [1, 1, 2, 3] and the sum is 4, so the expected result is 3
The weird thing is the code blow works fine, and it generates the correct result.
private int backtrack2(int[] nums, int sum) {
int[] count = new int[1];
backtrack2Helper(nums, sum, count, 0);
return count[0];
}
private int backtrack2Helper(int[] nums, int sum, int[] count, int pos) {
if (0 == sum) return 1;
if (pos == nums.length) return 0;
for (int i = pos; i < nums.length; ++i) {
if (sum - nums[i] >= 0) {
int temp = backtrack2Helper(nums, sum - nums[i], count, i + 1);
count[0] += temp;
}
}
return 0;
}
However, the code below can not generate the correct result:
private int backtrack2(int[] nums, int sum) {
int[] count = new int[1];
backtrack2Helper(nums, sum, count, 0);
return count[0];
}
private int backtrack2Helper(int[] nums, int sum, int[] count, int pos) {
if (0 == sum) return 1;
if (pos == nums.length) return 0;
for (int i = pos; i < nums.length; ++i) {
if (sum - nums[i] >= 0) {
count[0] += backtrack2Helper(nums, sum - nums[i], count, i + 1);
}
}
return 0;
}
The only difference is the if statement part in the helper function.
int temp = backtrack2Helper(nums, sum - nums[i], count, i + 1);
count[0] += temp;
and
count[0] += backtrack2Helper(nums, sum - nums[i], count, i + 1);
should be equivalent, right?
But the second one does not work correctly.
I was really confused and I debugged it step by step, finding that when the method in the second approach hit the return statement at last, count[0] was not added by the returned 0, but set to 0.
What's happening?

The difference results from the fact that backtrack2Helper() changes count[0].
Suppose, for example, that backtrack2Helper(nums, sum - nums[i], count, i + 1) changes that value of count[0] from 0 to 1 and returns 1.
In one snippet you are adding the changed value of count[0] to the value returned by the recursive call:
int temp = backtrack2Helper(nums, sum - nums[i], count, i + 1); // == 1
count[0] += temp; // == 1 + 1 == 2
But in the other snippet you are adding the original value of count[0] to the value returned by the recursive call:
count[0] += backtrack2Helper(nums, sum - nums[i], count, i + 1); // == 0 + 1 == 1
EDIT:
You can write a more elegant solution without the count[] array:
private static int backtrack2(int[] nums, int sum) {
return backtrack2Helper(nums, sum, 0);
}
private static int backtrack2Helper(int[] nums, int sum, int pos) {
if (0 == sum)
return 1;
if (pos == nums.length)
return 0;
int count = 0;
for (int i = pos; i < nums.length; ++i) {
if (sum - nums[i] >= 0) {
count += backtrack2Helper(nums, sum - nums[i], i + 1);
}
}
return count;
}
EDIT:
To improve the explanation regarding the difference of the two snippets, here's a simpler code that produces the same behavior:
int method2 (int[] arr)
{
arr[0] = 5;
return 0;
}
First snippet:
void method1 ()
{
int[] arr = new int[1]; // arr[0] is 0
int temp = method2 (arr); // temp is assigned 0, arr[0] is changed to 5 by method2
arr[0] += temp // arr[0] = arr[0] + temp == 5 + 0 == 5
}
Second snippet:
void method1 ()
{
int[] arr = new int[1]; // arr[0] is 0
arr[0] += method2 (arr); // arr[0] = arr[0] + method2 (arr) == 0 + 0 == 0
}

