P7515 [省选联考 2021 A 卷] 矩阵游戏

https://www.luogu.com.cn/record/90003104

Luogu/P7515/P7515.cpp

@@ -0,0 +1,111 @@
+#include <iostream>
+#include <queue>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int MAX = 1e6;
+
+void solve() {
+    int n, m;
+
+    cin >> n >> m;
+
+    std::vector<std::vector<int>>
+        a(n, std::vector<int>(m, 0)),
+        b(n - 1, std::vector<int>(m - 1, 0));
+    std::vector<std::vector<std::pair<int, int>>>
+        g(n + m, std::vector<std::pair<int, int>>());
+
+    for (auto &i : b) {
+        for (auto &x : i) {
+            cin >> x;
+        }
+    }
+
+    for (int i = n - 2; i >= 0; i--) {
+        for (int j = m - 2; j >= 0; j--) {
+            a[i][j] = b[i][j] - a[i + 1][j] - a[i + 1][j + 1] - a[i][j + 1];
+        }
+    }
+
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < m; j++) {
+            if ((i + j) & 1) {
+                g[i].emplace_back(j + n, a[i][j]);
+                g[j + n].emplace_back(i, MAX - a[i][j]);
+            } else {
+                g[j + n].emplace_back(i, a[i][j]);
+                g[i].emplace_back(j + n, MAX - a[i][j]);
+            }
+        }
+    }
+
+    std::vector<long long> dist(n + m);
+
+    auto spfa = [&]() -> bool {
+        std::queue<int> q;
+        std::vector<bool> vis(n + m, true);
+        std::vector<int> cnt(n + m);
+
+        for (int i = 0; i < n + m; i++) {
+            q.emplace(i);
+        }
+
+        while (!q.empty()) {
+            int u = q.front();
+            q.pop();
+
+            vis[u] = false;
+
+            for (auto e : g[u]) {
+                int v = e.first,
+                    w = e.second;
+
+                if (dist[v] > dist[u] + w) {
+                    dist[v] = dist[u] + w;
+
+                    if (!vis[v]) {
+                        if (++cnt[v] > n + m) return false;
+
+                        vis[v] = true;
+                        q.emplace(v);
+                    }
+                }
+            }
+        }
+
+        return true;
+    };
+
+    if (!spfa()) {
+        cout << "NO" << endl;
+
+        return;
+    }
+
+    cout << "YES" << endl;
+
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < m; j++) {
+            cout << a[i][j] + ((i + j) & 1 ? dist[i] - dist[j + n] : dist[j + n] - dist[i]) << ' ';
+        }
+
+        cout << endl;
+    }
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int t;
+
+    cin >> t;
+
+    while (t--) solve();
+
+    return 0;
+}