Longest subarray of only 0's or 1's with atmost K flips

Given a binary array a[] or size N and an integer K, the task is to find the longest subarray consisting of only 1s or only 0s when at most K elements can be flipped (i.e change 1 to 0 or 0 to 1).

Examples:

Input: a[] = {1, 0, 0, 1, 1, 0, 1}, K = 1.
Output: 4
Explanation: Flip element of index 0(0-based index) to 0. 
Then the maximum subarray with all 0 will be of length 3 [0-2]
Flip index 5 to 1. The maximum subarray with all 1's will be of length 4 [3-6] 
So the maximum of (3, 4) is 4. So the answer is 4 for this test case.

Input : a[] = {1, 0, 0, 1, 0, 1, 0, 1, 0, 1}, K = 2.
Output : 6
Explanation: Flip 2-1's to 0 or 2-0's to 1. 
So after flipping element of index 6 and 8 to 1,  
the maxlength of the subarray consisting of only 1's is 5 [5 to 9].
Flip element of index 3 and 5 to 0 then the maxlength 
of the subarray consisting of only 0's is 6 [1 to 6] 
The maximum of both of them is 6. So the answer is 6 for this input. 

Approach: This problem can be solved using two pointers approach and sliding window algorithm based on the following idea. 

Run for loop two times - 

• One loop to maintain subsegment [l, r] to contain not more than K 0s and find maximum length of subarray containing only 1s and
• Second loop to maintain subsegment [l, r] to contain not more than K 1s and find maximum length of subarray containing only 0s. 

Then return maximum of the both lengths.

Follow the given steps to solve the problem:

• Finding the longest subarray containing only 1s with at most K -flips:
  • Declare variable cnt and an integer pointer left which will point at index 0 in the beginning.
  • Now run a loop from 0 to N and at any position: 
    • If arr[i] equals 0, then increase the cnt variable.
    • At any position, if the cnt is greater than K, move the left pointer to the right side and again check if arr[left] equals 0,  
    • Then decrease the cnt variable and run this loop until cnt is greater than K.
  • Store the maximum length of subarray containing only 1's and calculate this length as (current index - left pointer + 1).
• Find the longest subarray containing only 0s with at most K-flips and store its length in the similar way.
• Return the maximum among both of the maximum lengths.

Below is the implementation for the above approach:

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the longest subarray
// following the given conditions
int longestSubSeg(int arr[], int N, int K)
{
    int cnt = 0;
    int left = 0;
    int maximum_len1 = 0;
    int maximum_len0 = 0;

    // Finding length of maximum subarray
    // containing 1's only with atmost k flips
    for (int i = 0; i < N; i++) {
        if (arr[i] == 0)
            cnt++;

        while (cnt > K) {
            if (arr[left] == 0)
                cnt--;
            left++;
        }
        maximum_len1 = max(maximum_len1, i - left + 1);
    }

    // Set these variables to 0 for further use
    cnt = 0;
    left = 0;

    // Finding length of maximum subarray
    // containing 0's only with atmost k flips
    for (int i = 0; i < N; i++) {
        if (arr[i] == 1)
            cnt++;

        while (cnt > K) {
            if (arr[left] == 1)
                cnt--;
            left++;
        }
        maximum_len0 = max(maximum_len0, i - left + 1);
    }

    return max(maximum_len1, maximum_len0);
}

// Driver code
int main()
{
    int arr[] = { 1, 0, 0, 1, 0, 1, 0, 1 };
    int K = 2;
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    cout << longestSubSeg(arr, N, K);
    return 0;
}

// Java program for the above approach

import java.io.*;

class GFG {

    // Function to find the longest subarray
    // following the given conditions
    static int longestSubSeg(int arr[], int N, int K)
    {
        int cnt = 0;
        int left = 0;
        int max_len1 = 0;
        int max_len0 = 0;

        // Finding length of maximum subarray
        // containing 1's only with atmost k flips
        for (int i = 0; i < N; i++) {
            if (arr[i] == 0)
                cnt++;

            while (cnt > K) {
                if (arr[left] == 0)
                    cnt--;
                left++;
            }
            max_len1 = Math.max(max_len1, i - left + 1);
        }

        // Initialize with again 0 for further use
        left = 0;
        cnt = 0;

