# Count different Bitwise OR values of equal length strings S1 and S2 by swapping exactly one pair of characters from the first string

Given two binary strings **S1 **and** S2**, both of length **N**, the task is to count the number of different values of Bitwise OR other than the Bitwise OR of the original strings **S1** and **S2** by swapping exactly one pair of characters from the string **S1**.

**Examples:**

Input:S1 = “1100”, S2 = “0011”Output:4Explanation:Bitwise OR of S1 and S2, if no swapping is performed is “1111”.

Below are swapping of characters performed to get the different values of Bitwise OR:

- If the characters at 0
^{th}and 2^{nd}index are swapped, then string S1 modifies to “0110”. Now, the Bitwise OR of both the string is “0111”.- If the characters at 0
^{th}and 3^{rd}index are swapped, then string S1 modifies to “0101”. Now, the Bitwise OR of both the string is”0111″.- If the characters at 1
^{st}and 2^{nd}index are swapped, then string S1 modifies to “1010”. Now, the Bitwise OR of both the string is “1011”.- If the characters at 1
^{st}and 3^{rd}index are swapped, then string S1 modifies to “1001”. Now, the Bitwise OR of both the string is”1011″.After the above steps, all the Bitwise-OR are different from the Bitwise OR of the original string. Therefore, the total count is 4.

Input:S1 = “01001”, S2 = “11011”Output:2

**Approach:** The given problem can be solved based on the following observations:

- If the same character is swapped in the string
**S1**, then it will not affect the bitwise OR. - If the different characters are swapped in the string
**S1**let say**S1[i] = ‘0’**and**S2[j] = ‘1’**then the bitwise OR of the value is changed as per the following rules:- If
**S2[i] = ‘0’**and**S2[j] = ‘0’**. - If
**S2[i] = ‘1’**and**S2[j] = ‘0’**. - If
**S2[i] = ‘0’**and**S2[j] = ‘1’**.

- If

From the above observations, Follow the below steps to solve the problem:

- Initialize four variable, say
**t00**,**t10**,**t11**,**t01**that stores the number of indexes**i**such that**S1[i] = ‘0’**and**S2[i] = ‘0’**,**S1[i] = ‘1’**and**S2[i] = ‘0’**,**S1[i] = ‘1’**and**S2[i] = ‘1’**, and**S1[i] = ‘0’**and**S2[i] = ‘1’**respectively. - Traverse the given strings
**S1**and**S2**, and increment the value of**t00**,**t10**,**t11**,**t01**as per the following:- If
**S1[i] = ‘0’**and**S2[i] =’0′**, then increment the value of**t00**by**1**. - If
**S1[i] = ‘1’**and**S2[i] = ‘0’**, then increment the value of**t10**by**1**. - If
**S1[i] = ‘1’**and**S2[i] = ‘1’**, then increment the value of**t11**by**1**. - If
**S1[i] = ‘0’**and**S2[i] = ‘1’**, then increment the value of**t01**by**1**.