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;
}

minimum operations required to make the longest character interval equal to K

I was asked this question in an contest.
Given a string containing only M and L, we can change any "M" to "L" or any "L" to "M". The objective of this function is to calculate the minimum number of changes we have to make in order to achieve the desired longest M-interval length K.
For example, given S = "MLMMLLM" and K = 3, the function should return 1. We can change the letter at position 4 (counting from 0) to obtain "MLMMMLM", in which the longest interval of letters "M" is exactly three characters long.
For another example, given S = "MLMMMLMMMM" and K = 2, the function should return 2. We can, for example, modify the letters at positions 2 and 7 to get the string "MLLMMLMLMM", which satisfies the desired property.
Here's what I have tried till now, but I am not getting correct output:
I am traversing the string and whenever longest char count exceeds K, I'm replacing M with L that point.
public static int solution(String S, int K) {
StringBuilder Str = new StringBuilder(S);
int longest=0;int minCount=0;
for(int i=0;i<Str.length();i++){
char curr=S.charAt(i);
if(curr=='M'){
longest=longest+1;
if(longest>K){
Str.setCharAt(i, 'L');
minCount=minCount+1;
}
}
if(curr=='L')
longest=0;
}
if(longest < K){
longest=0;int indexoflongest=0;minCount=0;
for(int i=0;i<Str.length();i++){
char curr=S.charAt(i);
if(curr=='M'){
longest=longest+1;
indexoflongest=i;
}
if(curr=='L')
longest=0;
}
Str.setCharAt(indexoflongest, 'M');
minCount=minCount+1;
}
return minCount;
}

There are 2 parts to this algorithm as we want to get the longest character interval equal to K.
We already have a interval >= K so now we need to appropriately change some characters so we greedily change every (k + 1) th character and again start counting from 0.
Now if the interval was less than K I will need to run a sliding window over the array. While running this window I am basically considering converting all L's to M's in this window of length K. But this comes with a side effect of increasing the length of the interval as there could be K's outside so this variable (int nec) keeps track of that. So now I have to also consider converting the 2 possible M's outside the (K length) window to L's.
Here's the complete runnable code in C++. Have a good day.
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector <int> vi;
typedef pair<int, int> ii;
int change(string s, int k) {
// handling interval >= k
bool flag = false;
int ans = 0;
int cnt = 0;
for(int i=0; i<s.size(); i++) {
if(s[i] == 'M') cnt++;
else cnt = 0;
if(cnt == k) flag = true;
if(cnt > k) s[i] = 'L', ans++, cnt = 0;
}
if(flag) return ans;
// handling max interval < k
// If the interval is too big.
if(k > s.size()) {
cerr << "Can't do it.\n"; exit(0);
}
// Sliding window
cnt = 0;
for(int i=0; i<k; i++) {
if(s[i] == 'L') cnt++;
}
ans = cnt + (s[k] == 'M'); // new edit
int nec = 0; // new edit
for(int i=k; i<s.size(); i++) {
if(s[i-k] == 'L') cnt--;
if(s[i] == 'L') cnt++;
nec = 0;
if(i-k != 0 && s[i-k-1] == 'M')
nec++;
if(i < s.size()-1 && s[i+1] == 'M')
nec++;
ans = min(ans, cnt + nec);
}
return ans;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
string s;
int k;
cin >> s >> k;
int ans = change(s, k);
cout << ans << "\n";
return 0;
}

int
process_data(const char *m, int k)
{
int m_cnt = 0, c_cnt = 0;
char ch;
const char *st = m;
int inc_cnt = -1;
int dec_cnt = -1;
while((ch = *m++) != 0) {
if (m_cnt++ < k) {
c_cnt += ch == 'M' ? 0 : 1;
if ((m_cnt == k) && (
(inc_cnt == -1) || (inc_cnt > c_cnt))) {
inc_cnt = c_cnt;
}
}
else if (ch == 'M') {
if (*st++ == 'M') {
/*
* losing & gaining M carries no change provided
* there is atleast one L in the chunk. (c_cnt != 0)
* Else it implies stretch of Ms
*/
if (c_cnt <= 0) {
int t;
c_cnt--;
/*
* compute min inserts needed to brak the
* stretch to meet max of k.
*/
t = (k - c_cnt) / (k+1);
dec_cnt += t;
}
}
else {
ASSERT(c_cnt > 0, "expect c_cnt(%d) > 0", c_cnt);
ASSERT(inc_cnt != -1, "expect inc_cnt(%d) != -1", inc_cnt);
/* Losing L and gaining M */
if (--c_cnt < inc_cnt) {
inc_cnt = c_cnt;
}
}
}
else {
if (c_cnt <= 0) {
/*
* take this as a first break and restart
* as any further addition of M should not
* happen. Ignore this L
*/
st = m;
c_cnt = 0;
m_cnt = 0;
}
else if (*st++ == 'M') {
/* losing m & gaining l */
c_cnt++;
}
else {
// losing & gaining L; no change
}
}
}
return dec_cnt != -1 ? dec_cnt : inc_cnt;
}