        // Finding length of maximum subarray
        // containing only 0's with atmost k flips
        for (int i = 0; i < N; i++) {
            if (arr[i] == 1)
                cnt++;

            while (cnt > K) {
                if (arr[left] == 1)
                    cnt--;
                left++;
            }
            max_len0 = Math.max(max_len0, i - left + 1);
        }

        return Math.max(max_len1, max_len0);
    }

    // Driver code
    public static void main(String[] args)
    {
        int a[] = { 1, 0, 0, 1, 0, 1, 0, 1 };
        int K = 2;
        int N = a.length;

        // Function call
        System.out.println(longestSubSeg(a, N, K));
    }
}

# Python program for the above approach

# Function to find the longest subarray
# following the given conditions
def longestSubSeg(arr, N, K):

    cnt = 0
    left = 0
    maximum_len1 = 0
    maximum_len0 = 0

    # Finding length of maximum subarray
    # containing 1's only with atmost k flips
    for i in range(0, N):
        if (arr[i] == 0):
            cnt = cnt+1

        while (cnt > K):
            if (arr[left] == 0):
                cnt = cnt-1
            left = left+1

        maximum_len1 = max(maximum_len1, i - left + 1)

    # Set these variables to 0 for further use
    cnt = 0
    left = 0

    # Finding length of maximum subarray
    # containing 0's only with atmost k flips
    for i in range(0, N):
        if (arr[i] == 1):
            cnt = cnt+1

        while (cnt > K):
            if (arr[left] == 1):
                cnt = cnt-1
            left = left+1

        maximum_len0 = max(maximum_len0, i - left + 1)

    return max(maximum_len1, maximum_len0)

# Driver code
arr = [1, 0, 0, 1, 0, 1, 0, 1]
K = 2
N = len(arr)

# Function call
print(longestSubSeg(arr, N, K))

# This code is contributed by Taranpreet

// C# program for the above approach

using System;

public class GFG {

    // Function to find the longest subarray following the
    // given conditions
    static int longestSubSeg(int[] arr, int N, int K)
    {
        int cnt = 0;
        int left = 0;
        int max_len1 = 0;
        int max_len0 = 0;

        // Finding length of maximum subarray containing 1's
        // only with atmost k flips
        for (int i = 0; i < N; i++) {
            if (arr[i] == 0)
                cnt++;

            while (cnt > K) {
                if (arr[left] == 0)
                    cnt--;
                left++;
            }
            max_len1 = Math.Max(max_len1, i - left + 1);
        }

        // Initialize with again 0 for further use
        left = 0;
        cnt = 0;

        // Finding length of maximum subarray containing
        // only 0's with atmost k flips
        for (int i = 0; i < N; i++) {
            if (arr[i] == 1)
                cnt++;

            while (cnt > K) {
                if (arr[left] == 1)
                    cnt--;
                left++;
            }
            max_len0 = Math.Max(max_len0, i - left + 1);
        }

        return Math.Max(max_len1, max_len0);
    }

    static public void Main()
    {

        // Code
        int[] a = { 1, 0, 0, 1, 0, 1, 0, 1 };
        int K = 2;
        int N = a.Length;

        // Function call
        Console.WriteLine(longestSubSeg(a, N, K));
    }
}

// This code is contributed by lokesh (lokeshmvs21).

    <script>
        // JavaScript program for the above approach


        // Function to find the longest subarray
        // following the given conditions
        const longestSubSeg = (arr, N, K) => {
            let cnt = 0;
            let left = 0;
            let maximum_len1 = 0;
            let maximum_len0 = 0;

            // Finding length of maximum subarray
            // containing 1's only with atmost k flips
            for (let i = 0; i < N; i++) {
                if (arr[i] == 0)
                    cnt++;

                while (cnt > K) {
                    if (arr[left] == 0)
                        cnt--;
                    left++;
                }
                maximum_len1 = Math.max(maximum_len1, i - left + 1);
            }

            // Set these variables to 0 for further use
            cnt = 0;
            left = 0;

            // Finding length of maximum subarray
            // containing 0's only with atmost k flips
            for (let i = 0; i < N; i++) {
                if (arr[i] == 1)
                    cnt++;

                while (cnt > K) {
                    if (arr[left] == 1)
                        cnt--;
                    left++;
                }
                maximum_len0 = Math.max(maximum_len0, i - left + 1);
            }

            return Math.max(maximum_len1, maximum_len0);
        }

        // Driver code

        let arr = [1, 0, 0, 1, 0, 1, 0, 1];
        let K = 2;
        let N = arr.length;

        // Function call
        document.write(longestSubSeg(arr, N, K));

        // This code is contributed by rakeshsahni

    </script>

6

Time Complexity: O(N)
Auxiliary Space: O(1)