- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Minimum flips in two binary arrays so that their XOR is equal to another array in C++.

## Problem statement

Given three arrays with 0’s and 1’s of size n, the task is to find minimum flip of bits in the first and second array such that the XOR of i’th index bit of first and second array is equal to i’th index bit of the third array.

Please note that we can only flip at most p bits of array 1 and at most q bits of array 2. Also rearranging array elements is not allowed.

Let us suppose p = 2 and q = 5

arr1[] = {1, 0, 1, 1, 0, 1, 0} arr2[] = {0, 1, 0, 1, 0, 0, 1} arr3[] = {0, 1, 1, 0, 0, 0, 0}

- (arr1[0] ^ arr2[0]) i.e (1 ^ 0) = 1 which is not equal to arr3[0]. Hence flip is required.
(arr1[1] ^ arr2[1]) i.e (0 ^ 1) = 1 which is equal to arr3[1]. Hence flip is not required.

(arr1[2] ^ arr2[2]) i.e (1 ^ 0) = 1 which is equal to arr3[2]. Hence flip is not required.

(arr1[3] ^ arr2[3]) i.e (1 ^ 1) = 0 which is equal to arr3[3]. Hence flip is not required.

(arr1[4] ^ arr2[4]) i.e (0 ^ 0) = 0 which is equal to arr3[4]. Hence flip is not required.

(arr1[5] ^ arr2[5]) i.e (1 ^ 0) = 1 which is not equal to arr3[5]. Hence flip is required.

(arr1[6] ^ arr2[6]) i.e (0 ^ 1) = 1 which is not equal to arr3[6]. Hence flip is required.

## Algorithm

1. If (arr1[i] ^ arr2[i]) == arr3[i] then continue as flip is not required. 2. If (arr1[i] ^ arr2[i]) != arr3[i] then flip is required. a. If arr3[i] == 0 then one of the following condition is true: i. (arr1[i] == 0) and (arr2[i] == 0) OR ii. (arr1[i] == 1) and (arr2[i] == 1) b. If arr3[i] == 1 then one of the following condition is true: i. (arr1[i] == 0) and (arr2[0] == 1) OR ii. (arr1[i] == 1) and (arr2[i] == 0) 3. If flip is required then we can either flip arr1[i] or arr2[i]. Hence we can conclude that number of flips required to make XOR of arr1 and arr2 equal to arr3 should be less than or equal to p + q.

## Example

#include <iostream> #define SIZE(arr) (sizeof(arr) / sizeof(arr[0])) using namespace std; int getRequiredFlips(int *arr1, int *arr2, int *arr3, int n, int p, int q){ int flips = 0; for (int i = 0; i < n; ++i) { if ((arr1[i] ^ arr2[i]) != arr3[i]) { ++flips; } } return flips <= (p + q) ? flips : -1; } int main(){ int arr1[] = {1, 0, 1, 1, 0, 1, 0}; int arr2[] = {0, 1, 0, 1, 0, 0, 1}; int arr3[] = {0, 1, 1, 0, 0, 0, 0}; int size = SIZE(arr1); cout << "Flips required: " << getRequiredFlips(arr1, arr2, arr3, size, 2, 5) << "\n"; return 0; }

## Output

When you compile and execute the above program. It generates the following output −

Flips required: 3

- Related Questions & Answers
- Count Triplets That Can Form Two Arrays of Equal XOR in C++
- Minimum Flips to Make a OR b Equal to c in C++
- Minimum toggles to partition a binary array so that it has first 0s then 1s in C++
- Ways to remove one element from a binary string so that XOR becomes zero in C++
- Find number of pairs in an array such that their XOR is 0 using C++.
- Count minimum bits to flip such that XOR of A and B equal to C in C++
- Finding minimum flips in a binary string using JavaScript
- Minimum Number of Flips to Convert Binary Matrix to Zero Matrix in C++
- Count all Quadruples from four arrays such that their XOR equals to ‘x’ in C++
- Add minimum number to an array so that the sum becomes even in C++?
- Find the minimum value to be added so that array becomes balanced in C++
- Find minimum value to assign all array elements so that array product becomes greater in C++
- Add minimum number to an array so that the sum becomes even in C programming
- Minimum Moves to Equal Array Elements in C++
- Count minimum right flips to set all values in an array in C++