2019/round3/chain_of_command.cpp

// Chain of Command
// Solution by Jacob Plachta

#define DEBUG 0

#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;

#define LL long long
#define LD long double
#define PR pair<int,int>

#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second

template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x*x); }
string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }

const int INF = (int)1e9;
const LD EPS = 1e-12;
const LD PI = acos(-1.0);

#if DEBUG
#define GETCHAR getchar
#else
#define GETCHAR getchar_unlocked
#endif

bool Read(int &x)
{
	char c,r=0,n=0;
	x=0;
		for(;;)
		{
			c=GETCHAR();
				if ((c<0) && (!r))
					return(0);
				if ((c=='-') && (!r))
					n=1;
				else
				if ((c>='0') && (c<='9'))
					x=x*10+c-'0',r=1;
				else
				if (r)
					break;
		}
		if (n)
			x=-x;
	return(1);
}

#define LIM 800001
#define MOD 1000000007

int N;
LL curSum;
int ind,sz[LIM],in[LIM],out[LIM],nxt[LIM];
int C[LIM],S[LIM];
int BLT[2][LIM]; // 0: B, 1: X
bool X[LIM],hasSetXUpward[LIM];
vector<int> ch[LIM],unsetXch[LIM];

void RecCalcSz(int i)
{
	int j;
	sz[i]=1;
		Fox(j,Sz(ch[i]))
		{
			int c=ch[i][j];
			RecCalcSz(c);
			sz[i]+=sz[c];
				if(sz[c]>sz[ch[i][0]])
					swap(ch[i][0],ch[i][j]);
		}
}

void RecHLD(int i)
{
	in[i]=ind++;
	int j;
		Fox(j,Sz(ch[i]))
		{
			int c=ch[i][j];
			nxt[c]=j ? c : nxt[i];
			RecHLD(c);
		}
	out[i]=ind;
}

void IncBLT(int b,int i)
{
	for (i++; i<=N; i+=(i&-i))
		BLT[b][i]++;
}

int QueryBLT(int b,int i)
{
	int s=0;
		for (i++; i>0; i-=(i&-i))
			s+=BLT[b][i];
	return(s);
}

int QueryBInSubtree(int i)
{
	return(QueryBLT(0,out[i]-1)-QueryBLT(0,in[i]-1));
}

int QueryXToRoot(int i)
{
	int x=1;
		while (i>=0)
		{
			int a=nxt[i];
			x+=QueryBLT(1,in[i])-QueryBLT(1,in[a]-1);
			i=C[a];
		}
	return(x);
}

void SetX(int i)
{
		if (X[i])
			return;
	X[i]=1;
	IncBLT(1,in[i]);
	curSum+=QueryBInSubtree(i);
}

void Bribe(int i)
{
	int j;
	IncBLT(0,in[i]);
	curSum+=QueryXToRoot(i);
		Fox(j,Sz(ch[i]))
			SetX(ch[i][j]);
		for(;;)
		{
				if (hasSetXUpward[i])
					break;
			hasSetXUpward[i]=1;
			int c=C[i];
				if (c<0)
					break;
				Fox(j,Sz(unsetXch[c]))
					if (unsetXch[c][j]!=i)
						SetX(unsetXch[c][j]);
			unsetXch[c].clear();
			unsetXch[c].pb(i);
			i=c;
		}
}

int main()
{
		if (DEBUG)
			freopen("in.txt","r",stdin);
	// vars
	int T,t;
	int i,r;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// init
				Fox(i,N)
				{
					ch[i].clear();
					unsetXch[i].clear();
				}
			// input
			Read(N);
				Fox(i,N)
				{
					Read(C[i]),C[i]--;
						if (C[i]<0)
							r=i;
						else
						{
							ch[C[i]].pb(i);
							unsetXch[C[i]].pb(i);
						}
				}
			// perform heavy-light decomposition
			ind=0;
			RecCalcSz(r);
			nxt[r]=r;
			RecHLD(r);
			// init
			curSum=0;
			Fill(BLT,0);
			Fill(X,0);
			Fill(hasSetXUpward,0);
			// process bribes
			int ans=1;
				Fox(i,N)
				{
					Bribe(i);
					ans=ans*(curSum%MOD)%MOD;
				}
			// output
			printf("Case #%d: %d\n",t,ans);
		}
	return(0);
}