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# Minimum number N such that total set bits of all numbers from 1 to N is at-least X

• Difficulty Level : Medium
• Last Updated : 23 Apr, 2021

Given a number X, the task is to find the minimum number N such that total set bits of all numbers from 1 to n is atleast X.

Examples:

```Input: x = 5
Output: 4
Set bits in 1-> 1
Set bits in 2-> 1
Set bits in 3-> 2
Set bits in 4-> 1
Hence first four numbers add upto 5

Input: x = 20
Output: 11 ```

Approach: Use binary search to get the minimum most number whose sum of bits till N is atleast X. At start, low is 0 and high is initialized according to the constraint. Check if count of set bits is atleast X, every time it is, change high to mid-1, else change it to mid+1. Everytime we do high = mid-1, store the minimal of answer.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach``#include ``using` `namespace` `std;``#define INF 99999``#define size 10` `// Function to count sum of set bits``// of all numbers till N``int` `getSetBitsFromOneToN(``int` `N)``{``    ``int` `two = 2, ans = 0;``    ``int` `n = N;` `    ``while` `(n) {``        ``ans += (N / two) * (two >> 1);` `        ``if` `((N & (two - 1)) > (two >> 1) - 1)``            ``ans += (N & (two - 1)) - (two >> 1) + 1;` `        ``two <<= 1;``        ``n >>= 1;``    ``}``    ``return` `ans;``}` `// Function to find the minimum number``int` `findMinimum(``int` `x)``{``    ``int` `low = 0, high = 100000;` `    ``int` `ans = high;` `    ``// Binary search for the lowest number``    ``while` `(low <= high) {` `        ``// Find mid number``        ``int` `mid = (low + high) >> 1;` `        ``// Check if it is atleast x``        ``if` `(getSetBitsFromOneToN(mid) >= x) {``            ``ans = min(ans, mid);``            ``high = mid - 1;``        ``}``        ``else``            ``low = mid + 1;``    ``}` `    ``return` `ans;``}` `// Driver Code``int` `main()``{``    ``int` `x = 20;``    ``cout << findMinimum(x);` `return` `0;``}`

## Java

 `// Java implementation of the above approach``import` `java.util.*;` `class` `solution``{``static` `int` `INF = ``99999``;``static` `int` `size = ``10``;` `// Function to count sum of set bits``// of all numbers till N``static` `int` `getSetBitsFromOneToN(``int` `N)``{``    ``int` `two = ``2``, ans = ``0``;``    ``int` `n = N;` `    ``while` `(n!=``0``) {``        ``ans += (N / two) * (two >> ``1``);` `        ``if` `((N & (two - ``1``)) > (two >> ``1``) - ``1``)``            ``ans += (N & (two - ``1``)) - (two >> ``1``) + ``1``;` `        ``two <<= ``1``;``        ``n >>= ``1``;``    ``}``    ``return` `ans;``}` `// Function to find the minimum number``static` `int` `findMinimum(``int` `x)``{``    ``int` `low = ``0``, high = ``100000``;` `    ``int` `ans = high;` `    ``// Binary search for the lowest number``    ``while` `(low <= high) {` `        ``// Find mid number``        ``int` `mid = (low + high) >> ``1``;` `        ``// Check if it is atleast x``        ``if` `(getSetBitsFromOneToN(mid) >= x) {``            ``ans = Math.min(ans, mid);``            ``high = mid - ``1``;``        ``}``        ``else``            ``low = mid + ``1``;``    ``}` `    ``return` `ans;``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `x = ``20``;``    ``System.out.println(findMinimum(x));` `}` `}` `//This code is contributed by``// Shashank_Sharma`

