HDU 1792 A New Change Problem（数学规律题，数论知识）

A New Change Problem

Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 533    Accepted Submission(s): 265

Problem Description

Now given two kinds of coins A and B,which satisfy that GCD(A,B)=1.Here you can assume that there are enough coins for both kinds.Please calculate the maximal value that you cannot pay and the total number that you cannot pay.

 

Input

The input will consist of a series of pairs of integers A and B, separated by a space, one pair of integers per line.

 

Output

For each pair of input integers A and B you should output the the maximal value that you cannot pay and the total number that you cannot pay, and with one line of output for each line in input.

 

Sample Input

2 3 3 4

 

Sample Output

1 1 5 3

 

Author

lcy

 

Recommend

lcy

 

 

题目就是给了两个互质的数A，B。

A*x+B*y（x>=0,y>=0)

问最大不能表示的数，和不能表示的数的个数。

 

数论知识；

个数就是（A-1）*（B-1）/2;

最大不能表示的数就是 A*B-A-B;

 

所有的数可以分成A类，就是对A取模余0~A-1的。

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简要推导见：http://hi.baidu.com/qq258513813/blog/item/81c1d5c57e9ac7009d163da6.html

 

代码：

#include<stdio.h>
int main()
{
    int A,B;
    while(scanf("%d%d",&A,&B)!=EOF)
    {
        printf("%d %d\n",A*B-A-B,(A-1)*(B-1)/2);
    }    
    return 0;
}