# Find any permutation of Binary String of given size not present in Array

Given an array **arr[]** of **N** distinct binary strings each having **N **characters, the task is to find any binary string having **N** characters such that it doesn’t occur in the given array **arr[]**.

**Example:**

Input:arr[] = {“10”, “01”}Output:00Explanation:String “00” does not appear in array arr[]. Another valid string can be “11” which does not occur in the array arr[] as well.

Input:arr[] {“111”, “011”, “001”}Output:101Explanation:String “101” does not appear in array arr[]. Another valid strings are “000”, “010”, “100”, and “110”.

**Naive Approach:** The given problem can be solved by generating all the binary strings having **N** bits and returning the 1^{st} string such that it does not occur in the given array** arr[]**.

**Time Complexity:** O(2^{N }* N^{2})**Auxiliary Space:** O(N)

**Efficient Approach:** The given problem can be optimized by using a method similar to Cantor’s Diagonal Argument. It can be observed that the resulting string must have at least one bit that is different from all the strings in **arr[]**. Therefore, the resulting binary string can be constructed by taking the complement of the 1^{st} element of the 1^{st} string as the 1^{st} element, the complement of the 2^{nd }element of the 2^{nd} string as the 2^{nd }element, and so on. Below are the steps to follow:

- Create a string
**ans**, which stores the resulting string. Initially, it is empty. - Iterate through the given strings in a diagonal order, i.e, 1
^{st}element of 1^{st }string, 2^{nd }element of 2^{nd}string, and so on, and append the compliment of the value at the current index into the string**ans**. - The string stored in
**ans**after iterating through the complete array**arr[]**is one of the valid strings required.

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 a binary string of` `// N bits that does not occur in the` `// given array arr[]` `string findString(vector<string>& arr, ` `int` `N)` `{` ` ` `// Stores the resultant string` ` ` `string ans = ` `""` `;` ` ` `// Loop to iterate over all the given` ` ` `// strings in a diagonal order` ` ` `for` `(` `int` `i = 0; i < N; i++) {` ` ` `// Append the complement of element` ` ` `// at current index into ans` ` ` `ans += arr[i][i] == ` `'0'` `? ` `'1'` `: ` `'0'` `;` ` ` `}` ` ` `// Return Answer` ` ` `return` `ans;` `}` `// Driver code` `int` `main()` `{` ` ` `vector<string> arr{ ` `"111"` `, ` `"011"` `, ` `"001"` `};` ` ` `int` `N = arr.size();` ` ` `cout << findString(arr, N);` ` ` `return` `0;` `}` |

## Java

`// Java Program for the above approach` `import` `java.io.*;` `class` `GFG {` ` ` ` ` `// Function to find a binary string of` ` ` `// N bits that does not occur in the` ` ` `// given array arr[]` ` ` `static` `String findString(String arr[], ` `int` `N)` ` ` `{` ` ` `// Stores the resultant string` ` ` `String ans = ` `""` `;` ` ` `// Loop to iterate over all the given` ` ` `// strings in a diagonal order` ` ` `for` `(` `int` `i = ` `0` `; i < N; i++) {` ` ` `// Append the complement of element` ` ` `// at current index into ans` ` ` `ans += arr[i].charAt(i) == ` `'0'` `? ` `'1'` `: ` `'0'` `;` ` ` `}` ` ` `// Return Answer` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args) {` ` ` `String arr[] = { ` `"111"` `, ` `"011"` `, ` `"001"` `};` ` ` `int` `N = arr.length;` ` ` `System.out.println(findString(arr, N));` ` ` `}` `}` `// This code is contributed by Dharanendra L V.` |

## Python3

`# Python 3 Program for the above approach` `# Function to find a binary string of` `# N bits that does not occur in the` `# given array arr[]` `def` `findString(arr, N):` ` ` ` ` `# Stores the resultant string` ` ` `ans ` `=` `""` ` ` `# Loop to iterate over all the given` ` ` `# strings in a diagonal order` ` ` `for` `i ` `in` `range` `(N):` ` ` ` ` `# Append the complement of element` ` ` `# at current index into ans` ` ` `ans ` `+` `=` `'1'` `if` `arr[i][i] ` `=` `=` `'0'` `else` `'0'` ` ` `# Return Answer` ` ` `return` `ans` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `arr ` `=` `[` `"111"` `, ` `"011"` `, ` `"001"` `]` ` ` `N ` `=` `len` `(arr)` ` ` `print` `(findString(arr, N))` ` ` `# This code is contributed by bgangwar59.` |

## C#

`// C# Program for the above approach` `using` `System;` `class` `GFG {` ` ` `// Function to find a binary string of` ` ` `// N bits that does not occur in the` ` ` `// given array arr[]` ` ` `static` `string` `findString(` `string` `[] arr, ` `int` `N)` ` ` `{` ` ` ` ` `// Stores the resultant string` ` ` `string` `ans = ` `""` `;` ` ` `// Loop to iterate over all the given` ` ` `// strings in a diagonal order` ` ` `for` `(` `int` `i = 0; i < N; i++) {` ` ` `// Append the complement of element` ` ` `// at current index into ans` ` ` `ans += arr[i][i] == ` `'0'` `? ` `'1'` `: ` `'0'` `;` ` ` `}` ` ` `// Return Answer` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `string` `[] arr = { ` `"111"` `, ` `"011"` `, ` `"001"` `};` ` ` `int` `N = arr.Length;` ` ` `Console.WriteLine(findString(arr, N));` ` ` `}` `}` `// This code is contributed by ukasp.` |

## Javascript

`<script>` ` ` `// JavaScript Program to implement` ` ` `// the above approach` ` ` `// Function to find a binary string of` ` ` `// N bits that does not occur in the` ` ` `// given array arr[]` ` ` `function` `findString(arr, N)` ` ` `{` ` ` ` ` `// Stores the resultant string` ` ` `let ans = ` `""` `;` ` ` `// Loop to iterate over all the given` ` ` `// strings in a diagonal order` ` ` `for` `(let i = 0; i < N; i++) {` ` ` `// Append the complement of element` ` ` `// at current index into ans` ` ` `ans += arr[i][i] == ` `'0'` `? ` `'1'` `: ` `'0'` `;` ` ` `}` ` ` `// Return Answer` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code` ` ` `let arr = [` `"111"` `, ` `"011"` `, ` `"001"` `];` ` ` `let N = arr.length;` ` ` `document.write(findString(arr, N));` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output:**

000

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