## Python3

 `# Python3 implementation of the``# above approach``INF ``=` `99999``size ``=` `10` `# Function to count sum of set bits``# of all numbers till N``def` `getSetBitsFromOneToN(N):` `    ``two, ans ``=` `2``, ``0``    ``n ``=` `N` `    ``while` `(n > ``0``):``        ``ans ``+``=` `(N ``/``/` `two) ``*` `(two >> ``1``)` `        ``if` `((N & (two ``-` `1``)) > (two >> ``1``) ``-` `1``):``            ``ans ``+``=` `(N & (two ``-` `1``)) ``-` `(two >> ``1``) ``+` `1` `        ``two <<``=` `1``        ``n >>``=` `1``    ``return` `ans` `# Function to find the minimum number``def` `findMinimum(x):` `    ``low ``=` `0``    ``high ``=` `100000` `    ``ans ``=` `high` `    ``# Binary search for the lowest number``    ``while` `(low <``=` `high):` `        ``# Find mid number``        ``mid ``=` `(low ``+` `high) >> ``1` `        ``# Check if it is atleast x``        ``if` `(getSetBitsFromOneToN(mid) >``=` `x):` `            ``ans ``=` `min``(ans, mid)``            ``high ``=` `mid ``-` `1``        ``else``:``            ``low ``=` `mid ``+` `1``    ` `    ``return` `ans` `# Driver Code``x ``=` `20``print``(findMinimum(x))` `# This code is contributed by``# Mohit kumar 29`

## C#

 `// C# implementation of the above approach``using` `System ;` `class` `solution``{``static` `int` `INF = 99999;``static` `int` `size = 10;` `// Function to count sum of set bits``// of all numbers till N``static` `int` `getSetBitsFromOneToN(``int` `N)``{``    ``int` `two = 2, ans = 0;``    ``int` `n = N;` `    ``while` `(n!=0) {``        ``ans += (N / two) * (two >> 1);` `        ``if` `((N & (two - 1)) > (two >> 1) - 1)``            ``ans += (N & (two - 1)) - (two >> 1) + 1;` `        ``two <<= 1;``        ``n >>= 1;``    ``}``    ``return` `ans;``}` `// Function to find the minimum number``static` `int` `findMinimum(``int` `x)``{``    ``int` `low = 0, high = 100000;` `    ``int` `ans = high;` `    ``// Binary search for the lowest number``    ``while` `(low <= high) {` `        ``// Find mid number``        ``int` `mid = (low + high) >> 1;` `        ``// Check if it is atleast x``        ``if` `(getSetBitsFromOneToN(mid) >= x) {``            ``ans = Math.Min(ans, mid);``            ``high = mid - 1;``        ``}``        ``else``            ``low = mid + 1;``    ``}` `    ``return` `ans;``}` `    ``// Driver Code``    ``public` `static` `void` `Main()``    ``{``        ``int` `x = 20;``        ``Console.WriteLine(findMinimum(x));``    ` `    ``}``    ``// This code is contributed by Ryuga``}`

## PHP

 `> 1);` `        ``if` `((``\$N` `& (``\$two` `- 1)) > (``\$two` `>> 1) - 1)``            ``\$ans` `+= (``\$N` `& (``\$two` `- 1)) -``                          ``(``\$two` `>> 1) + 1;` `        ``\$two` `<<= 1;``        ``\$n` `>>= 1;``    ``}``    ``return` `\$ans``;``}` `// Function to find the minimum number``function` `findMinimum(``\$x``)``{``    ``\$low` `= 0;``    ``\$high` `= 100000;` `    ``\$ans` `= ``\$high``;` `    ``// Binary search for the lowest number``    ``while` `(``\$low` `<= ``\$high``)``    ``{` `        ``// Find mid number``        ``\$mid` `= (``\$low` `+ ``\$high``) >> 1;` `        ``// Check if it is atleast x``        ``if` `(getSetBitsFromOneToN(``\$mid``) >= ``\$x``)``        ``{``            ``\$ans` `= min(``\$ans``, ``\$mid``);``            ``\$high` `= ``\$mid` `- 1;``        ``}``        ``else``            ``\$low` `= ``\$mid` `+ 1;``    ``}` `    ``return` `\$ans``;``}` `// Driver Code``\$x` `= 20;``echo` `findMinimum(``\$x``);` `// This code is contributed``// by Sach_Code``?>`

## Javascript

 ``
Output:

`11`

Time Complexity: O(log N * log N)

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