解法一：数学

依次统计各个位置上“1”出现的次数，注意分情况讨论。先写一个暴力解法用于验证算法的正确性。

#include <bits/stdc++.h>
using namespace std;
long long force(long long n) {
    long long cnt = 0;
    string str;
    for (long long i = 1; i <= n; ++i) {
        str = to_string(i);
        for (auto ch:str) {
            if (ch == '1') {
                ++cnt;
            }
        }
    }
    return cnt;
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int N;
    cin >> N;
    // cout << force(N) << endl;
    long long cnt = 0;
    long long x = 1, min, max;
    long long index = 1;
    long long tmp;
    while (x <= N) {
        min = x;
        max = x * 2 - 1;
        if (N >= max) {
            cnt += ((N - max) / (x * 10) + 1) * x;
            tmp = N % (x * 10);
            if (tmp >= min && tmp < max) {
                cnt += tmp - min + 1;
            }
        } else {
            cnt += N - min + 1;
        }
        x *= 10;
    }
    cout << cnt << endl;
}