Sum of ones

#include <bits/stdc++.h>

using namespace std;

//Definitions for quicker writing
#define REP(i,a,b) for (int i = a; i < b; i++)

//Typedefs for quicker writing
typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pi;


long long countOneBits(long long n) {
    long long count = 0;
    long long powerOf2 = 1;
    
    // Traverse over each bit position
    while (powerOf2 <= n) {
        // Count full cycles of '0's and '1's in current bit position
        long long fullCycles = (n + 1) / (powerOf2 * 2);
        long long remainder = (n + 1) % (powerOf2 * 2);
        
        // Add number of '1's from full cycles
        count += fullCycles * powerOf2;
        
        // Add '1's from the remainder part
        if (remainder > powerOf2) {
            count += remainder - powerOf2;
        }
        
        // Move to the next bit position
        powerOf2 *= 2;
    }
    
    return count;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);

    // Input
    long long n;
    cin >> n;

    // Output the total number of 1 bits from 1 to n
    cout << countOneBits(n) << "\n";

    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED