Submission #2046113

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Source Code Expand

#include <bits/stdc++.h>
#define ADD(a, b) a = (a + ll(b)) % mod
#define MUL(a, b) a = (a * ll(b)) % mod
#define MAX(a, b) a = max(a, b)
#define MIN(a, b) a = min(a, b)
#define rep(i, a, b) for(int i = int(a); i < int(b); i++)
#define rer(i, a, b) for(int i = int(a) - 1; i >= int(b); i--)
#define all(a) (a).begin(), (a).end()
#define sz(v) (int)(v).size()
#define pb push_back
#define sec second
#define fst first
#define debug(fmt, ...) Debug(__LINE__, ":", fmt, ##__VA_ARGS__)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<int, pi> ppi;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vl> mat;
typedef complex<double> comp;
void Debug() {cout << '\n'; }
template<class FIRST, class... REST>void Debug(FIRST arg, REST... rest){
	cout<<arg<<" ";Debug(rest...);}
template<class T>ostream& operator<<(ostream& out,const vector<T>& v) {
	out<<"[";if(!v.empty()){rep(i,0,sz(v)-1)out<<v[i]<<", ";out<<v.back();}out<<"]";return out;}
template<class S, class T>ostream& operator<<(ostream& out,const pair<S, T>& v){
	out<<"("<<v.first<<", "<<v.second<<")";return out;}
const int MAX_N = 200010;
const int MAX_V = 100010;
const double eps = 1e-6;
const ll mod = 1000000007;
const int inf = 1 << 29;
const ll linf = 1LL << 60;
const double PI = 3.14159265358979323846;
///////////////////////////////////////////////////////////////////////////////////////////////////

ll fac[MAX_N], inv[MAX_N], fiv[MAX_N]; //fiv:inv(fac(i))

ll mod_pow(ll a, ll n) {
	if(n == 0) return 1;
	ll res = mod_pow(a, n / 2);
	if(n % 2 == 0) return res * res % mod;
	else return a * res % mod * res % mod;
}

ll invf(ll a) {
	return mod_pow(a, mod - 2);
}

void C_init(int n) {
	fac[0] = fac[1] = 1; inv[1] = 1;
	fiv[0] = fiv[1] = 1;
	rep(i, 2, n + 1) {
		fac[i] = fac[i - 1] * i % mod;
		inv[i] = mod - inv[mod % i] * (mod / i) % mod;
		fiv[i] = fiv[i - 1] * inv[i] % mod;
	}
}

ll C(int a, int b) { //assume a >= b
	if(a < b || a < 0 || b < 0) return 0;
	return fac[a] * fiv[b] % mod * fiv[a - b] % mod;
}

int N;
vi G[MAX_N];
ll dp[2010][2010][3];
int ts[2010];

void loop(int v) {

	int n = sz(G[v]);
	ts[v] = 1;
	rep(i, 0, n) {
		int to = G[v][i]; 
		loop(to);
		ts[v] += ts[to];
	}

	int m = ts[v];

	vector<vl> tdp[2] = {vector<vl>(m + 1, vl(3, 0)), vector<vl>(m + 1, vl(3, 0))};
	tdp[0][1][0] = 1;
	int now = 0, nex = 1;
	int cnt = 1;
	rep(i, 0, n) {
		int to = G[v][i];

		rep(j, 0, cnt + ts[to] + 1) {
			rep(k, 0, 3) {
				tdp[nex][j][k] = 0;
			}
		}

		rep(j, 0, cnt + 1) {
			rep(k, 0, ts[to] + 1) {
				rep(l, 0, 3) ADD(tdp[nex][j + k][0], tdp[now][j][0] * dp[to][k][l] % mod);
				rep(l, 0, 3) ADD(tdp[nex][j + k][1], tdp[now][j][1] * dp[to][k][l] % mod);
				rep(l, 0, 3) ADD(tdp[nex][j + k][2], tdp[now][j][2] * dp[to][k][l] % mod);

				if(k < ts[to]) {
					ADD(tdp[nex][j + k][1], tdp[now][j][0] * dp[to][k + 1][0] % mod * 2 % mod);
					ADD(tdp[nex][j + k][1], tdp[now][j][0] * dp[to][k + 1][1] % mod);
					ADD(tdp[nex][j + k][2], tdp[now][j][1] * dp[to][k + 1][0] % mod);
					ADD(tdp[nex][j + k][2], tdp[now][j][1] * dp[to][k + 1][1] % mod * fiv[2] % mod);
				}
			}
		}
		cnt += ts[to];
		swap(now, nex);
	}
	rep(j, 0, m + 1) 
		rep(k, 0, 3) {
			dp[v][j][k] = tdp[now][j][k];
		}
}

void solve() {
	cin >> N;
	C_init(N);
	rep(i, 0, N - 1) {
		int a; cin >> a; a--;
		G[a].pb(i + 1);
	}
	loop(0);

	ll res = 0;
	rep(j, 0, N + 1) {
		rep(k, 0, 3) {
			if((N - j) % 2 == 0) ADD(res, dp[0][j][k] * fac[j] % mod);
			else ADD(res, mod - dp[0][j][k] * fac[j] % mod);
		}
	}
	cout << res << "\n";
}

int main() {
#ifndef LOCAL
	ios::sync_with_stdio(false);
    cin.tie(0);
#endif
    cout << fixed;
	cout.precision(20);
	srand((unsigned int)time(NULL));
#ifdef LOCAL
	//freopen("in.txt", "wt", stdout); //for tester
    freopen("in.txt", "rt", stdin);
#endif	
	solve();
#ifdef LOCAL
    cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
	return 0;
}

Submission Info

Judge Result