# Largest number with binary representation is m 1’s and m-1 0’s

Given n, find the greatest number which is strictly not more then n and whose binary representation consists of m consecutive ones, then m-1 consecutive zeros and nothing else**Examples:**

Input : n = 7 Output : 6 Explanation: 6's binary representation is 110, and 7's is 111, so 6 consists of 2 consecutive 1's and then 1 consecutive 0. Input : 130 Output : 120 Explanation: 28 and 120 are the only numbers <=120, 28 is 11100 consists of 3 consecutive 1's and then 2 consecutive 0's. 120 is 1111000 consists of 4 consecutive 1's and then 3 consecutive 0's. So 120 is the greatest of number<=120 which meets the given condition.

A **naive approach** will be to traverse from 1 to N and check for every binary representation which consists of m consecutive 1’s and m-1 consecutive 0’s and store the largest of them which meets the given condition.

An **efficient approach** is to observe a pattern of numbers,

[**1(1), 6(110), 28(11100), 120(1111000), 496(111110000), ….] **

To get the formula for the numbers which satisfies the conditions we take 120 as an example-

120 is represented as 1111000 which has m = 4 1’s and m = 3 0’s. Converting 1111000 to decimal we get:

2^3+2^4+2^5+2^6 which can be represented as (2^m-1 + 2^m+ 2^m+1 + … 2^m+2, 2^2*m)

2^3*(1+2+2^2+2^3) which can be represented as (2^(m-1)*(1+2+2^2+2^3+..2^(m-1))

2^3*(2^4-1) which can be represented as **[2^(m-1) * (2^m -1)].**

So all the numbers that meet the given condition can be represented as

[2^(m-1) * (2^m -1)]

We can iterate till the number does not exceeds N and print the largest of all possible elements. A closer observation will shows that at **m = 33 it will exceed the 10^18 mark **, so we are calculating the number in unit’s time as **log(32)** is near to constant which is required in calculating the **pow **.

So, the overall complexity will be O(1).

## C++

`// CPP program to find largest number` `// smaller than equal to n with m set` `// bits then m-1 0 bits.` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Returns largest number with m set` `// bits then m-1 0 bits.` `long` `long` `answer(` `long` `long` `n)` `{` ` ` `// Start with 2 bits.` ` ` `long` `m = 2;` ` ` `// initial answer is 1` ` ` `// which meets the given condition` ` ` `long` `long` `ans = 1;` ` ` `long` `long` `r = 1;` ` ` `// check for all numbers` ` ` `while` `(r < n) {` ` ` `// compute the number` ` ` `r = (` `int` `)(` `pow` `(2, m) - 1) * (` `pow` `(2, m - 1));` ` ` `// if less then N` ` ` `if` `(r < n)` ` ` `ans = r;` ` ` `// increment m to get the next number` ` ` `m++;` ` ` `}` ` ` `return` `ans;` `}` `// driver code to check the above condition` `int` `main()` `{` ` ` `long` `long` `n = 7;` ` ` `cout << answer(n);` ` ` `return` `0;` `}` |

## Java

`// java program to find largest number` `// smaller than equal to n with m set` `// bits then m-1 0 bits.` `public` `class` `GFG {` ` ` ` ` `// Returns largest number with` ` ` `// m set bits then m-1 0 bits.` ` ` `static` `long` `answer(` `long` `n)` ` ` `{` ` ` ` ` `// Start with 2 bits.` ` ` `long` `m = ` `2` `;` ` ` ` ` `// initial answer is 1 which` ` ` `// meets the given condition` ` ` `long` `ans = ` `1` `;` ` ` `long` `r = ` `1` `;` ` ` ` ` `// check for all numbers` ` ` `while` `(r < n) {` ` ` ` ` `// compute the number` ` ` `r = ((` `long` `)Math.pow(` `2` `, m) - ` `1` `) *` ` ` `((` `long` `)Math.pow(` `2` `, m - ` `1` `));` ` ` ` ` `// if less then N` ` ` `if` `(r < n)` ` ` `ans = r;` ` ` ` ` `// increment m to get` ` ` `// the next number` ` ` `m++;` ` ` `}` ` ` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code ` ` ` `public` `static` `void` `main(String args[]) {` ` ` ` ` `long` `n = ` `7` `;` ` ` `System.out.println(answer(n));` ` ` `}` `}` `// This code is contributed by Sam007` |

