bzoj 1412 [ZJOI2009]狼和羊的故事 最小割建图

题面

题目传送门

解法

把\(S\)集看作和羊连接，\(T\)看作和狼连接

然后就转化成了基本的最小割模型了

对于0的处理，可以把它放在羊和狼两排点的中间，由\(S\rightarrow\)羊\(\rightarrow0\rightarrow\)狼\(\rightarrow T\)

然后跑dinic即可

代码

#include <bits/stdc++.h>
#define inf 1 << 30
#define N 110
using namespace std;
template <typename node> void chkmax(node &x, node y) {x = max(x, y);}
template <typename node> void chkmin(node &x, node y) {x = min(x, y);}
template <typename node> void read(node &x) {
    x = 0; int f = 1; char c = getchar();
    while (!isdigit(c)) {if (c == '-') f = -1; c = getchar();}
    while (isdigit(c)) x = x * 10 + c - '0', c = getchar(); x *= f;
}
struct Edge {
    int next, num, c;
} e[N * N * N];
int dx[5] = {0, -1, 1, 0, 0}, dy[5] = {0, 0, 0, -1, 1};
int n, m, s, t, cnt, a[N][N], l[N * N], cur[N * N];
void add(int x, int y, int c) {
    e[++cnt] = (Edge) {e[x].next, y, c};
    e[x].next = cnt;
}
void Add(int x, int y, int c) {
    add(x, y, c), add(y, x, 0);
}
int calc(int x, int y) {
    return (x - 1) * m + y;
}
bool bfs(int s) {
    for (int i = 1; i <= t; i++) l[i] = -1;
    queue <int> q; q.push(s);
    while (!q.empty()) {
        int x = q.front(); q.pop();
        for (int p = e[x].next; p; p = e[p].next) {
            int k = e[p].num, c = e[p].c;
            if (c && l[k] == -1)
                l[k] = l[x] + 1, q.push(k);
        }
    }
    return l[t] != -1;
}
int dfs(int x, int lim) {
    if (x == t) return lim;
    int used = 0;
    for (int p = cur[x]; p; p = e[p].next) {
        int k = e[p].num, c = e[p].c;
        if (c && l[k] == l[x] + 1) {
            int w = dfs(k, min(c, lim - used));
            e[p].c -= w, e[p ^ 1].c += w; used += w;
            if (e[p].c) cur[x] = p;
            if (used == lim) return lim;
        }
    }
    if (!used) l[x] = -1;
    return used;
}
int dinic() {
    int ret = 0;
    while (bfs(s)) {
        for (int i = 0; i <= t; i++)
            cur[i] = e[i].next;
        ret += dfs(s, inf);
    }
    return ret;
}
int main() {
    read(n), read(m);
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++)
            read(a[i][j]);
    s = 0, t = cnt = n * m + 1;
    if (cnt % 2 == 0) cnt++;
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= m; j++) {
            int x = calc(i, j);
            if (a[i][j] == 1) Add(s, x, inf);
            if (a[i][j] == 2) {Add(x, t, inf); continue;}
            for (int k = 1; k <= 4; k++) {
                int tx = i + dx[k], ty = j + dy[k];
                if (!tx || !ty || tx > n || ty > m) continue;
                int y = calc(tx, ty);
                if (a[tx][ty] == 2) Add(x, y, 1);
                    else if (!a[tx][ty]) Add(x, y, 1);
            }
        }
    cout << dinic() << "\n";
    return 0;
}