Submission #3919562

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Source Code Expand

#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
#define svec(v) cout<<#v<<":";rep(pachico,v.size())cout<<" "<<v[pachico];cout<<endl
#define svecp(v) cout<<#v<<":";each(pachico,v)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(pachico,s)cout<<" "<<pachico;cout<<endl
#define smap(m) cout<<#m<<":";each(pachico,m)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl

using namespace std;

typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 2005;

// 根がi, 連成j個, 根があと何個つながれるか(0/1/2), ペアの偶奇
int dp[MAX_N][2][MAX_N][3][2];
int sb[MAX_N];

vector<int> G[MAX_N];

int add(int x,int y)
{
    return (x + y)%MOD;
}

int sub(int x,int y)
{
    return (x+MOD-y)%MOD;
}

int mul(int x,int y)
{
    return (ll)x*y%MOD;
}

int inv[MAX_N],fac[MAX_N],finv[MAX_N];

void make()
{
	fac[0] = fac[1] = 1;
	finv[0] = finv[1] = 1;
	inv[1] = 1;
	for(int i=2;i<MAX_N;i++){
		inv[i] = MOD - (ll)inv[MOD%i] * (MOD/i) % MOD;
		fac[i] = (ll)fac[i-1] * i % MOD;
		finv[i] = (ll)finv[i-1] * inv[i] % MOD;
	}
}

int comb(int a,int b)
{
	if(a<b){
		return 0;
	}
	return fac[a] * ((ll)finv[b] * finv[a-b] % MOD) % MOD;
}

int dfs(int u, int p){
    sb[u]++;
    dp[u][0][1][2][0] = 1;
    int mx = 1;
    each(v, G[u]){
        if(v != p){
            sb[u] += dfs(v, u);
            srep(i,1,mx+1){
                // k = 0 のとき
                // くっつかない
                for(int j = sb[v]; j >= 1; j--){
                    rep(l,2){
                        rep(m,2){
                            dp[u][1][i+j][0][l^m] = add(dp[u][1][i+j][0][l^m], mul(dp[u][0][i][0][l], mul(add(dp[v][0][j][0][m], dp[v][0][j][1][m]) + dp[v][0][j][2][m], comb(i+j, i))));
                        }
                    }
                }
                // k = 1
                // くっつく
                for(int j = sb[v]; j >= 1; j--){
                    rep(l,2){
                        rep(m,2){
                            dp[u][1][i+j-1][0][l^m^1] = add(dp[u][1][i+j-1][0][l^m^1], mul(dp[u][0][i][1][l], mul(dp[v][0][j][2][m], comb(i+j-1, i))));
                            dp[u][1][i+j-1][0][l^m^1] = add(dp[u][1][i+j-1][0][l^m^1], mul(dp[u][0][i][1][l], mul(mul(dp[v][0][j][1][m], inv[2]), comb(i+j-1, i))));
                        }
                    }
                }
                // くっつかない
                for(int j = sb[v]; j >= 1; j--){
                    rep(l,2){
                        rep(m,2){
                            dp[u][1][i+j][1][l^m] = add(dp[u][1][i+j][1][l^m], mul(dp[u][0][i][1][l], mul(dp[v][0][j][0][m], comb(i+j, i))));
                            dp[u][1][i+j][1][l^m] = add(dp[u][1][i+j][1][l^m], mul(dp[u][0][i][1][l], mul(mul(mul(dp[v][0][j][1][m], inv[2]), i), comb(i+j, i+1))));
                            dp[u][1][i+j][1][l^m] = add(dp[u][1][i+j][1][l^m], mul(dp[u][0][i][1][l], mul(mul(dp[v][0][j][1][m], inv[2]), comb(i+j, i))));
                            dp[u][1][i+j][1][l^m] = add(dp[u][1][i+j][1][l^m], mul(dp[u][0][i][1][l], mul(mul(dp[v][0][j][2][m], i), comb(i+j, i+1))));
                        }
                    }
                }
                // k = 2
                // くっつく
                for(int j = sb[v]; j >= 1; j--){
                    rep(l,2){
                        rep(m,2){
                            dp[u][1][i+j-1][1][l^m^1] = add(dp[u][1][i+j-1][1][l^m^1], mul(dp[u][0][i][2][l], mul(2 * dp[v][0][j][2][m], comb(i+j-1, i))));
                            dp[u][1][i+j-1][1][l^m^1] = add(dp[u][1][i+j-1][1][l^m^1], mul(dp[u][0][i][2][l], mul(dp[v][0][j][1][m], comb(i+j-1, i))));
                        }
                    }
                }
                // くっつかない
                for(int j = sb[v]; j >= 1; j--){
                    rep(l,2){
                        rep(m,2){
                            dp[u][1][i+j][2][l^m] = add(dp[u][1][i+j][2][l^m], mul(dp[u][0][i][2][l], mul(dp[v][0][j][0][m], comb(i+j, i))));
                            dp[u][1][i+j][2][l^m] = add(dp[u][1][i+j][2][l^m], mul(dp[u][0][i][2][l], mul(mul(dp[v][0][j][1][m], i), comb(i+j, i+1))));
                            dp[u][1][i+j][2][l^m] = add(dp[u][1][i+j][2][l^m], mul(dp[u][0][i][2][l], mul(mul(dp[v][0][j][2][m], i-1), comb(i+j, i+1))));
                        }
                    }
                }
            }
            swap(dp[u][0], dp[u][1]);
            rep(j,mx+1){
                rep(k,2){
                    rep(l,2){
                        dp[u][1][j][k][l] = 0;
                    }
                }
            }
            mx += sb[v];
        }
    }
    // rep(j,mx){
    //     rep(k,3){
    //         rep(l,2){
    //             cout << u << " " << j << " " << k << " " << l << " " << dp[u][0][j][k][l] << "\n";
    //         }
    //     }
    // }
    return sb[u];
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    rep(i,n-1){
        int a;
        cin >> a;
        G[a-1].pb(i+1);
    }
    make();
    dfs(0, -1);
    int ans = 0;
    rep(i,n){
        rep(j,3){
            ans = add(ans, dp[0][0][i+1][j][0]);
            ans = sub(ans, dp[0][0][i+1][j][1]);
        }
    }
    cout << ans << "\n";
    return 0;
}

Submission Info

Judge Result