【BZOJ1565】【NOI2009】植物大战僵尸

好久没写博客了

题目

题目在这里

思路&做法

没什么好说的

应该很容易看出是 最大闭合子图 吧？

不过要注意一下的是，这题 可能有植物是不可能被击溃的 ， 所以要先跑一遍 拓扑排序 把这些点排除掉

代码

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

using namespace std;

const int N = 810, M = 500010;

const int INF = 0x7F7F7F7F;

int n, m;

int val[40][40];
vector< pair<int, int> > vec[40][40];

bool vis[N]; //vis为0的点就是不可能击溃的点

struct edge
{	int from, to, flow, cap;
	edge() { }
	edge(int _1, int _2, int _3, int _4) : from(_1), to(_2), flow(_3), cap(_4) { }
};

struct Dinic
{	edge edges[M];
	int head[N], nxt[M], tot;

	int L, R;

	inline void init()
	{	memset(head, -1, sizeof(head));
		tot = 0;
	}

	void add_edge(int x, int y, int z)
	{	edges[tot] = edge(x, y, 0, z);
		nxt[tot] = head[x];
		head[x] = tot++;
		edges[tot] = edge(y, x, 0, 0);
		nxt[tot] = head[y];
		head[y] = tot++;
	}

	int s, t;

	int d[N];

	bool bfs()
	{	memset(d, -1, sizeof(d));
		queue<int> q;
		q.push(s);
		d[s] = 0;
		while (!q.empty())
		{	int x = q.front(); q.pop();
			for (int i = head[x]; ~i; i = nxt[i])
			{	edge & e = edges[i];
				if (vis[e.to] && e.cap > e.flow && d[e.to] == -1)
				{	d[e.to] = d[x] + 1;
					q.push(e.to);
				}
			}
		}
		return d[t] != -1;
	}

	int cur[N];

	int dfs(int x, int a)
	{	if (x == t || a == 0) return a;
		int flow = 0, f;
		for (int & i = cur[x]; ~i; i = nxt[i])
		{	edge & e = edges[i];
			if (vis[e.to] && d[e.to] == d[x] + 1 && (f = dfs(e.to, min(a, e.cap-e.flow))) > 0)
			{	e.flow += f;
				edges[i^1].flow -= f;
				a -= f;
				flow += f;
				if (!a) break;
			}
		}
		return flow;
	}

	int maxflow(int _s, int _t)
	{	s = _s, t = _t;
		int flow = 0;
		while (bfs())
		{	for (int i = L; i <= R; i++)
				cur[i] = head[i];
			flow += dfs(s, INF);
		}
		return flow;
	}
} dinic;

int S, T;

int in[N];

int num[N];

inline int id(int x, int y) { return (x-1)*m + y; }

void topo()
{	queue<int> q;
	for (int i = 1; i <= n*m; i++)
		if (!in[i]) q.push(i);
	while (!q.empty())
	{	int x = q.front(); q.pop();
		vis[x] = 1;
		for (int i = dinic.head[x]; ~i; i = dinic.nxt[i])
		{	edge & e = dinic.edges[i];
			if (e.to == S || e.to == T || in[e.to] == 0 || e.cap > e.flow)
				continue;
			if ((--in[e.to]) == 0)
				q.push(e.to);
		}
	}
}

void build()
{	S = n * m + 1, T = n * m + 2;
	dinic.init();
	dinic.L = 0, dinic.R = n * m + 2;
	for (int i = 1; i <= n; i++)
	{	for (int j = 1; j <= m; j++)
		{	if (val[i][j] > 0)
				dinic.add_edge(S, id(i, j), val[i][j]);
			if (val[i][j] < 0)
				dinic.add_edge(id(i, j), T, -val[i][j]);
			for (int k = 0; k < vec[i][j].size(); k++)
			{	dinic.add_edge(id(vec[i][j][k].first, vec[i][j][k].second), id(i, j), INF);
				in[id(vec[i][j][k].first, vec[i][j][k].second)]++;
			}
			if (j > 1)
				dinic.add_edge(id(i, j-1), id(i, j), INF),
				in[id(i, j-1)]++;
		}
	}
}

int main()
{	scanf("%d %d", &n, &m);
	for (int i = 1; i <= n; i++)
		for (int j = 1; j <= m; j++)
		{	int l;
			scanf("%d %d", &val[i][j], &l);
			num[id(i, j)] = val[i][j];
			for (int k = 1; k <= l; k++)
			{	int x, y;
				scanf("%d %d", &x, &y);
				x++, y++;
				vec[i][j].push_back(make_pair(x, y));
			}
		}
	build();
	topo();	
	int ans = 0;
	for (int i = 1; i <= n*m; i++)
		if (vis[i] && num[i] > 0)
			ans += num[i];
	vis[S] = vis[T] = 1;
	ans -= dinic.maxflow(S, T);
	printf("%d\n", ans);
	return 0;
}