Maximum number of consecutive 1s after flipping all 0s in a K length subarray

Given a binary array arr[] of length N, and an integer K, the task is to find the maximum number of consecutive ones after flipping all zero in a subarray of length K.

Examples:

Input: arr[]= {0, 0, 1, 1, 1, 1, 0, 1, 1, 0}, K = 2
Output:
Explanation:
On taking the subarray [6, 7] and flip zero to one we get 7 consecutive ones.
 

Input: arr[]= {0, 0, 1, 1, 0, 0, 0, 0}, K = 3
Output:
Explanation:
On taking the subarray [4, 6] and flip zero to one we get 5 consecutive ones. 
 

Approach: To solve the problem follow the steps given below:



  • Initialize a variable let’s say trav which is going to iterate in the array from each position i  to (0 to i-1) in the left direction and from (i+k  to n-1) in the right direction.
  • Check and keep an account that no zero comes in its way in any direction while iterating in the array.
  • If there is a 0 then break out from the loop in that direction.
  • So ultimately for i to i+k if there is any zero we are already flipping it to 1 so no need to count number of ones in this range as it will be equal to integer K only.

Below is the implementation of the above approach:

C++

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// CPP program for the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the maximum number of
// consecutive 1's after flipping all
// zero in a K length subarray
int findmax(int arr[], int n, int k)
{
    // Initialize variable
    int trav, i;
    int c = 0, maximum = 0;
  
    // Iterate unil n-k+1 as we
    // have to go till i+k
    for (i = 0; i < n - k + 1; i++) {
        trav = i - 1;
        c = 0;
  
        /*Iterate in the array in left direction
        till you get 1 else break*/
        while (trav >= 0 && arr[trav] == 1) {
            trav--;
            c++;
        }
        trav = i + k;
  
        /*Iterate in the array in right direction
        till you get 1 else break*/
        while (trav < n && arr[trav] == 1) {
            trav++;
            c++;
        }
        c += k;
  
        // Compute the maximum length
        if (c > maximum)
            maximum = c;
    }
  
    // Return the length
    return maximum;
}
  
// Driver code
int main()
{
    int k = 3;
    // Array initialization
    int arr[] = { 0, 0, 1, 1, 0, 0, 0, 0 };
  
    // Size of array
    int n = sizeof arr / sizeof arr[0];
    int ans = findmax(arr, n, k);
    cout << ans << '\n';
}

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Python3

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# Python3 program for the above approach
  
# Function to find the maximum number of
# consecutive 1's after flipping all
# zero in a K length subarray
def findmax(arr, n, k):
      
    # Initialize variable
    trav, i = 0, 0
    c = 0
    maximum = 0
  
    # Iterate unil n-k+1 as we
    # have to go till i+k
    while i < n - k + 1:
        trav = i - 1
        c = 0
  
        # Iterate in the array in left direction
        # till you get 1 else break
        while trav >= 0 and arr[trav] == 1:
            trav -= 1
            c += 1
        trav = i + k
  
        # Iterate in the array in right direction
        # till you get 1 else break
        while (trav < n and arr[trav] == 1):
            trav += 1
            c += 1
  
        c += k
  
        # Compute the maximum length
        if (c > maximum):
            maximum = c
        i += 1
  
    # Return the length
    return maximum
  
# Driver code
if __name__ == '__main__':
    k = 3
      
    # Array initialization
    arr = [0, 0, 1, 1, 0, 0, 0, 0]
  
    # Size of array
    n = len(arr)
    ans = findmax(arr, n, k)
    print(ans)
  
# This code is contributed by Mohit Kumar

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Output: 

5

 

 

Time complexity: O(N) 
 

 

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