找1到n所有整数出现1的个数

编程之美2.4

n=12时，1，11，12这3个数包含1，所以1的个数是5.

Line 9是为了防止factor溢出。

#include <iostream>
#include <stdlib.h>
#include <time.h>
using namespace std;

int countOne(int n) {
    int ans = 0;
    int factor = 1;
    while (n / factor >= 10) { // avoid overflow
        int high = n / factor / 10;
        int low = n % factor;
        int current = (n / factor) % 10;
        if (current == 0) {
            ans += high * factor;
        } else if (current == 1) {
            ans += high * factor + low + 1;
        } else {
            ans += (high + 1) * factor;
        }
        factor *= 10;
    }
    if (n / factor == 1) ans += (n % factor) + 1;
    else if (n / factor != 0) ans += factor;
    return ans;
}

int bruteForce(int n) {
    int ans = 0;
    for (int i = 1; i <= n; ++i) {
        int tmp = i;
        while (tmp) {
            if (tmp % 10 == 1) ans++;
            tmp /= 10;
        }
    }
    return ans;
}

int main() {
    srand(time(NULL));

    for (int i = 0; i < 100; ++i) {
        int n = rand() % 9999999;
        int c1 = countOne(n);
        int c2 = bruteForce(n);
        if (c1 != c2) {
            cout << c1 << " " << c2 << " " << n << endl;
        }
    }
    return 0;
}