Count total unset bits in all the numbers from 1 to N

Given a positive integer N, the task is to count the total number of unset bits in the binary representation of all the numbers from 1 to N. Note that leading zeroes will not be counted as unset bits.

Examples:

Input: N = 5
Output: 4



Integer Binary Representation Count of unset bits
1 1 0
2 10 1
3 11 0
4 100 2
5 101 1

0 + 1 + 0 + 2 + 1 = 4

Input: N = 14
Output: 17

Approach:

  1. Iterate the loop from 1 to N.
  2. While number is greater than 0 divide it by 2 and check the remainder.
  3. If remainder is equal to 0 then increase the value of count by 1.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the count of unset
// bits in the binary representation of
// all the numbers from 1 to n
int countUnsetBits(int n)
{
  
    // To store the count of unset bits
    int cnt = 0;
  
    // For every integer from the range [1, n]
    for (int i = 1; i <= n; i++) {
  
        // A copy of the current integer
        int temp = i;
  
        // Count of unset bits in
        // the current integer
        while (temp) {
  
            // If current bit is unset
            if (temp % 2 == 0)
                cnt++;
  
            temp = temp / 2;
        }
    }
    return cnt;
}
  
// Driver code
int main()
{
    int n = 5;
  
    cout << countUnsetBits(n);
  
    return 0;
}

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Python3

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# Python3 implementation of the approach 
  
# Function to return the count of unset 
# bits in the binary representation of 
# all the numbers from 1 to n 
def countUnsetBits(n) : 
  
    # To store the count of unset bits 
    cnt = 0
  
    # For every integer from the range [1, n] 
    for i in range(1, n + 1) :
          
        # A copy of the current integer 
        temp = i; 
  
        # Count of unset bits in 
        # the current integer 
        while (temp) :
  
            # If current bit is unset 
            if (temp % 2 == 0) :
                cnt += 1
  
            temp = temp // 2
  
    return cnt; 
  
# Driver code 
if __name__ == "__main__"
  
    n = 5
  
    print(countUnsetBits(n)); 
      
# This code is contributed by AnkitRai01

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Output:

4


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