## Python3

`# Python3 program to find` `# largest number smaller` `# than equal to n with m` `# set bits then m-1 0 bits.` `import` `math` `# Returns largest number` `# with m set bits then` `# m-1 0 bits.` `def` `answer(n):` ` ` ` ` `# Start with 2 bits.` ` ` `m ` `=` `2` `;` ` ` ` ` `# initial answer is` ` ` `# 1 which meets the` ` ` `# given condition` ` ` `ans ` `=` `1` `;` ` ` `r ` `=` `1` `;` ` ` ` ` `# check for all numbers` ` ` `while` `r < n:` ` ` ` ` `# compute the number` ` ` `r ` `=` `(` `int` `)((` `pow` `(` `2` `, m) ` `-` `1` `) ` `*` ` ` `(` `pow` `(` `2` `, m ` `-` `1` `)));` ` ` ` ` `# if less then N` ` ` `if` `r < n:` ` ` `ans ` `=` `r;` ` ` ` ` `# increment m to get` ` ` `# the next number` ` ` `m ` `=` `m ` `+` `1` `;` ` ` `return` `ans;` `# Driver Code` `print` `(answer(` `7` `));` `# This code is contributed by mits.` |

## C#

`// C# program to find largest number` `// smaller than equal to n with m set` `// bits then m-1 0 bits.` `using` `System;` `class` `GFG {` `// Returns largest number with` `// m set bits then m-1 0 bits.` `static` `long` `answer(` `long` `n)` `{` ` ` ` ` `// Start with 2 bits.` ` ` `long` `m = 2;` ` ` `// initial answer is 1 which` ` ` `// meets the given condition` ` ` `long` `ans = 1;` ` ` `long` `r = 1;` ` ` `// check for all numbers` ` ` `while` `(r < n) {` ` ` `// compute the number` ` ` `r = ((` `long` `)Math.Pow(2, m) - 1) *` ` ` `((` `long` `)Math.Pow(2, m - 1));` ` ` `// if less then N` ` ` `if` `(r < n)` ` ` `ans = r;` ` ` `// increment m to get` ` ` `// the next number` ` ` `m++;` ` ` `}` ` ` `return` `ans;` `}` ` ` `// Driver Code` ` ` `static` `public` `void` `Main ()` ` ` `{` ` ` `long` `n = 7;` ` ` `Console.WriteLine(answer(n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find largest number` `// smaller than equal to n with m set` `// bits then m-1 0 bits.` `// Returns largest number with m set` `// bits then m-1 0 bits.` `function` `answer( ` `$n` `)` `{` ` ` ` ` `// Start with 2 bits.` ` ` `$m` `= 2;` ` ` `// initial answer is 1` ` ` `// which meets the` ` ` `// given condition` ` ` `$ans` `= 1;` ` ` `$r` `= 1;` ` ` `// check for all numbers` ` ` `while` `(` `$r` `< ` `$n` `)` ` ` `{` ` ` `// compute the number` ` ` `$r` `= (pow(2, ` `$m` `) - 1) *` ` ` `(pow(2, ` `$m` `- 1));` ` ` `// if less then N` ` ` `if` `(` `$r` `< ` `$n` `)` ` ` `$ans` `= ` `$r` `;` ` ` `// increment m to get` ` ` `// the next number` ` ` `$m` `++;` ` ` `}` ` ` `return` `$ans` `;` `}` ` ` `// Driver Code` ` ` `$n` `= 7;` ` ` `echo` `answer(` `$n` `);` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// Javascript program to find largest number` `// smaller than equal to n with m set` `// bits then m-1 0 bits.` ` ` `// Returns largest number with` ` ` `// m set bits then m-1 0 bits.` ` ` `function` `answer(n)` ` ` `{` ` ` ` ` `// Start with 2 bits.` ` ` `let m = 2;` ` ` ` ` `// initial answer is 1 which` ` ` `// meets the given condition` ` ` `let ans = 1;` ` ` `let r = 1;` ` ` ` ` `// check for all numbers` ` ` `while` `(r < n) {` ` ` ` ` `// compute the number` ` ` `r = (Math.pow(2, m) - 1) *` ` ` `(Math.pow(2, m - 1));` ` ` ` ` `// if less then N` ` ` `if` `(r < n)` ` ` `ans = r;` ` ` ` ` `// increment m to get` ` ` `// the next number` ` ` `m++;` ` ` `}` ` ` ` ` `return` `ans;` ` ` `}` `// Driver code` ` ` `let n = 7;` ` ` `document.write(answer(n));` ` ` `</script>` |

**Output:**

6