# Length of the Longest Consecutive 1s in Binary Representation

Given a number n, find length of the longest consecutive 1s in its binary representation.**Examples :**

Input : n = 14 Output : 3 The binary representation of 14 is1110. Input : n = 222 Output : 4 The binary representation of 222 is 11011110.

**Naive Approach:** One simple way would be to simply loop over the bits, and keep track of the number of consecutive set bits, and the maximum that this value has reached. In this approach, we need to convert it to binary (base-2) representation and then find and print the result.

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**Using Bit Magic: **The idea is based on the concept that if we AND a bit sequence with a shifted version of itself, we’re effectively removing the trailing 1 from every sequence of consecutive 1s.

11101111 (x) & 11011110 (x << 1) ---------- 11001110 (x & (x << 1)) ^ ^ | | trailing 1 removed

So the operation x = (x & (x << 1)) reduces length of every sequence of 1s by one in binary representation of x. If we keep doing this operation in a loop, we end up with x = 0. The number of iterations required to reach 0 is actually length of the longest consecutive sequence of 1s.

## C++

`// C++ program to find length of the longest` `// consecutive 1s in binary representation of` `// a number.` `#include<bits/stdc++.h>` `using` `namespace` `std;` `int` `maxConsecutiveOnes(` `int` `x)` `{` ` ` `// Initialize result` ` ` `int` `count = 0;` ` ` `// Count the number of iterations to` ` ` `// reach x = 0.` ` ` `while` `(x!=0)` ` ` `{` ` ` `// This operation reduces length` ` ` `// of every sequence of 1s by one.` ` ` `x = (x & (x << 1));` ` ` `count++;` ` ` `}` ` ` `return` `count;` `}` `// Driver code` `int` `main()` `{` ` ` `cout << maxConsecutiveOnes(14) << endl;` ` ` `cout << maxConsecutiveOnes(222) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to find length of the longest` `// consecutive 1s in binary representation of` `// a number.` `class` `MaxConsecutiveOnes` `{` ` ` `private` `static` `int` `maxConsecutiveOnes(` `int` `x)` ` ` `{` ` ` `// Initialize result` ` ` `int` `count = ` `0` `;` ` ` `// Count the number of iterations to` ` ` `// reach x = 0.` ` ` `while` `(x!=` `0` `)` ` ` `{` ` ` `// This operation reduces length` ` ` `// of every sequence of 1s by one.` ` ` `x = (x & (x << ` `1` `));` ` ` `count++;` ` ` `}` ` ` `return` `count;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String strings[])` ` ` `{` ` ` `System.out.println(maxConsecutiveOnes(` `14` `));` ` ` `System.out.println(maxConsecutiveOnes(` `222` `));` ` ` `}` `}` |

## Python3

`# Python program to find` `# length of the longest` `# consecutive 1s in` `# binary representation of` `# a number.` `def` `maxConsecutiveOnes(x):` ` ` `# Initialize result` ` ` `count ` `=` `0` ` ` ` ` `# Count the number of iterations to` ` ` `# reach x = 0.` ` ` `while` `(x!` `=` `0` `):` ` ` ` ` `# This operation reduces length` ` ` `# of every sequence of 1s by one.` ` ` `x ` `=` `(x & (x << ` `1` `))` ` ` ` ` `count` `=` `count` `+` `1` ` ` ` ` `return` `count` `# Driver code` `print` `(maxConsecutiveOnes(` `14` `))` `print` `(maxConsecutiveOnes(` `222` `))` `# This code is contributed` `# by Anant Agarwal.` |

## C#

`// C# program to find length of the` `// longest consecutive 1s in binary` `// representation of a number.` `using` `System;` `class` `GFG {` ` ` ` ` `// Function to find length of the` ` ` `// longest consecutive 1s in binary` ` ` `// representation of a number` ` ` `private` `static` `int` `maxConsecutiveOnes(` `int` `x)` ` ` `{` ` ` ` ` `// Initialize result` ` ` `int` `count = 0;` ` ` `// Count the number of iterations` ` ` `// to reach x = 0.` ` ` `while` `(x != 0)` ` ` `{` ` ` ` ` `// This operation reduces length` ` ` `// of every sequence of 1s by one.` ` ` `x = (x & (x << 1));` ` ` `count++;` ` ` `}` ` ` `return` `count;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `Console.WriteLine(maxConsecutiveOnes(14));` ` ` `Console.Write(maxConsecutiveOnes(222));` ` ` `}` `}` `// This code is contributed by Nitin Mittal.` |

## PHP

`<?php` `// PHP program to find length` `// of the longest consecutive` `// 1s in binary representation of` `// a number.` `function` `maxConsecutiveOnes(` `$x` `)` `{` ` ` `// Initialize result` ` ` `$count` `= 0;` ` ` `// Count the number of` ` ` `// iterations to reach x = 0.` ` ` `while` `(` `$x` `!= 0)` ` ` `{` ` ` `// This operation reduces` ` ` `// length of every sequence` ` ` `// of 1s by one.` ` ` `$x` `= (` `$x` `& (` `$x` `<< 1));` ` ` `$count` `++;` ` ` `}` ` ` `return` `$count` `;` `}` `// Driver code` `echo` `maxConsecutiveOnes(14), ` `"\n"` `;` `echo` `maxConsecutiveOnes(222), ` `"\n"` `;` `// This code is contributed by Ajit` `?>` |

## Javascript

`<script>` `// Javascript program to find length` `// of the longest consecutive 1s in` `// binary representation of a number.` `function` `maxConsecutiveOnes(x)` `{` ` ` ` ` `// Initialize result` ` ` `let count = 0;` ` ` `// Count the number of iterations to` ` ` `// reach x = 0.` ` ` `while` `(x != 0)` ` ` `{` ` ` ` ` `// This operation reduces length` ` ` `// of every sequence of 1s by one.` ` ` `x = (x & (x << 1));` ` ` `count++;` ` ` `}` ` ` `return` `count;` `}` `// Driver code` `document.write(maxConsecutiveOnes(14) + ` `"<br/>"` `);` `document.write(maxConsecutiveOnes(222));` `// This code is contributed by code_hunt ` `</script>` |

**Output :**

3 4

Time Complexity: O(log x)

Auxiliary Space: O(1)

https://youtu.be/X06Vml

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