- If
- After completing the above steps, print the value of
**t00 * t10 + t01 * t10 + t00 * t11**as the resultant number of swaps required having different Bitwise OR from the original Bitwise OR.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the number of ways` `// to obtain different Bitwise OR` `void` `differentBitwiseOR(string s1,` ` ` `string s2)` `{` ` ` `int` `n = s1.size();` ` ` `// Stores the count of pairs t00,` ` ` `// t10, t01, t11` ` ` `int` `t00 = 0, t10 = 0, t01 = 0, t11 = 0;` ` ` `// Traverse the characters of` ` ` `// the string S1 and S2` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` `// Count the pair (0, 0)` ` ` `if` `(s1[i] == ` `'0'` ` ` `&& s2[i] == ` `'0'` `) {` ` ` `t00++;` ` ` `}` ` ` `// Count the pair (1, 0)` ` ` `if` `(s1[i] == ` `'1'` ` ` `&& s2[i] == ` `'0'` `) {` ` ` `t10++;` ` ` `}` ` ` `// Count the pair (1, 1)` ` ` `if` `(s1[i] == ` `'1'` ` ` `&& s2[i] == ` `'1'` `) {` ` ` `t11++;` ` ` `}` ` ` `// Count the pair (0, 1)` ` ` `if` `(s1[i] == ` `'0'` ` ` `&& s2[i] == ` `'1'` `) {` ` ` `t01++;` ` ` `}` ` ` `}` ` ` `// Number of ways to calculate the` ` ` `// different bitwise OR` ` ` `int` `ans = t00 * t10 + t01 * t10` ` ` `+ t00 * t11;` ` ` `// Print the result` ` ` `cout << ans;` `}` `// Driver Code` `int` `main()` `{` ` ` `string S1 = ` `"01001"` `;` ` ` `string S2 = ` `"11011"` `;` ` ` `differentBitwiseOR(S1, S2);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` `// Function to find the number of ways` `// to obtain different Bitwise OR` `static` `void` `differentBitwiseOR(String s1, String s2)` `{` ` ` `int` `n = s1.length();` ` ` `// Stores the count of pairs t00,` ` ` `// t10, t01, t11` ` ` `int` `t00 = ` `0` `, t10 = ` `0` `, t01 = ` `0` `, t11 = ` `0` `;` ` ` `// Traverse the characters of` ` ` `// the string S1 and S2` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++)` ` ` `{` ` ` ` ` `// Count the pair (0, 0)` ` ` `if` `(s1.charAt(i) == ` `'0'` `&& ` ` ` `s2.charAt(i) == ` `'0'` `)` ` ` `{` ` ` `t00++;` ` ` `}` ` ` `// Count the pair (1, 0)` ` ` `if` `(s1.charAt(i) == ` `'1'` `&&` ` ` `s2.charAt(i) == ` `'0'` `) ` ` ` `{` ` ` `t10++;` ` ` `}` ` ` `// Count the pair (1, 1)` ` ` `if` `(s1.charAt(i) == ` `'1'` `&& ` ` ` `s2.charAt(i) == ` `'1'` `) ` ` ` `{` ` ` `t11++;` ` ` `}` ` ` `// Count the pair (0, 1)` ` ` `if` `(s1.charAt(i) == ` `'0'` `&&` ` ` `s2.charAt(i) == ` `'1'` `)` ` ` `{` ` ` `t01++;` ` ` `}` ` ` `}` ` ` `// Number of ways to calculate the` ` ` `// different bitwise OR` ` ` `int` `ans = t00 * t10 + t01 * t10 + t00 * t11;` ` ` `// Print the result` ` ` `System.out.print(ans);` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `String S1 = ` `"01001"` `;` ` ` `String S2 = ` `"11011"` `;` ` ` `differentBitwiseOR(S1, S2);` `}` `}` `// This code is contributed by subhammahato348` |

