2017 多校训练 1006 Function

　　

Function

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 273    Accepted Submission(s): 99

Problem Description

You are given a permutation a from 0 to n−1 and a permutation b from 0 to m−1.

Define that the domain of function f is the set of integers from 0 to n−1, and the range of it is the set of integers from 0 to m−1.

Please calculate the quantity of different functions f satisfying that f(i)=bf(ai) for each i from 0 to n−1.

Two functions are different if and only if there exists at least one integer from 0 to n−1 mapped into different integers in these two functions.

The answer may be too large, so please output it in modulo 109+7.

 

 

Input

The input contains multiple test cases.

For each case:

The first line contains two numbers n, m. (1≤n≤100000,1≤m≤100000)

The second line contains n numbers, ranged from 0 to n−1, the i-th number of which represents ai−1.

The third line contains m numbers, ranged from 0 to m−1, the i-th number of which represents bi−1.

It is guaranteed that ∑n≤106, ∑m≤106.

 

 

Output

For each test case, output "Case #x: y" in one line (without quotes), where x indicates the case number starting from 1 and y denotes the answer of corresponding case.

 

 

Sample Input

3 2 1 0 2 0 1 3 4 2 0 1 0 2 3 1

 

 

Sample Output

Case #1: 4 Case #2: 4

 

 

Source

2017 Multi-University Training Contest - Team 1

 

/*
* @Author: Lyucheng
* @Date:   2017-07-25 15:25:56
* @Last Modified by:   Lyucheng
* @Last Modified time: 2017-07-25 20:42:28
*/
/*
 题意：给你两个序列，定义一种函数 f(i)=b[f(ai)] ，问你已给出的序列可以构造出的函数的数量

 思路：实际上就是从a集合到b集合的映射的组合，a中的一个循环节是一个整体，如果b中循环节的长度和a循环节的长度相同
    或者是因子，那么就可以置换过来，满足这个条件，将结果组合一下就好

 感悟：好气啊，想出来，但是没想到因子这个条件... 
*/
#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <time.h>

#define MAXN 100005
const long long MOD = 1e9+7;
#define LL long long
using namespace std;

int n,m;
int a[MAXN];
int b[MAXN];
bool visa[MAXN];
bool visb[MAXN];
vector<int> va;
vector<int> vb;
int ca=1;

void init(){
    va.clear();
    vb.clear();
    memset(visa,false,sizeof visa);
    memset(visb,false,sizeof visb);
    memset(a,0,sizeof a);
    memset(b,0,sizeof b);
}

int main(){
    // freopen("in.txt", "r", stdin);
    // freopen("out.txt", "w", stdout);
    while(scanf("%d%d",&n,&m)!=EOF){

        init();
        for(int i=0;i<n;i++){
            scanf("%d",&a[i]);
        }
        for(int i=0;i<m;i++){
            scanf("%d",&b[i]);
        }

        for(int i=0;i<n;i++){//求A的循环节
            if(visa[i]==true) continue;

            int cur=0;
            int x=a[i];
            while(x!=a[x]){
                if(visa[x]==true) break;//走到了标记过的点 可能遇到没返回自己的循环了，也可能返回自己了
                visa[x]=true;
                cur++;
                x=a[x];
            }
            if(x==a[i]){
                if(cur==0)
                    va.push_back(1);
                else
                    va.push_back(cur);
            }else{
                va.push_back(1);
                int cnt=0;
                while(x!=a[x]){
                    cnt++;
                    if(cnt>=cur) break;
                    visa[x]=false;
                    x=a[x];
                }
                visa[a[i]]=true;
            }
        }

        for(int i=0;i<m;i++){//求B的循环节
            if(visb[i]==true) continue;

            int cur=0;
            int x=b[i];
            while(x!=b[x]){
                if(visb[x]==true) break;//走到了标记过的点 可能遇到没返回自己的循环了，也可能返回自己了
                visb[x]=true;
                cur++;
                x=b[x];
            }
            if(x==b[i]){
                if(cur==0)
                    vb.push_back(1);
                else
                    vb.push_back(cur);
            }else{
                vb.push_back(1);
                int cnt=0;
                while(x!=b[x]){
                    cnt++;
                    if(cnt>=cur) break;
                    visb[x]=false;
                    x=b[x];
                }
                visb[b[i]]=true;
            }
        }

        LL res=1;
        for(int i=0;i<va.size();i++){
            LL cur=0;
            for(int j=0;j<vb.size();j++){
                if(va[i]%vb[j]==0){
                    cur+=( (LL)(vb[j]) ) %MOD;
                    cur%=MOD;
                }
            }
            res=( (res%MOD) * (cur%MOD) )%MOD;
        }

        printf("Case #%d: %d\n",ca++,res);
    }
    return 0;
}