105 lines
2.7 KiB
C++
105 lines
2.7 KiB
C++
#include <bits/stdc++.h>
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using namespace std;
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const int INF = 0x3f3f3f3f;
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const int N = 1010;
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const int M = 200010;
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int n, m;
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int S, T, K;
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int h[N], rh[N];
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int e[M], w[M], ne[M], idx;
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int dist[N];
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bool st[N];
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int cnt[N];
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void add(int h[], int a, int b, int c) {
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e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx++;
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}
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// 只有点号和距离时，按距离由小到大排序
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struct N1 {
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int u, d;
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const bool operator<(const N1 &b) const {
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return b.d < d; // 谁的距离短谁靠前
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}
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};
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// 当有点号+距离+估值函数时，按估值函数值由小到大排序
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struct N2 {
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int u, d, f;
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const bool operator<(const N2 &b) const {
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return b.f < f;
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}
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};
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// 经典的Dijkstra,计算终点到图中其它所有点的最短路径
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void dijkstra() {
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priority_queue<N1> q;
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q.push({T, 0});
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memset(dist, 0x3f, sizeof dist);
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dist[T] = 0;
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while (q.size()) {
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N1 t = q.top();
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q.pop();
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int u = t.u;
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if (st[u]) continue;
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st[u] = true;
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for (int i = rh[u]; ~i; i = ne[i]) {
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int v = e[i];
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if (dist[v] > dist[u] + w[i]) {
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dist[v] = dist[u] + w[i];
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q.push({v, dist[v]});
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}
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}
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}
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}
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int astar() {
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priority_queue<N2> q;
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q.push({S, 0, dist[S]}); // 起点入队列
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while (q.size()) {
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int u = q.top().u;
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int d = q.top().d;
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q.pop();
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cnt[u]++; // u出队一次
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if (u == T && cnt[u] == K) return d; // 找到到终点的第K短路
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for (int i = h[u]; ~i; i = ne[i]) {
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int v = e[i];
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if (dist[v] < INF) // 如果是无效借力点，跳过
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q.push({v, d + w[i], d + w[i] + dist[v]}); // 点，距离，估值函数值
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}
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}
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return -1;
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}
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int main() {
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cin >> n >> m;
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memset(h, -1, sizeof h);//正向图
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memset(rh, -1, sizeof rh);//反向图
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while (m--) {
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int a, b, c;
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cin >> a >> b >> c;
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add(h, a, b, c); // 正向建图，常规逻辑
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add(rh, b, a, c); // 反向建图，用于获取终点t到图中所有点的最短路径。为估值函数作准备
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}
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cin >> S >> T >> K;
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// ① 如果起点与终点最开始是一样的，那么就需要入队列k+1次,这是一个坑
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if (S == T) K++;
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// ② 先跑一遍Dijkstra,方便计算出估值函数
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dijkstra();
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// ③ 利用Dijkstra计算出来的终点到任意点的值，再加上当前走过的距离，等于AStar的估值函数
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cout << astar() << endl; // A*算法
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return 0;
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}
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