福建省冬令营 Day3 T1 geronimo geronimo

Posted 2020-08-29

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题解：

将轮换拆解成置换，答案即为置换大小的最小公倍数

  1 #include<algorithm>
  2 #include<iostream>
  3 #include<cstring>
  4 #include<cstdlib>
  5 #include<cstdio>
  6 #include<cmath>
  7 using namespace std;
  8 inline int Get()
  9 {
 10     int x = 0;
 11     char c = getchar();
 12     while(c < ‘0‘ || c > ‘9‘) c = getchar();
 13     while(c >= ‘0‘ && c <= ‘9‘)
 14     {
 15         x = x * 10 + c - ‘0‘;
 16         c = getchar();
 17     }
 18     return x;
 19 }
 20 const int me = 1000233;
 21 int n, m;
 22 int mo;
 23 int tot;
 24 int p[me], v[me];
 25 int si[me];
 26 int cou[me];
 27 bool vis[me];
 28 inline void Prime()
 29 {
 30     for(int i = 2; i <= n; ++i)
 31     {
 32         if(!vis[i]) p[++m] = i;
 33         for(int j = 1; j <= m; ++j)
 34         {
 35             int c = p[j];
 36             if(i * c > n) break;
 37             vis[i * c] = true;
 38             if(!(i % c)) break;
 39         }
 40     }
 41 }
 42 inline void Round()
 43 {
 44     for(int i = 1; i <= n; ++i)
 45     {
 46         if(vis[i]) continue;
 47         ++tot;
 48         int u = i;
 49         while(!vis[u])
 50         {
 51             vis[u] = true;
 52             ++si[tot];
 53             u = v[u];
 54         }
 55         if(!si[tot]) --tot;
 56     }
 57 }
 58 inline void Seperate()
 59 {
 60     for(int i = 1; i <= tot; ++i)
 61     {
 62         int s = 0;
 63         int now = si[i];
 64         while(now != 1)
 65         {
 66             ++s;
 67             int sum = 0;
 68             while(!(now % p[s])) now /= p[s], ++sum;
 69             cou[s] = max(cou[s], sum);
 70         }
 71     }
 72 }
 73 inline long long Pow(int x, int y)
 74 {
 75     long long sum = 1;
 76     while(y)
 77     {
 78         if(y & 1) sum = (sum * x) % mo;
 79         x = (x * x) % mo;
 80         y >>= 1;
 81     }
 82     return sum;
 83 }
 84 inline void Ans()
 85 {
 86     long long ans = 1;
 87     for(int i = 1; i <= m; ++i)
 88         if(cou[i])
 89             ans = ans * Pow(p[i], cou[i]) % mo;
 90     printf("%lld", ans);
 91 }
 92 int main()
 93 {
 94     n = Get(), mo = Get();
 95     for(int i = 1; i <= n; ++i) v[i] = Get();
 96     Prime();
 97     for(int i = 1; i <= n; ++i) vis[i] = false;
 98     Round();
 99     Seperate();
100     Ans();
101 }