# Maximize number of 0s by flipping a subarray

Given a binary array, find the maximum number zeros in an array with one flip of a subarray allowed. A flip operation switches all 0s to 1s and 1s to 0s.

Examples:

```Input :  arr[] = {0, 1, 0, 0, 1, 1, 0}
Output : 6
We can get 6 zeros by flipping the subarray {1, 1}

Input :  arr[] = {0, 0, 0, 1, 0, 1}
Output : 5
```

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Method 1 (Simple : O(n2))
A simple solution is to consider all subarrays and find a subarray with maximum value of (count of 1s) – (count of 0s). Let this value be max_diff. Finally return count of zeros in original array plus max_diff.

## C++

 `// C++ program to maximize number of zeroes in a ` `// binary array by at most one flip operation ` `#include ` `using` `namespace` `std; ` ` `  `// A Kadane's algorithm based solution to find maximum ` `// number of 0s by flipping a subarray. ` `int` `findMaxZeroCount(``bool` `arr[], ``int` `n) ` `{ ` `    ``// Initialize max_diff = maximum of (Count of 0s - ` `    ``// count of 1s) for all subarrays. ` `    ``int` `max_diff = 0; ` ` `  `    ``// Initialize count of 0s in original array ` `    ``int` `orig_zero_count = 0; ` ` `  `    ``// Consider all Subarrays by using two nested two ` `    ``// loops ` `    ``for` `(``int` `i=0; i

## Java

 `// Java code for Maximize number of 0s by flipping  ` `// a subarray ` `class` `GFG { ` `      `  `    ``// A Kadane's algorithm based solution to find maximum ` `    ``// number of 0s by flipping a subarray.  ` `    ``public` `static` `int` `findMaxZeroCount(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``// Initialize max_diff = maximum of (Count of 0s - ` `        ``// count of 1s) for all subarrays. ` `        ``int` `max_diff = ``0``; ` `      `  `        ``// Initialize count of 0s in original array ` `        ``int` `orig_zero_count = ``0``; ` `      `  `        ``// Consider all Subarrays by using two nested two ` `        ``// loops ` `        ``for` `(``int` `i=``0``; i

## Python3

 `# Python3 program to maximize number of  ` `# zeroes in a binary array by at most  ` `# one flip operation ` ` `  `# A Kadane's algorithm based solution ` `# to find maximum number of 0s by ` `# flipping a subarray. ` `def` `findMaxZeroCount(arr, n): ` `     `  `    ``# Initialize max_diff = maximum  ` `    ``# of (Count of 0s - count of 1s) ` `    ``# for all subarrays. ` `    ``max_diff ``=` `0` `     `  `    ``# Initialize count of 0s in ` `    ``# original array ` `    ``orig_zero_count ``=` `0` `     `  `    ``# Consider all Subarrays by using ` `    ``# two nested two loops  ` `    ``for` `i ``in` `range``(n): ` `         `  `        ``# Increment count of zeros  ` `        ``if` `arr[i] ``=``=` `0``: ` `            ``orig_zero_count ``+``=` `1` `         `  `        ``# Initialize counts of 0s and 1s ` `        ``count1, count0 ``=` `0``, ``0` `         `  `        ``# Consider all subarrays starting ` `        ``# from arr[i] and find the  ` `        ``# difference between 1s and 0s.  ` `        ``# Update max_diff if required  ` `        ``for` `j ``in` `range``(i, n): ` `            ``if` `arr[j] ``=``=` `1``: ` `                ``count1 ``+``=` `1` `            ``else``:  ` `                ``count0 ``+``=` `1` `                 `  `            ``max_diff ``=` `max``(max_diff, count1 ``-`  `                                     ``count0) ` `     `  `    ``# Final result would be count of 0s  ` `    ``# in original array plus max_diff.  ` `    ``return` `orig_zero_count ``+` `max_diff ` ` `  `# Driver code ` `arr ``=` `[ ``0``, ``1``, ``0``, ``0``, ``1``, ``1``, ``0` `] ` `n ``=` `len``(arr) ` ` `  `print``(findMaxZeroCount(arr, n)) ` ` `  `# This code is contributed by stutipathak31jan `

Output:

```6
```

Method 2 (Efficient : O(n))
This problem can be reduced to largest subarray sum problem. The idea is to consider every 0 as -1 and every 1 as 1, find the sum of largest subarray sum in this modified array. This sum is our required max_diff ( count of 0s – count of 1s in any subarray). Finally we return the max_diff plus count of zeros in original array.

