PAT-1049. Counting Ones (30)

1049. Counting Ones (30)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

---

暴力枚举超时，经过探究，发现可以算出每一位是1的个数，对于这种找规律的题，我们可以观察简单的例子来推出规律，写出程序，测试复杂情况是否可行。

具体规律看代码，讲起来很复杂。

#include <bits/stdc++.h>

using namespace std;

int N;
int total;

void getOnes(int n, int m, int cnt) {
    if(n == 0) return;
    int a = n % 10;
    int b = n / 10;
    int c = cnt;
    int d = 1;
    while(c--) {
        d *= 10;
    }
    if(a < 1) {
        total += b*d;
    }
    else if(a > 1) {
        total += (b+1)*d;
    }
    else {
        total += b*d+m+1;
    }
    m += a*d;
    getOnes(b, m, cnt+1);
}

int main()
{
    cin>> N;
    getOnes(N, 0, 0);
    cout<< total;
    return 0;
}