Minimum numbers needed to express every integer below N as a sum in C++

Problem statement

We have an integer N. We need to express N as a sum of K integers such that by adding some or all of these integers we can get all the numbers in the range 1 to N. The task is to find minimum value of K

Example

If N = 8 then final answer i.e. K would be 3

If we take integers 1, 2, 3, and 4 then adding some or all of these groups we can get all number in the range 1 to N

e.g.
1 = 1
2 = 2
3 = 3
4 = 4
5 = 1 + 5
6 = 4 + 2
7 = 4 + 3
8 = 1 + 3 + 4

Algorithm

Count number of bits from given integer

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int getMinNumbers(int n) {
   int cnt = 0;
   while (n) {
      ++cnt;
      n = n >> 1;
   }
   return cnt;
}
int main() {
   int n = 8;
   cout << "Minimum required numbers = " <<getMinNumbers(n) << endl;
   return 0;
}

When you compile and execute above program. It generates following output

Output

Minimum required numbers = 4

Narendra Kumar

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Updated on: 23-Dec-2019

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