Corrected code:
int
process_data(const char *m, int k)
{
int m_cnt = 0, c_cnt = 0;
char ch;
const char *st = m;
int inc_cnt = -1;
int dec_cnt = -1;
while((ch = *m++) != 0) {
if (m_cnt++ < k) {
c_cnt += ch == 'M' ? 0 : 1;
if ((m_cnt == k) && (
(inc_cnt == -1) || (inc_cnt > c_cnt))) {
inc_cnt = c_cnt;
}
}
else if (ch == 'M') {
if (*st++ == 'M') {
/*
* losing & gaining M carries no change provided
* there is atleast one L in the chunk. (c_cnt != 0)
* Else it implies stretch of Ms
*/
if (c_cnt <= 0) {
c_cnt--;
}
}
else {
ASSERT(c_cnt > 0, "expect c_cnt(%d) > 0", c_cnt);
ASSERT(inc_cnt != -1, "expect inc_cnt(%d) != -1", inc_cnt);
/* Losing L and gaining M */
if (--c_cnt < inc_cnt) {
inc_cnt = c_cnt;
}
}
}
else {
if (c_cnt <= 0) {
/*
* compute min inserts needed to brak the
* stretch to meet max of k.
*/
dec_cnt += (dec_cnt == -1 ? 1 : 0) + ((k - c_cnt) / (k+1));
/*
* take this as a first break and restart
* as any further addition of M should not
* happen. Ignore this L
*/
st = m;
c_cnt = 0;
m_cnt = 0;
}
else if (*st++ == 'M') {
/* losing m & gaining l */
c_cnt++;
}
else {
// losing & gaining L; no change
}
}
}
if (c_cnt <= 0) {
/*
* compute min inserts needed to brak the
* stretch to meet max of k.
*/
dec_cnt += (dec_cnt == -1 ? 1 : 0) + ((k - c_cnt) / (k+1));
}
return dec_cnt != -1 ? dec_cnt : inc_cnt;
}

Getting the first occurrence in binary search

I am trying to get the first occurrence of the number 5.The answer should be 2 in this case but i am getting 3 here.
public static void main(String[] args) {
int A[] = {1, 3, 5, 5, 5, 17, 20};
int index = BinarySearch(A, 5);
System.out.println(index);
}
public static int BinarySearch(int[] A, int x) {
int low = 0;
int high = A.length - 1;
while (low <= high) {
//(low + high) / 2
int mid = low + (high-low)/2; // more optimal -> low + (high-low)/2 (avoid integer overflow)
if (x == A[mid]) {
return mid;
} else if (x < A[mid]) {
high = mid - 1;
} else {
low = mid + 1;
}
}
return -1;
}

When you find the value you are looking for, you return the mid index immediately without checking if there are smaller indices having the same value.
You have to continue searching :
public static int BinarySearch(int[] A, int x) {
int low = 0;
int high = A.length - 1;
int mid = -1;
while (low <= high) {
mid = low + (high-low)/2;
if (x <= A[mid]) { // this ensures you keep searching for the first index having
// the number you are looking for
//
// changing x <= A[mid] to x < A[mid] will give you the
// last index having the number you are looking for instead
high = mid - 1;
} else {
low = mid + 1;
}
}
if (mid >= 0 && x == A[mid]) {
return mid;
}
return -1;
}

What substring search algorithm is used by different JREs?

java.lang.String JavaDoc says nothing about the default indexOf(String) substring search algorithm. So my question is - which substring algorithms is used by different JREs?

