P3355 骑士共存问题

https://www.luogu.com.cn/record/96050988

Luogu/P3355/P3355.cpp

@@ -0,0 +1,136 @@
+#include <iostream>
+#include <algorithm>
+#include <queue>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 205,
+          M = N * N;
+const int INF = 0x3f3f3f3f;
+const int d[][2]{{1, 2}, {1, -2}, {-1, 2}, {-1, -2}, {2, 1}, {2, -1}, {-2, 1}, {-2, -1}};
+
+int n, m, s, t;
+int idx, head[M << 1], ver[M << 4], edge[M << 4], next[M << 4];
+int dis[M << 1], cur[M << 1];
+bool g[N][N];
+
+void add(int u, int v, int w) {
+    next[idx] = head[u];
+    ver[idx] = v;
+    edge[idx] = w;
+    head[u] = idx++;
+}
+
+int id(int x, int y) {
+    return x * n + y;
+}
+
+bool bfs() {
+    std::fill_n(dis, M << 1, 0);
+
+    std::queue<int> q;
+
+    q.emplace(s);
+    dis[s] = 1;
+    cur[s] = head[s];
+
+    while (!q.empty()) {
+        int u = q.front();
+        q.pop();
+
+        for (int i = head[u]; ~i; i = next[i]) {
+            int v = ver[i],
+                w = edge[i];
+
+            if (w && !dis[v]) {
+                dis[v] = dis[u] + 1;
+                cur[v] = head[v];
+
+                if (v == t) return true;
+
+                q.emplace(v);
+            }
+        }
+    }
+
+    return false;
+}
+
+int dinic(int u, int limit) {
+    if (u == t) return limit;
+
+    int flow = 0;
+    for (int i = cur[u]; ~i && flow < limit; i = next[i]) {
+        cur[u] = i;
+
+        int v = ver[i],
+            w = edge[i];
+
+        if (w && dis[v] == dis[u] + 1) {
+            int k = dinic(v, std::min(w, limit - flow));
+
+            if (!k) dis[v] = 0;
+
+            edge[i] -= k;
+            edge[i ^ 1] += k;
+            flow += k;
+        }
+    }
+
+    return flow;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    std::fill_n(head, M << 1, -1);
+
+    cin >> n >> m;
+
+    for (int i = 1, x, y; i <= m; i++) {
+        cin >> x >> y;
+
+        g[x][y] = true;
+    }
+
+    s = 0, t = id(n, n) + 1;
+
+    for (int i = 1; i <= n; i++) {
+        for (int j = 1; j <= n; j++) {
+            if (g[i][j]) continue;
+
+            if ((i + j) % 2) {
+                add(s, id(i, j), 1);
+                add(id(i, j), s, 0);
+
+                for (auto d : d) {
+                    int x = i + d[0],
+                        y = j + d[1];
+
+                    if (x < 1 || x > n || y < 1 || y > n || g[x][y]) continue;
+
+                    add(id(i, j), id(x, y), INF);
+                    add(id(x, y), id(i, j), 0);
+                }
+            } else {
+                add(id(i, j), t, 1);
+                add(t, id(i, j), 0);
+            }
+        }
+    }
+
+    int ans = 0, flow;
+
+    while (bfs()) {
+        while (flow = dinic(s, INF)) ans += flow;
+    }
+
+    std::cerr << ans << endl;
+
+    cout << n * n - m - ans << endl;
+
+    return 0;
+}