#1733. 【NOIP 2022 模拟赛 by AzusaCat】小黄鸭与最短路（path）

https://sjzezoj.com/submission/63370

S2OJ/1733/1733.cpp

@@ -0,0 +1,118 @@
+#include <iostream>
+#include <algorithm>
+#include <array>
+#include <limits>
+#include <queue>
+#include <tuple>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 5e4 + 5,
+          Q = 3e5 + 5;
+
+int n, q, k, l;
+long long t;
+std::tuple<int, int, int> edges[Q];
+std::vector<int> ans;
+std::array<std::vector<std::pair<int, long long>>, N> g;
+std::array<bool, N> vis;
+std::array<long long, N> dist;
+
+void dijkstra() {
+    std::fill(vis.begin(), vis.end(), false);
+    std::fill(dist.begin(), dist.end(), std::numeric_limits<long long>::max() / 3);
+
+    std::priority_queue<std::pair<long long, int>, std::vector<std::pair<long long, int>>, std::greater<std::pair<long long, int>>> q;
+
+    q.emplace(0, 1);
+    dist[1] = 0;
+
+    while (!q.empty()) {
+        int u = q.top().second;
+        q.pop();
+
+        if (vis[u]) continue;
+        vis[u] = true;
+
+        for (auto e : g[u]) {
+            int v = e.first;
+            long long w = e.second;
+
+            if (dist[v] > dist[u] + w) {
+                dist[v] = dist[u] + w;
+                q.emplace(dist[v], v);
+            }
+        }
+    }
+}
+
+bool check(int l, int r) {
+    std::fill(g.begin(), g.end(), std::vector<std::pair<int, long long>>());
+
+    for (int i = l; i <= r; i++) {
+        int u = std::get<0>(edges[i]),
+            v = std::get<1>(edges[i]);
+        long long w = std::get<2>(edges[i]);
+
+        g[u].emplace_back(v, w);
+        g[v].emplace_back(u, w);
+    }
+
+    dijkstra();
+
+    return dist[n] <= t;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> q >> t;
+
+    k = std::__lg(q) + 1;
+
+    for (int i = 1; i <= q; i++) {
+        cin >> std::get<0>(edges[i]) >> std::get<1>(edges[i]) >> std::get<2>(edges[i]);
+    }
+
+    while (l <= q) {
+        bool flag = false;
+
+        for (int i = 0; i <= k; i++) {
+            int r = std::min(l + (1 << i), q);
+            if (check(l, r)) {
+                int ql = i ? l + (1 << i - 1) : 0,
+                    qr = l + (1 << i),
+                    res = qr;
+
+                while (ql <= qr) {
+                    int mid = (ql + qr) >> 1;
+                    if (check(l, mid)) {
+                        qr = mid - 1;
+                        res = mid;
+                    } else {
+                        ql = mid + 1;
+                    }
+                }
+
+                ans.emplace_back(res);
+                l = res + 1;
+                flag = true;
+
+                break;
+            }
+
+            if (r == q) break;
+        }
+
+        if (!flag) break;
+    }
+
+    cout << ans.size() << endl;
+    for (int x : ans) cout << x << ' ';
+    cout << endl;
+
+    return 0;
+}