There's src.zip in JDK which shows implementation:
/**
* Code shared by String and StringBuffer to do searches. The
* source is the character array being searched, and the target
* is the string being searched for.
*
* #param source the characters being searched.
* #param sourceOffset offset of the source string.
* #param sourceCount count of the source string.
* #param target the characters being searched for.
* #param targetOffset offset of the target string.
* #param targetCount count of the target string.
* #param fromIndex the index to begin searching from.
*/
static int indexOf(char[] source, int sourceOffset, int sourceCount,
char[] target, int targetOffset, int targetCount,
int fromIndex) {
if (fromIndex >= sourceCount) {
return (targetCount == 0 ? sourceCount : -1);
}
if (fromIndex < 0) {
fromIndex = 0;
}
if (targetCount == 0) {
return fromIndex;
}
char first = target[targetOffset];
int max = sourceOffset + (sourceCount - targetCount);
for (int i = sourceOffset + fromIndex; i <= max; i++) {
/* Look for first character. */
if (source[i] != first) {
while (++i <= max && source[i] != first);
}
/* Found first character, now look at the rest of v2 */
if (i <= max) {
int j = i + 1;
int end = j + targetCount - 1;
for (int k = targetOffset + 1; j < end && source[j] ==
target[k]; j++, k++);
if (j == end) {
/* Found whole string. */
return i - sourceOffset;
}
}
}
return -1;
}

fwiw (in case this Q is about the performance of different algorithms) on appropriate hardware and with a sufficiently recent oracle jvm (6u21 and later as detailed in the bug report), String.indexOf is implemented via the relevant SSE 4.2 intrinsics.. see chapter 2.3 in this intel reference doc

Here is what found for now:
Oracle JDK 1.6/1.7, OpenJDK 6/7
static int indexOf(char[] source, int sourceOffset, int sourceCount,
char[] target, int targetOffset, int targetCount,
int fromIndex) {
if (fromIndex >= sourceCount) {
return (targetCount == 0 ? sourceCount : -1);
}
if (fromIndex < 0) {
fromIndex = 0;
}
if (targetCount == 0) {
return fromIndex;
}
char first = target[targetOffset];
int max = sourceOffset + (sourceCount - targetCount);
for (int i = sourceOffset + fromIndex; i <= max; i++) {
/* Look for first character. */
if (source[i] != first) {
while (++i <= max && source[i] != first);
}
/* Found first character, now look at the rest of v2 */
if (i <= max) {
int j = i + 1;
int end = j + targetCount - 1;
for (int k = targetOffset + 1; j < end && source[j] ==
target[k]; j++, k++);
if (j == end) {
/* Found whole string. */
return i - sourceOffset;
}
}
}
return -1;
}
IBM JDK 5.0
public int indexOf(String subString, int start) {
if (start < 0) start = 0;
int subCount = subString.count;
if (subCount > 0) {
if (subCount + start > count) return -1;
char[] target = subString.value;
int subOffset = subString.offset;
char firstChar = target[subOffset];
int end = subOffset + subCount;
while (true) {
int i = indexOf(firstChar, start);
if (i == -1 || subCount + i > count) return -1; // handles subCount > count || start >= count
int o1 = offset + i, o2 = subOffset;
while (++o2 < end && value[++o1] == target[o2]);
if (o2 == end) return i;
start = i + 1;
}
} else return start < count ? start : count;
}
Sabre SDK
public int indexOf(String str, int fromIndex)
{
if (fromIndex < 0)
fromIndex = 0;
int limit = count - str.count;
for ( ; fromIndex <= limit; fromIndex++)
if (regionMatches(fromIndex, str, 0, str.count))
return fromIndex;
return -1;
}
Feel free to update this post.

As most of the time indexOf is used for small substrings in reasonable small strings it is I believe save to assume that a fairly straight forward algorithm like the one shown by Victor is used. There are more advanced algorithms that work better for large strings but AFAIK these all perform worse for relative short strings.