PAT_A1049 Counting Ones【困难】

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。