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

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

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

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