The task is simple: given any positive integer N, you are supposed to count the total number of 1's in the decimal form of the integers from 1 to N. For example, given N being 12, there are five 1's in 1, 10, 11, and 12.
Input Specification:
Each input file contains one test case which gives the positive N (≤230).
Output Specification:
For each test case, print the number of 1's in one line.
Sample Input:
12
Sample Output:
5
#include<bits/stdc++.h>
using namespace std;
int n, ans;
int main(){
scanf("%d", &n);
int r = 0, l = 0, a = 1, now;
while(n/a != 0){
l = n/(a*10);
now = n/a%10;
r = n%a;
if(now == 0) ans += (l * a);
else if(now == 1) ans += l * a + r + 1;
else ans += (l+1) * a;
a *= 10;
}
printf("%d\n", ans);
return 0;
}
总结
数学问题/简单数学 需要严格推理，具体见算法笔记上机指南p199.
每次迭代，记录当前位出现1的个数；对当前位的数，分<1, ==1, >1三种情况讨论。