polya定理，环形涂色

环形涂色裸题

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<algorithm>
  4 #include<vector>
  5 #include<cstring>
  6 #include<map>
  7 #include<set>
  8 #include<cmath>
  9 #include<queue>
 10 #include<bitset>
 11 #include<utility>
 12 #include<functional>
 13 #include<iomanip>
 14 #include<sstream>
 15 #include<ctime>
 16 #include<cassert>
 17 #define A first
 18 #define B second
 19 #define mp make_pair
 20 #define pb push_back
 21 #define pw(x) (1ll << (x))
 22 #define sz(x) ((int)(x).size())
 23 #define all(x) (x).begin(),(x).end()
 24 #define rep(i,l,r) for(int i=(l);i<(r);i++)
 25 #define per(i,r,l) for(int i=(r);i>=(l);i--)
 26 #define FOR(i,l,r) for(int i=(l);i<=(r);i++)
 27 #define eps 1e-9
 28 #define PIE acos(-1)
 29 #define cl(a,b) memset(a,b,sizeof(a))
 30 #define fastio ios::sync_with_stdio(false);cin.tie(0);
 31 #define lson l , mid , ls
 32 #define rson mid + 1 , r , rs
 33 #define ls (rt<<1)
 34 #define rs (ls|1)
 35 #define INF 0x3f3f3f3f
 36 #define lowbit(x) (x&(-x))
 37 #define sqr(a) a*a
 38 #define ll long long
 39 #define ull unsigned long long
 40 #define vi vector<int>
 41 #define pii pair<int, int>
 42 #define dd(x) cout << #x << " = " << (x) << ", "
 43 #define de(x) cout << #x << " = " << (x) << "\n"
 44 #define endl "\n"
 45 using namespace std;
 46 const int mod=1e9+7;
 47 int n,m,k,c;
 48 const int maxn=500+7;
 49 int vis[maxn],lab[maxn];
 50 //**********************************
 51 ll qpow(ll a,ll b)
 52 {
 53     ll ans=1;
 54     while(b){
 55         if(b&1)ans=ans*a%mod;
 56         a=a*a%mod;
 57         b>>=1;
 58     }
 59     return ans;
 60 }
 61 ll getloop()
 62 {
 63     cl(vis,0);
 64     int cnt=0;
 65     FOR(i,1,n){
 66         if(vis[i])continue;
 67         cnt++;
 68         int j=i;
 69         do{
 70             vis[j]=1;
 71             j=lab[j];
 72         }while(!vis[j]);
 73     }
 74     return cnt;
 75 }
 76 void work()
 77 {
 78     if(!n){
 79         puts("0\n");return ;
 80     }
 81     ll ans=0;
 82     rep(i,0,n){
 83         FOR(j,1,n)lab[j]=(j+i)%n+1;
 84         ans+=qpow(k,getloop());
 85 //        FOR(j,1,n/2)swap(lab[j],lab[n+1-j]);ans+=qpow(k,getloop()); 
 86         ans%=mod;
 87 //        de(ans);
 88     }
 89     ans=ans*qpow(n,mod-2)%mod;
 90 //    ans/=n;
 91 //    ans=ans*c%mod;
 92     cout<<ans<<endl;
 93 }
 94 //**********************************
 95 
 96 //**********************************
 97 int main()
 98 {
 99 //    while(~scanf("%d",&n))work();
100     cin>>m>>n>>c;
101     k=qpow(c,m*m);
102 //    de(k);
103     work();
104     return 0;
105 }

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