Raising Modulo Numbers
2016-07-23 16:02
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Raising Modulo Numbers
DescriptionPeople 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 segmentwas 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 AiBi from all playersincluding 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. InputThe 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 bedivided 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. OutputFor 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
Time Limit: 1000MS | Memory Limit: 30000K | |
Total Submissions: 5510 | Accepted: 3193 |
3 16 4 2 3 3 4 4 5 5 6 36123 1 2374859 3029382 17 1 3 18132Sample Output
21319513题解:求n组的a的b次方之和对m取余的值,根据同余定理 (a+b)%m=(a%m+b%m)%m 可知就是求n组的a的b次方对m取余的值之和对m取余。 对于a的b次方对m取余的值可以用快速幂模板求出。代码:#include<cstdio>#include<cmath>long long pow(int x,int y,int m){long long ans=1,base=x;while(y>0){if(y&1)ans=(ans*base)%m;base=(base*base)%m;y>>=1;}return ans;}int main(){int t;int n,m;int a,b;scanf("%d",&t);while(t--){scanf("%d%d",&m,&n);long long sum=0;for(int i=0;i<n;i++){scanf("%d%d",&a,&b);long long cnt=pow(a,b,m);sum=(sum+cnt)%m;}printf("%lld\n",sum);}}
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