# Count numbers up to N having Kth bit set

Given two integers **N** and **K, **the task is to find the count of numbers up to **N** having **K-th** bit set.

**Examples:**

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Input:N = 14, K = 2Output:7Explanation:The numbers less than equal to 14, having 2^{nd}bit set are 4, 5, 6, 7, 12, 13, and 14.

Input:N = 6, K = 1Output:3Explanation:The numbers less than equal to 6 having 1^{st}bit set are 1, 3, 5.

**Naive Approach: **The simplest approach is to traverse from **1 **to **N**, and check for each number whether its K-th bit is set or not.

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

**Efficient Approach: **The above approach can be optimized** **by dividing the task into two parts:

- First, right shift
**N**,**K+1**times followed by left shifting the result**K**times, which gives the count of numbers satisfying the given condition - Now, check if the
**K**bit is set in^{th}**N**or not. - If the
**K**bit is set in^{th}**N,**then add the count of numbers from the nearest power of 2 less than N to the answer.

Below is the implementation of the above approach:

## C++

`// C++ program for above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to return the count` `// of number of 1's at ith bit` `// in a range [1, n - 1]` `long` `long` `getcount(` `long` `long` `n, ` `int` `k)` `{` ` ` `// Store count till nearest` ` ` `// power of 2 less than N` ` ` `long` `long` `res = (n >> (k + 1)) << k;` ` ` `// If K-th bit is set in N` ` ` `if` `((n >> k) & 1)` ` ` `// Add to result the nearest` ` ` `// power of 2 less than N` ` ` `res += n & ((1ll << k) - 1);` ` ` `// Return result` ` ` `return` `res;` `}` `// Driver Code` `int` `main()` `{` ` ` `long` `long` `int` `N = 14;` ` ` `int` `K = 2;` ` ` `// Function Call` ` ` `cout << getcount(N + 1, K) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program for above approach` `class` `GFG` `{` ` ` `// Function to return the count` ` ` `// of number of 1's at ith bit` ` ` `// in a range [1, n - 1]` ` ` `static` `long` `getcount(` `long` `n, ` `int` `k)` ` ` `{` ` ` `// Store count till nearest` ` ` `// power of 2 less than N` ` ` `long` `res = (n >> (k + ` `1` `)) << k;` ` ` `// If K-th bit is set in N` ` ` `if` `(((n >> k) & ` `1` `) != ` `0` `)` ` ` `// Add to result the nearest` ` ` `// power of 2 less than N` ` ` `res += n & ((` `1` `<< k) - ` `1` `);` ` ` `// Return result` ` ` `return` `res;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `long` `N = ` `14` `;` ` ` `int` `K = ` `2` `;` ` ` `// Function Call` ` ` `System.out.println(getcount(N + ` `1` `, K));` ` ` `}` `}` `// This code is contributed by divyesh072019` |

## Python3

`# Python3 program for above approach` `# Function to return the count` `# of number of 1's at ith bit` `# in a range [1, n - 1]` `def` `getcount(n, k):` ` ` ` ` `# Store count till nearest` ` ` `# power of 2 less than N` ` ` `res ` `=` `(n >> (k ` `+` `1` `)) << k` ` ` `# If K-th bit is set in N` ` ` `if` `((n >> k) & ` `1` `):` ` ` ` ` `# Add to result the nearest` ` ` `# power of 2 less than N` ` ` `res ` `+` `=` `n & ((` `1` `<< k) ` `-` `1` `)` ` ` `# Return result` ` ` `return` `res` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `N ` `=` `14` ` ` `K ` `=` `2` ` ` `# Function Call` ` ` `print` `(getcount(N ` `+` `1` `, K))` `# This code is contributed by mohit kumar 29` |

## C#

`// C# program for above approach` `using` `System;` `class` `GFG{` `// Function to return the count` `// of number of 1's at ith bit` `// in a range [1, n - 1]` `static` `long` `getcount(` `long` `n, ` `int` `k)` `{` ` ` ` ` `// Store count till nearest` ` ` `// power of 2 less than N` ` ` `long` `res = (n >> (k + 1)) << k;` ` ` ` ` `// If K-th bit is set in N` ` ` `if` `(((n >> k) & 1) != 0)` ` ` ` ` `// Add to result the nearest` ` ` `// power of 2 less than N` ` ` `res += n & ((1 << k) - 1);` ` ` ` ` `// Return result` ` ` `return` `res;` `}` `// Driver Code ` `static` `void` `Main()` `{` ` ` `long` `N = 14;` ` ` `int` `K = 2;` ` ` ` ` `// Function Call` ` ` `Console.WriteLine(getcount(N + 1, K));` `}` `}` `// This code is contributed by divyeshrabadiya07` |

## Javascript

`<script>` ` ` `// Javascript program for above approach` ` ` ` ` `// Function to return the count` ` ` `// of number of 1's at ith bit` ` ` `// in a range [1, n - 1]` ` ` `function` `getcount(n, k)` ` ` `{` ` ` `// Store count till nearest` ` ` `// power of 2 less than N` ` ` `let res = (n >> (k + 1)) << k;` ` ` `// If K-th bit is set in N` ` ` `if` `(((n >> k) & 1) != 0)` ` ` `// Add to result the nearest` ` ` `// power of 2 less than N` ` ` `res += n & ((1 << k) - 1);` ` ` `// Return result` ` ` `return` `res;` ` ` `}` ` ` ` ` `let N = 14;` ` ` `let K = 2;` ` ` ` ` `// Function Call` ` ` `document.write(getcount(N + 1, K));` ` ` `</script>` |

**Output:**

7

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