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最新推荐文章于 2024-10-08 01:30:55 发布

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最新推荐文章于 2024-10-08 01:30:55 发布

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分类专栏： C++算法

本文链接：https://blog.youkuaiyun.com/qq_35916858/article/details/79262017

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本文探讨了一个有趣的组合数学问题：如何利用不同颜色为相连成圈的气球进行染色，使得相邻气球颜色各不相同。提供了一种有效的方法来计算可能的染色方案数量，并给出具体的C++实现代码。

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链接：https://www.nowcoder.net/acm/contest/55/H
来源：牛客网

时间限制：C/C++ 1秒，其他语言2秒
空间限制：C/C++ 262144K，其他语言524288K
64bit IO Format: %lld

题目描述

Yuanyuan Long is a dragon like this picture?

I don’t know, maybe you can ask him. But I’m sure Yuanyuan Long likes ballons, he has a lot of ballons.

One day, he gets n white ballons and k kinds of pigment, and he thought a problem:

1. Number these ballons b1, b2, … , bi, …, to bn.

2. Link these ballons to a circle in order, and color these ballons.

3. He need to make sure that any neighbor ballons have different colors.

He wants to know how many solutions to solve this problem. Can you get the answer to him? The answer maybe very large, get the answer MOD 100000007.

For Example: with 3 ballons and 3 kinds of pigment

Your answer is 3*2*1 MOD 100000007 = 6.

The answer maybe large, you can use integer type long long.

输入描述:

The first line is the cases T. ( T <=
100)
For next T lines, each line contains n and
k. (2<= n <= 10000,  2<= k
<=100)

输出描述:

For each test case, output the answer on
each line.

思路:用m种颜色在n个区域涂色公式 (m-1)^n+(m-1)(-1)^n

# include <iostream>
# include <cstdlib>
# include <cstring>
using namespace std;
# define min(x,y)  ((x)<(y)?(x):(y))
# define max(x,y)    ((x)>(y)?(x):(y))
const int maxn=1e6+112;
const int mod = 100000007 ;
typedef long long ll;
int n;
int a[1005],b[1005];
int vis[maxn];
// 用m种颜色在n个区域涂色   公式 (m-1)^n+(m-1)(-1)^n
int main()
{
	int n,T,k;
	cin>>T;
    while(T--){
       cin>>n>>k;
       int m = k - 1;
       ll ans = 1;
       for(int i=1;i<=n;i++){
           ans = ans*m%mod;
       }
       if(n&1){
         ans = ans - m;
       }else{
         ans = ans + m;
       }
       cout<<ans<<endl;
    }

	return 0;
}