#1586. 【2022.9.21 NOIP 模拟赛】口粮输送

https://sjzezoj.com/submission/57466

S2OJ/1586/1586.cpp

@@ -0,0 +1,128 @@
+#include <iostream>
+#include <algorithm>
+#include <array>
+#include <numeric>
+#include <tuple>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int INF = 0x3f3f3f3f;
+
+class DSU {
+  private:
+    std::vector<int> fa;
+
+  public:
+    DSU(int _n = 0)
+        : fa(_n) {
+        std::iota(fa.begin(), fa.end(), 0);
+    }
+
+    int find(int x) {
+        return fa[x] == x ? x : fa[x] = find(fa[x]);
+    }
+
+    bool merge(int x, int y) {
+        x = find(x);
+        y = find(y);
+
+        fa[x] = y;
+
+        return x != y;
+    }
+};
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int t;
+
+    cin >> t;
+
+    while (t--) {
+        int n, m;
+
+        cin >> n >> m;
+
+        std::vector<int> a(n), b(n);
+        std::vector<std::tuple<int, int, int>> edges;
+        std::vector<bool> f(1 << n, false);
+
+        for (int i = 0, u, v, w; i < m; i++) {
+            cin >> u >> v >> w;
+
+            edges.emplace_back(u - 1, v - 1, w);
+        }
+
+        for (int i = 0; i < n; i++) {
+            cin >> a[i] >> b[i];
+        }
+
+        auto check = [&](int s) -> bool {
+            auto in_block = [&](int x) -> bool {
+                return s >> x & 1;
+            };
+
+            int sum = 0, root = 0;
+            DSU dsu(n);
+            std::vector<std::tuple<int, int, int>> block_edges;
+
+            for (auto& edge : edges) {
+                int u, v;
+
+                std::tie(u, v, std::ignore) = edge;
+
+                if (in_block(u) && in_block(v)) {
+                    block_edges.emplace_back(edge);
+                }
+            }
+
+            std::sort(block_edges.begin(), block_edges.end(), [](auto& lhs, auto& rhs) {
+                return std::get<2>(lhs) < std::get<2>(rhs);
+            });
+
+            for (int i = 0; i < n; i++) {
+                if (in_block(i)) sum += a[i] - b[i];
+            }
+
+            for (auto& edge : block_edges) {
+                int u, v, w;
+
+                std::tie(u, v, w) = edge;
+
+                if (dsu.merge(u, v)) sum -= w;
+            }
+
+            for (int i = 0; i < n; i++) {
+                if (in_block(i) && dsu.find(i) == i) {
+                    root = i;
+                }
+            }
+
+            for (int i = 0; i < n; i++) {
+                if (in_block(i) && dsu.find(i) != root) {
+                    return false;
+                }
+            }
+
+            return sum >= 0;
+        };
+
+        f[0] = true;
+        for (int s = 1; s < 1 << n; s++) {
+            f[s] = check(s);
+
+            for (int i = s; i; i = (i - 1) & s) {
+                f[s] = f[s] || f[i] && f[s ^ i];
+            }
+        }
+
+        cout << (f[(1 << n) - 1] ? "Yes" : "No") << endl;
+    }
+
+    return 0;
+}