Submission #3943060

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Source Code Expand

#include<iostream>
#include<string>
#include<vector>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<algorithm>
#include<functional>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cassert>
#include<ctime>
using namespace std;

#define mind(a,b) (a>b?b:a)
#define maxd(a,b) (a>b?a:b)
#define absd(x) (x<0?-(x):x)
#define pow2(x) ((x)*(x))
#define rep(i,n) for(int i=0; i<n; ++i)
#define repr(i,n) for(int i=n-1; i>=0; --i)
#define repl(i,s,n) for(int i=s; i<=n; ++i)
#define replr(i,s,n) for(int i=n; i>=s; --i)
#define repf(i,s,n,j) for(int i=s; i<=n; i+=j)
#define repe(e,obj) for(auto e : obj)

#define SP << " " <<
#define COL << " : " <<
#define COM << ", " <<
#define ARR << " -> " <<
#define PNT(STR) cout << STR << endl
#define POS(X,Y) "(" << X << ", " << Y << ")"
#define DEB(A) " (" << #A << ") " << A
#define DEBREP(i,n,val) for(int i=0; i<n; ++i) cout << val << " "; cout << endl
#define ALL(V) (V).begin(), (V).end()
#define INF 1000000007
#define INFLL 1000000000000000007LL
#define EPS 1e-9

typedef unsigned int uint;
typedef unsigned long ulong;
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#define P_TYPE int
typedef pair<P_TYPE, P_TYPE> P;
typedef pair<P, P_TYPE> PI;
typedef pair<P_TYPE, P> IP;
typedef pair<P, P> PP;
typedef priority_queue<P, vector<P>, greater<P> > pvqueue;

#define N 305

int n;
double memo[N][N][N];
double dfs(int a, int b, int c) {
  if(memo[a][b][c] >= -1) {
    return memo[a][b][c];
  }
  double r = 0;
  if(a) {
    r += (dfs(a-1, b, c)+1) * a;
  }
  if(b) {
    r += (dfs(a+1, b-1, c)+1) * b;
  }
  if(c) {
    r += (dfs(a, b+1, c-1)+1) * c;
  }
  int p = (a + b + c);
  return memo[a][b][c] = (r + n - p) / p;
}
int c[4];

int main() {
  cin >> n;
  rep(i, n) {
    int a; cin >> a;
    ++c[a];
  }
  rep(a, N) {
    rep(b, N) {
      rep(c, N) {
        memo[a][b][c] = -2;
      }
    }
  }
  memo[0][0][0] = 0;
  printf("%.10f\n", dfs(c[1], c[2], c[3]));
  return 0;
}

Submission Info

Judge Result