## C++

 `// C++ program to maximize number of zeroes in a ` `// binary array by at most one flip operation ` `#include ` `using` `namespace` `std; ` ` `  `// A Kadane's algorithm based solution to find maximum ` `// number of 0s by flipping a subarray. ` `int` `findMaxZeroCount(``bool` `arr[], ``int` `n) ` `{ ` `    ``// Initialize count of zeros and maximum difference ` `    ``// between count of 1s and 0s in a subarray ` `    ``int` `orig_zero_count = 0; ` ` `  `    ``// Initiale overall max diff for any subarray ` `    ``int` `max_diff = 0; ` ` `  `    ``// Initialize current diff ` `    ``int` `curr_max = 0; ` ` `  `    ``for` `(``int` `i=0; i

## Java

 `// Java code for Maximize number of 0s by  ` `// flipping a subarray ` `class` `GFG { ` `      `  `    ``// A Kadane's algorithm based solution to find maximum ` `    ``// number of 0s by flipping a subarray. ` `    ``public` `static` `int` `findMaxZeroCount(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``// Initialize count of zeros and maximum difference ` `        ``// between count of 1s and 0s in a subarray ` `        ``int` `orig_zero_count = ``0``; ` `      `  `        ``// Initiale overall max diff for any subarray ` `        ``int` `max_diff = ``0``; ` `      `  `        ``// Initialize current diff ` `        ``int` `curr_max = ``0``; ` `      `  `        ``for` `(``int` `i = ``0``; i < n; i ++) ` `        ``{ ` `            ``// Count of zeros in original array (Not related ` `            ``// to Kadane's algorithm) ` `            ``if` `(arr[i] == ``0``) ` `               ``orig_zero_count ++; ` `      `  `            ``// Value to be considered for finding maximum sum ` `            ``int` `val = (arr[i] == ``1``)? ``1` `: -``1``; ` `      `  `            ``// Update current max and max_diff ` `            ``curr_max = Math.max(val, curr_max + val); ` `            ``max_diff = Math.max(max_diff, curr_max); ` `        ``} ` `        ``max_diff = Math.max(``0``, max_diff); ` `      `  `        ``return` `orig_zero_count + max_diff; ` `    ``} ` `     `  `    ``/* Driver program to test above function */` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `arr[] = {``0``, ``1``, ``0``, ``0``, ``1``, ``1``, ``0``}; ` `         `  `        ``System.out.println(findMaxZeroCount(arr, arr.length)); ` `    ``} ` `  ``} ` `// This code is contributed by Arnav Kr. Mandal. `

## Python3

 `# Python3 program to maximize number  ` `# of zeroes in a binary array by at  ` `# most one flip operation ` ` `  `# A Kadane's algorithm based solution ` `# to find maximum number of 0s by  ` `# flipping a subarray. ` `def` `findMaxZeroCount(arr, n): ` `     `  `    ``# Initialize count of zeros and ` `    ``# maximum difference between count ` `    ``# of 1s and 0s in a subarray  ` `    ``orig_zero_count ``=` `0` `     `  `    ``# Initialize overall max diff ` `    ``# for any subarray  ` `    ``max_diff ``=` `0` `     `  `    ``# Initialize current diff  ` `    ``curr_max ``=` `0` `     `  `    ``for` `i ``in` `range``(n): ` `         `  `        ``# Count of zeros in original  ` `        ``# array (Not related to  ` `        ``# Kadane's algorithm)  ` `        ``if` `arr[i] ``=``=` `0``: ` `            ``orig_zero_count ``+``=` `1` `         `  `        ``# Value to be considered for ` `        ``# finding maximum sum ` `        ``val ``=` `1` `if` `arr[i] ``=``=` `1` `else` `-``1` `         `  `        ``# Update current max and max_diff ` `        ``curr_max ``=` `max``(val, curr_max ``+` `val) ` `        ``max_diff ``=` `max``(max_diff, curr_max) ` `         `  `    ``max_diff ``=` `max``(``0``, max_diff) ` `     `  `    ``return` `orig_zero_count ``+` `max_diff ` ` `  `# Driver code ` `arr ``=` `[ ``0``, ``1``, ``0``, ``0``, ``1``, ``1``, ``0` `] ` `n ``=` `len``(arr) ` ` `  `print``(findMaxZeroCount(arr, n)) ` ` `  `# This code is contributed by stutipathak31jan `

Output:

`6`

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Improved By : stutipathak31jan

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