CSU1162-Balls in the Boxes-快速幂、数论-优快云博客

本文链接：https://blog.youkuaiyun.com/Zickshen/article/details/73731292

本文介绍了一种解决Mr. Mindless提出的数学问题的方法：如何计算特定数量的球放入特定数量盒子的不同组合方式。通过模运算处理大数问题，利用C++实现高效算法。

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Q: Balls in the Boxes

Description

Mr. Mindless has many balls and many boxes,he wants to put all the balls into some of the boxes.Now, he wants to know how many different solutions he can have.

you know,he could put all the balls in one box,and there could be no balls in some of the boxes.Now,he tells you the number of balls and the numbers of boxes, can you to tell him the number of different solutions? Because the number is so large, you can just tell him the solutions mod by a given number C.

Both of boxes and balls are all different.

Input

There are multiple testcases. In each test case, there is one line cantains three integers:the number of boxes ,the number of balls,and the given number C separated by a single space.All the numbers in the input are bigger than 0 and less than 2^63.

Output

For each testcase,output an integer,denotes the number you will tell Mr. Mindless

Sample Input

3 2 4
4 3 5

Sample Output

1
4

其实结果就是a^b%c

推理网上找找，我也是看着才懂的

模板+1

#include <bits/stdc++.h>
#define N 10100
#define INF 0x3f3f3f3f
#define LL long long
#define ULL unsigned long long
#define mem(a,n) memset(a,n,sizeof(a))
#define fread freopen("in.txt","r",stdin)
#define fwrite freopen("out.txt","w",stdout)
#pragma comment(linker, "/STACK:102400000,102400000") 
using namespace std;
ULL MultiMod(ULL a,ULL b,ULL mod)
{
    ULL res=0;
    while(b){
        if(b&1){
            res=(res+a)%mod;
            b-=1;
        }else{
            a=(a+a)%mod;
            b>>=1;
        }
    }
    return res;
}
ULL PowMod(ULL a,ULL b,ULL mod)
{
    ULL res=1;
    while(b){
        if(b&1){
            res=MultiMod(res,a,mod);
            b-=1;
        }else{  
            a=MultiMod(a,a,mod);
            b>>=1;
        }
    }
    return res;
}
int main()
{
    ios::sync_with_stdio(false);
    ULL a,b,c;
    while(cin>>a>>b>>c){
        cout<<PowMod(a,b,c)<<endl;
    }
    return 0;
}


/**********************************************************************
    Problem: 1162
    User: CSUzick
    Language: C++
    Result: AC
    Time:24 ms
    Memory:1688 kb
**********************************************************************/