[最小割] ARC 074 F - Lotus Leaves

最新推荐文章于 2020-10-03 16:47:18 发布

原创最新推荐文章于 2020-10-03 16:47:18 发布 · 410 阅读

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本文介绍了一种利用最小割算法解决特定路径问题的方法。通过建立一个包含源点和汇点的图，并对每行每列设置节点，连接行内的荷叶节点，问题转化为寻找最少的节点移除数量以断开源点与汇点的连接。文章提供了完整的C++代码实现，展示了如何通过最大流算法来计算最小割。

$Solution$

这样建图：对每一行每一列都建一个点，连向行内的荷叶。
那这道题就相当于删去最少的点使得源汇点不连通。
按这里一样建图就好了。
~~又忘记写当前弧优化了~~

#include <bits/stdc++.h>
using namespace std;

const int N = 233;
const int INF = 1 << 28;

struct edge {
    int to, cap, next;
    edge(int t = 0, int c = 0, int n = 0):to(t), next(n), cap(c) {}
};
edge G[N * N * 10];
int head[N * N], cur[N * N];
int Gcnt, n, m, S, T, clc, cnt, ans;
char mp[N][N];
int dis[N * N], vis[N * N];
int in[N][N], out[N][N];
int r[N], c[N];
queue<int> Q;

inline void AddEdge(int from, int to, int cap) {
    G[++Gcnt] = edge(to, cap, head[from]); head[from] = Gcnt;
    G[++Gcnt] = edge(from, 0, head[to]); head[to] = Gcnt;
}
inline bool bfs(int S, int T) {
    dis[S] = 0; Q.push(S); vis[S] = ++clc;
    while (!Q.empty()) {
        int u = Q.front(); Q.pop();
        for (int i = head[u]; i; i = G[i].next) {
            edge &e = G[i];
            if (e.cap && vis[e.to] != clc) {
                dis[e.to] = dis[u] + 1;
                vis[e.to] = clc; Q.push(e.to);
            }
        }
    }
    return vis[T] == clc;
}
inline int dfs(int u, int a) {
    int flow = 0, f;
    if (u == T || a == 0) return a;
    for (int &i = cur[u]; i; i = G[i].next) {
        edge &e = G[i];
        if (e.cap && dis[e.to] == dis[u] + 1
                && (f = dfs(e.to, min(a, e.cap))) > 0) {
            e.cap -= f; flow += f;
            G[i ^ 1].cap += f; a -= f;
            if (a == 0) break;
        }
    }
    return flow;
}
inline int MaxFlow(int S, int T) {
    int flow = 0;
    while (bfs(S, T)) {
        for (int i = 1; i <= cnt; i++) cur[i] = head[i];
        flow += dfs(S, INF);
    }
    return flow;
}

int main(void) {
    freopen("1.in", "r", stdin);
    freopen("1.out", "w", stdout);
    Gcnt = 1;
    scanf("%d %d\n", &n, &m);
    S = ++cnt; T = ++cnt;
    for (int i = 1; i <= n; i++) {
        scanf("%s", mp[i] + 1);
        for (int j = 1; j <= m; j++)
            if (mp[i][j] == 'o') {
                in[i][j] = ++cnt;
                out[i][j] = ++cnt;
            }
    }
    for (int i = 1; i <= n; i++) r[i] = ++cnt;
    for (int i = 1; i <= m; i++) c[i] = ++cnt;
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++)
            if (mp[i][j] == 'S') {
                AddEdge(S, r[i], INF);
                AddEdge(S, c[j], INF);
            } else if (mp[i][j] == 'T') {
                AddEdge(r[i], T, INF);
                AddEdge(c[j], T, INF);
            } else if (mp[i][j] == 'o') {
                AddEdge(r[i], in[i][j], INF);
                AddEdge(c[j], in[i][j], INF);
                AddEdge(in[i][j], out[i][j], 1);
                AddEdge(out[i][j], r[i], INF);
                AddEdge(out[i][j], c[j], INF);
            }
    ans = MaxFlow(S, T);
    if (ans > n * m) ans = -1;
    cout << ans << endl;
    return 0;
}