POJ 1995-Raising Modulo Numbers-整数快速幂

素颜马尾好姑娘i 2022-08-21 01:26 6阅读 0赞

Raising Modulo Numbers

<table> 
 <tbody> 
  <tr> 
   <td><strong>Time Limit:</strong>&nbsp;1000MS</td> 
   <td>&nbsp;</td> 
   <td><strong>Memory Limit:</strong>&nbsp;30000K</td> 
  </tr> 
  <tr> 
   <td><strong>Total Submissions:</strong>&nbsp;6012</td> 
   <td>&nbsp;</td> 
   <td><strong>Accepted:</strong>&nbsp;3515</td> 
  </tr> 
 </tbody> 
</table>

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 Bi from 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

(A1B1\+A2B2\+ ... +AHBH)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

Source

[CTU Open 1999][]

题意：

先输入Z表示有几组测试数据，M表示每组数据要mod的模，H表示有几对A和B。

求解下面这个公式的值：

(A1B1\+A2B2\+ ... +AHBH)mod M .

知识点：

整数快速幂，直接套函数模板。

这里可以每输入一组A和B的值就mod M一次，然后把这组的全部相加，输入完毕时再次mod M，得到ans答案输出。

#include <iostream>
    #include <cstdio>
    const int p=45005;
    typedef long long ll;
    using namespace std;
    long long quick(ll a,ll b,ll m )
    {
        ll ans=1;
        while(b)
        {
            if(b&1)
            {
                ans=(ans*a)%m;
                --b;
            }
            b/=2;
            a=a*a%m;
        }
        return ans;
    }
    int main()
    {
        int i,z,t,m;
        ll ans,a,b;
        scanf("%I64d",&z);
        while(z--)
        {
            ans=0;
            scanf("%d",&m);
            scanf("%d",&t);
            for(i=0; i<t; ++i)
            {
                scanf("%I64d%I64d",&a,&b);
                ans=(ans+quick(a,b,m))%m;
            }
            printf("%lld\n",ans);
        }
        return 0;
    }

[CTU Open 1999]: http://poj.org/searchproblem?field=source&key=CTU+Open+1999