10994 - Simple Addition(规律)

 

Problem E
Simple Addition
Input: Standard Input

Output: Standard Output

 

Let’s define a simple recursive function F (n), where

 

Let’s define another function S (p, q),

 

In this problem you have to Calculate S (p, q) on given value of   p and q.

 

Input

The input file contains several lines of inputs. Each line contains two non negative integers p and q (p <= q) separated by a single space. p and q will fit in 32 bit signed integer. In put is terminated by a line which contains two negative integers. This line should not be processed.

 

For each set of input print a single line of the value of S(p, q).

 

       Sample Input                               Output for Sample Input

1 10 10 20 30 40 -1 -1

46 48 52

题意：求题目中那个公式从p到q F【i] 的和

思路:每个数肯定是1-9.这样的规律，个位1-9，十位1-9，百位1-9.如此一来，只要把各位加完，加十位，加百位，一个个加完，最后就是答案了。加的时候可以直接用等差数列和公式

代码:

 

#include <stdio.h>

int p, q;

long long Sum(long long s, long long e) {
    if (s > e)
	return 0;
    return (s + e) * (e - s + 1) / 2;
}
long long cal(long long n) {
    if (n <= 0) return 0;
    long long ans = 0;
    while (n) {
	ans += n / 10 * 45;
	ans += Sum(1, n % 10);
	n /= 10;
    }
    return ans;
}

int main() {
    while (~scanf("%d%d", &p, &q) && p != -1 && q != -1) {
	printf("%lld\n", cal(q) - cal(p - 1));
    }
    return 0;
}