## Python3

`# Python program for the above approach` `# Function to find the number of ways` `# to obtain different Bitwise OR` `def` `differentBitwiseOR(s1, s2):` ` ` `n ` `=` `len` `(s1)` ` ` `# Stores the count of pairs t00,` ` ` `# t10, t01, t11` ` ` `t00 ` `=` `0` ` ` `t10 ` `=` `0` ` ` `t01 ` `=` `0` ` ` `t11 ` `=` `0` ` ` `# Traverse the characters of` ` ` `# the string S1 and S2` ` ` `for` `i ` `in` `range` `(n):` ` ` `# Count the pair (0, 0)` ` ` `if` `(s1[i] ` `=` `=` `'0'` `and` `s2[i] ` `=` `=` `'0'` `):` ` ` `t00 ` `+` `=` `1` ` ` `# Count the pair (1, 0)` ` ` `if` `(s1[i] ` `=` `=` `'1'` `and` `s2[i] ` `=` `=` `'0'` `):` ` ` `t10 ` `+` `=` `1` ` ` `# Count the pair (1, 1)` ` ` `if` `(s1[i] ` `=` `=` `'1'` `and` `s2[i] ` `=` `=` `'1'` `):` ` ` `t11 ` `+` `=` `1` ` ` `# Count the pair (0, 1)` ` ` `if` `(s1[i] ` `=` `=` `'0'` `and` `s2[i] ` `=` `=` `'1'` `):` ` ` `t01 ` `+` `=` `1` ` ` ` ` `# Number of ways to calculate the` ` ` `# different bitwise OR` ` ` `ans ` `=` `t00 ` `*` `t10 ` `+` `t01 ` `*` `t10 ` `+` `t00 ` `*` `t11` ` ` `# Print the result` ` ` `print` `(ans)` `# Driver Code` `S1 ` `=` `"01001"` `S2 ` `=` `"11011"` `differentBitwiseOR(S1, S2)` `# This code is contributed by _saurabh_jaiswal` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` `// Function to find the number of ways` `// to obtain different Bitwise OR` `static` `void` `differentBitwiseOR(String s1,` ` ` `String s2)` `{` ` ` `int` `n = s1.Length;` ` ` `// Stores the count of pairs t00,` ` ` `// t10, t01, t11` ` ` `int` `t00 = 0, t10 = 0, t01 = 0, t11 = 0;` ` ` `// Traverse the characters of` ` ` `// the string S1 and S2` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `{` ` ` ` ` `// Count the pair (0, 0)` ` ` `if` `(s1[i] == ` `'0'` `&& s2[i] == ` `'0'` `) ` ` ` `{` ` ` `t00++;` ` ` `}` ` ` `// Count the pair (1, 0)` ` ` `if` `(s1[i] == ` `'1'` `&& s2[i] == ` `'0'` `) ` ` ` `{` ` ` `t10++;` ` ` `}` ` ` `// Count the pair (1, 1)` ` ` `if` `(s1[i] == ` `'1'` `&& s2[i] == ` `'1'` `) ` ` ` `{` ` ` `t11++;` ` ` `}` ` ` `// Count the pair (0, 1)` ` ` `if` `(s1[i] == ` `'0'` `&& s2[i] == ` `'1'` `)` ` ` `{` ` ` `t01++;` ` ` `}` ` ` `}` ` ` `// Number of ways to calculate the` ` ` `// different bitwise OR` ` ` `int` `ans = t00 * t10 + t01 * t10 + t00 * t11;` ` ` `// Print the result` ` ` `Console.Write(ans);` `}` `// Driver Code` `public` `static` `void` `Main()` `{` ` ` `String S1 = ` `"01001"` `;` ` ` `String S2 = ` `"11011"` `;` ` ` ` ` `differentBitwiseOR(S1, S2);` `}` `}` `// This code is contributed by subhammahato348` |

## Javascript

`<script>` ` ` ` ` `// JavaScript program for the above approach` ` ` `// Function to find the number of ways` ` ` `// to obtain different Bitwise OR` ` ` `function` `differentBitwiseOR(s1, s2) {` ` ` `let n = s1.length;` ` ` `// Stores the count of pairs t00,` ` ` `// t10, t01, t11` ` ` `let t00 = 0, t10 = 0, t01 = 0, t11 = 0;` ` ` `// Traverse the characters of` ` ` `// the string S1 and S2` ` ` `for` `(let i = 0; i < n; i++) {` ` ` `// Count the pair (0, 0)` ` ` `if` `(s1[i] == ` `'0'` ` ` `&& s2[i] == ` `'0'` `) {` ` ` `t00++;` ` ` `}` ` ` `// Count the pair (1, 0)` ` ` `if` `(s1[i] == ` `'1'` ` ` `&& s2[i] == ` `'0'` `) {` ` ` `t10++;` ` ` `}` ` ` `// Count the pair (1, 1)` ` ` `if` `(s1[i] == ` `'1'` ` ` `&& s2[i] == ` `'1'` `) {` ` ` `t11++;` ` ` `}` ` ` `// Count the pair (0, 1)` ` ` `if` `(s1[i] == ` `'0'` ` ` `&& s2[i] == ` `'1'` `) {` ` ` `t01++;` ` ` `}` ` ` `}` ` ` `// Number of ways to calculate the` ` ` `// different bitwise OR` ` ` `let ans = t00 * t10 + t01 * t10` ` ` `+ t00 * t11;` ` ` `// Print the result` ` ` `document.write(ans);` ` ` `}` ` ` `// Driver Code` ` ` `let S1 = ` `"01001"` `;` ` ` `let S2 = ` `"11011"` `;` ` ` `differentBitwiseOR(S1, S2);` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output:**

2

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