# Generate all binary permutations such that there are more or equal 1’s than 0’s before every point in all permutations

Generate all permutations of a given length such that every permutation has more or equals 1’s than 0’s in all prefixes of the permutation.

**Examples: **

Input: len = 4 Output: 1111 1110 1101 1100 1011 1010 Note that a permutation like 0101 can not be in output because there are more 0's from index 0 to 2 in this permutation. Input: len = 3 Output: 111 110 101 Input: len = 2 Output: 11 10

Like permutation generation problems, recursion is the simplest approach to solve this. We start with an empty string, attach 1 to it and recur. While recurring, if we find more 1’s at any point, we append a 0 and make one more recursive call.

Below is the implementation:

## C++

`// C++ program to generate all permutations of 1's and 0's such that` `// every permutation has more 1's than 0's at all indexes.` `#include <iostream>` `#include <cstring>` `using` `namespace` `std;` `// ones & zeroes --> counts of 1's and 0's in current string 'str'` `// len ---> desired length of every permutation` `void` `generate(` `int` `ones, ` `int` `zeroes, string str, ` `int` `len)` `{` ` ` `// If length of current string becomes same as desired length` ` ` `if` `(len == str.length())` ` ` `{` ` ` `cout << str << ` `" "` `;` ` ` `return` `;` ` ` `}` ` ` `// Append a 1 and recur` ` ` `generate(ones+1, zeroes, str+` `"1"` `, len);` ` ` `// If there are more 1's, append a 0 as well, and recur` ` ` `if` `(ones > zeroes)` ` ` `generate(ones, zeroes+1, str+` `"0"` `, len);` `}` `// Driver program to test above function` `int` `main()` `{` ` ` `string str = ` `""` `;` ` ` `generate(0, 0, str, 4);` ` ` `return` `0;` `}` |

## Java

`// Java program to generate all permutations of 1's and 0's such that` `// every permutation has more 1's than 0's at all indexes.` `class` `GFG {` `// ones & zeroes --> counts of 1's and 0's in current string 'str'` `// len ---> desired length of every permutation` ` ` `static` `void` `generate(` `int` `ones, ` `int` `zeroes, String str, ` `int` `len) {` ` ` `// If length of current string becomes same as desired length` ` ` `if` `(len == str.length()) {` ` ` `System.out.print(str + ` `" "` `);` ` ` `return` `;` ` ` `}` ` ` `// Append a 1 and recur` ` ` `generate(ones + ` `1` `, zeroes, str + ` `"1"` `, len);` ` ` `// If there are more 1's, append a 0 as well, and recur` ` ` `if` `(ones > zeroes) {` ` ` `generate(ones, zeroes + ` `1` `, str + ` `"0"` `, len);` ` ` `}` ` ` `}` `// Driver program to test above function` ` ` `public` `static` `void` `main(String[] args) {` ` ` `String str = ` `""` `;` ` ` `generate(` `0` `, ` `0` `, str, ` `4` `);` ` ` `}` `}` `/* This Java code is contributed by PrinciRaj1992*/` |

## Python3

`# Python 3 program to generate all permutations of 1's and 0's such that` `# every permutation has more 1's than 0's at all indexes.` `# ones & zeroes --> counts of 1's and 0's in current string 'str'` `# len ---> desired length of every permutation` `def` `generate(ones, zeroes, ` `str` `, len1):` ` ` `# If length of current string becomes same as desired length` ` ` `if` `(len1 ` `=` `=` `len` `(` `str` `)):` ` ` `print` `(` `str` `,end ` `=` `" "` `)` ` ` `return` ` ` ` ` `# Append a 1 and recur` ` ` `generate(ones` `+` `1` `, zeroes, ` `str` `+` `"1"` `, len1)` ` ` `# If there are more 1's, append a 0 as well, and recur` ` ` `if` `(ones > zeroes):` ` ` `generate(ones, zeroes` `+` `1` `, ` `str` `+` `"0"` `, len1)` `# Driver program to test above function` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `str` `=` `""` ` ` `generate(` `0` `, ` `0` `, ` `str` `, ` `4` `)` `# This code is contributed by` `# Surendra_Gangwar` |

## C#

`// C# program to generate all permutations of 1's and 0's such that` `// every permutation has more 1's than 0's at all indexes.` ` ` `using` `System;` ` ` `public` `class` `GFG {` ` ` `// ones & zeroes --> counts of 1's and 0's in current string 'str'` `// len ---> desired length of every permutation` ` ` `static` `void` `generate(` `int` `ones, ` `int` `zeroes, String str, ` `int` `len) {` ` ` `// If length of current string becomes same as desired length` ` ` `if` `(len == str.Length) {` ` ` `Console.Write(str + ` `" "` `);` ` ` `return` `;` ` ` `}` ` ` ` ` `// Append a 1 and recur` ` ` `generate(ones + 1, zeroes, str + ` `"1"` `, len);` ` ` ` ` `// If there are more 1's, append a 0 as well, and recur` ` ` `if` `(ones > zeroes) {` ` ` `generate(ones, zeroes + 1, str + ` `"0"` `, len);` ` ` `}` ` ` `}` ` ` `// Driver program to test above function` ` ` `public` `static` `void` `Main() {` ` ` `String str = ` `""` `;` ` ` `generate(0, 0, str, 4);` ` ` `}` `}` ` ` `/* This Java code is contributed by 29AjayKumar*/` |

## Javascript

`<script>` ` ` `// JavaScript program to generate all permutations of 1's and 0's such that` ` ` `// every permutation has more 1's than 0's at all indexes.` ` ` `// ones & zeroes --> counts of 1's and 0's in current string 'str'` ` ` `// len ---> desired length of every permutation` ` ` `function` `generate(ones, zeroes, str, len) {` ` ` `// If length of current string becomes same as desired length` ` ` `if` `(len === str.length) {` ` ` `document.write(str + ` `" "` `);` ` ` `return` `;` ` ` `}` ` ` `// Append a 1 and recur` ` ` `generate(ones + 1, zeroes, str + ` `"1"` `, len);` ` ` `// If there are more 1's, append a 0 as well, and recur` ` ` `if` `(ones > zeroes) {` ` ` `generate(ones, zeroes + 1, str + ` `"0"` `, len);` ` ` `}` ` ` `}` ` ` `// Driver program to test above function` ` ` `var` `str = ` `""` `;` ` ` `generate(0, 0, str, 4);` `</script>` |

**Output:**

1111 1110 1101 1100 1011 1010

This article was contributed by **Sachin**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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