[BZOJ 1040] [ZJOI2008] 骑士 【基环+外向树DP】

#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <cstdio>

using namespace std;

const int MaxN = 1000000 + 5;

typedef long long LL;

const LL INF = 99999999999999999;

int n, R, R1, R2, Rt;
int A[MaxN];

LL Ans, Temp;
LL F[MaxN][2];

bool Visit[MaxN];

struct Edge
{
	int u, v, t;
	Edge *Next;
} E[MaxN * 2], *P = E, *Point[MaxN];

inline void AddEdge(int x, int y, int z) 
{
	++P; P -> u = x; P -> v = y; P -> t = z;
	P -> Next = Point[x]; Point[x] = P;
}

inline LL gmax(LL a, LL b) {return a > b ? a : b;}

void DFS(int x, int y) 
{
	Visit[x] = true;
	for (Edge *j = Point[x]; j; j = j -> Next) 
	{
		if (j -> t == y) continue;
		if (Visit[j -> v]) 
		{
			R1 = x; 
			R2 = j -> v;
			Rt = j -> t;
		}
		else DFS(j -> v, j -> t);
	}
}

void Solve(int x, int y) 
{
	F[x][0] = 0; F[x][1] = A[x];
	for (Edge *j = Point[x]; j; j = j -> Next)
	{
		if (j -> t == y || j -> t == Rt) continue;
		Solve(j -> v, j -> t);
		F[x][0] += gmax(F[j -> v][0], F[j -> v][1]);
		F[x][1] += F[j -> v][0]; 
	}
	if (x == R) F[x][1] = -INF;
}

int main() 
{
	scanf("%d", &n);
	int a;
	for (int i = 1; i <= n; ++i) 
	{
		scanf("%d%d", &A[i], &a);
		AddEdge(i, a, i);
		AddEdge(a, i, i);
	}
	memset(Visit, 0, sizeof(Visit));
	Ans = 0;
	for (int i = 1; i <= n; ++i) 
	{
		if (Visit[i]) continue;
		DFS(i, 0);
		R = R1;
		Solve(i, 0);
		Temp = gmax(F[i][0], F[i][1]);
		R = R2;
		Solve(i, 0);
		Temp = gmax(Temp, gmax(F[i][0], F[i][1]));
		Ans += Temp;
	}
	printf("%lld\n", Ans);
	return 0;
}