Raising Modulo Numbers

最新推荐文章于 2023-11-11 11:25:23 发布

原创最新推荐文章于 2023-11-11 11:25:23 发布 · 800 阅读

0 ·

CC 4.0 BY-SA版权

快速幂专栏收录该内容

3 篇文章

订阅专栏

本文介绍了一种基于快速幂取模算法的游戏实现方法。玩家选择两个数字并计算所有玩家数字组合的幂次总和模给定数值的结果。文章提供了一个C语言程序示例，用于自动计算游戏结果。

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 5507		Accepted: 3190

Description

People are different. Some secretly read magazines full of interesting girls' pictures, others create an A-bomb in their cellar, others like using Windows, and some like difficult mathematical games. Latest marketing research shows, that this market segment was so far underestimated and that there is lack of such games. This kind of game was thus included into the KOKODáKH. The rules follow:

Each player chooses two numbers Ai and Bi and writes them on a slip of paper. Others cannot see the numbers. In a given moment all players show their numbers to the others. The goal is to determine the sum of all expressions Ai ^Bifrom all players including oneself and determine the remainder after division by a given number M. The winner is the one who first determines the correct result. According to the players' experience it is possible to increase the difficulty by choosing higher numbers.

You should write a program that calculates the result and is able to find out who won the game.

Input

The input consists of Z assignments. The number of them is given by the single positive integer Z appearing on the first line of input. Then the assignements follow. Each assignement begins with line containing an integer M (1 <= M <= 45000). The sum will be divided by this number. Next line contains number of players H (1 <= H <= 45000). Next exactly H lines follow. On each line, there are exactly two numbers Ai and Bi separated by space. Both numbers cannot be equal zero at the same time.

Output

For each assingnement there is the only one line of output. On this line, there is a number, the result of expression

(A₁^B₁+A₂^B₂+ ... +A_H^B_H)mod M.

Sample Input

3
16
4
2 3
3 4
4 5
5 6
36123
1
2374859 3029382
17
1
3 18132

Sample Output

2
13195
13

所谓的快速幂，实际上是快速幂取模的缩写，简单的说，就是快速的求一个幂式的模(余)。在程序设计过程中，经常要去求一些大数对于某个数的余数，为了得到更快、计算范围更大的算法，产生了快速幂取模算法。

应用的有关知识点公式的引理，即积的取余等于取余的积的取余。

#include<stdio.h>
int main()
{
    int n,m,a,b,c,w,h;
    scanf("%d",&n);
    while(n--)
    {
        scanf("%d%d",&m,&a);
        int sum=0;
        while(a--)
        {
            scanf("%d%d",&c,&b);
            int w=c%m;
            h=1;
            while(b>0)
            {
            	if(b%2==1)
            	h=(h*w)%m;
                b=b/2;
               w=(w*w)%m;//这个地方需要注意
            }
            sum=(sum+h)%m;
        }
        printf("%d\n",sum%m);
    }
    return 0;
}