【BZOJ1565】[NOI2009]植物大战僵尸【最大权闭合图】【拓扑排序】

【题目链接】

很容易看出是最大权闭合图，主要是处理环的情况。

我们发现如果按照最大全闭合图那样建图，那么环上点不能取，而且指向的环上的点也不能取，这就麻烦了...所以我们拓扑序按照反向图找环就行了。

/* Pigonometry */
#include <cstdio>
#include <algorithm>

using namespace std;

const int maxn = 1005, maxm = 500005, maxq = 10000, inf = 0x3f3f3f3f;

int n, m, head[maxn], cur[maxn], cnt, A[maxn], du[maxn], depth[maxn], bg, ed, q[maxq];
bool vis[maxn];

struct _edge {
	int v, w, next;
} g[maxm << 1];

inline int iread() {
	int f = 1, x = 0; char ch = getchar();
	for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;
	for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
	return f * x;
}

inline void add(int u, int v, int w) {
	g[cnt] = (_edge){v, w, head[u]};
	head[u] = cnt++;
}

inline void insert(int u, int v, int w) {
	add(u, v, w); add(v, u, 0);
}

inline void topo() {
	int h = 0, t = 0, u, i;
	for(int i = n * m; i; i--) if(!du[i]) vis[q[t++] = i] = 1;
	while(h != t) for(i = head[u = q[h++]]; ~i; i = g[i].next) if(!g[i].w) {
		du[g[i].v]--;
		if(!du[g[i].v]) vis[q[t++] = g[i].v] = 1;
	}
}

inline bool bfs() {
	for(int i = 0; i <= ed; i++) depth[i] = -1;
	int h = 0, t = 0, u, i; depth[q[t++] = bg] = 1;
	while(h != t) for(i = head[u = q[h++]]; ~i; i = g[i].next) if(g[i].w && !~depth[g[i].v]) {
		depth[g[i].v] = depth[u] + 1;
		if(g[i].v == ed) return 1;
		q[t++] = g[i].v;
	}
	return 0;
}

inline int dfs(int x, int flow) {
	if(x == ed) return flow;
	int left = flow;
	for(int i = cur[x]; ~i; i = g[i].next) if(g[i].w && depth[g[i].v] == depth[x] + 1) {
		int tmp = dfs(g[i].v, min(left, g[i].w));
		left -= tmp; g[i].w -= tmp; g[i ^ 1].w += tmp;
		if(g[i].w) cur[x] = i;
		if(!left) return flow;
	}
	if(left == flow) depth[x] = -1;
	return flow - left;
}

int main() {
	n = iread(); m = iread(); bg = 0; ed = n * m + 1;
	for(int i = 0; i <= ed; i++) head[i] = -1; cnt = 0;

	for(int i = 1; i <= n; i++) for(int j = 1; j <= m; j++) {
		int now = (i - 1) * m + j;
		A[now] = iread();
		if(j != m) {
			insert(now, now + 1, inf);
			du[now]++;
		}
		for(int k = iread(); k; k--) {
			int u = iread(), v = iread(); u++; v++;
			insert((u - 1) * m + v, now, inf);
			du[(u - 1) * m + v]++;
		}
	}

	topo();

	int ans = 0;
	for(int i = n * m; i; i--) if(vis[i]) {
		if(A[i] > 0) ans += A[i], insert(bg, i, A[i]);
		else insert(i, ed, -A[i]);
	}

	while(bfs()) {
		for(int i = 0; i <= ed; i++) cur[i] = head[i];
		ans -= dfs(bg, inf);
	}

	printf("%d\n", ans);
	return 0;
}