72 lines
2.1 KiB
C++
72 lines
2.1 KiB
C++
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#include <bits/stdc++.h>
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using namespace std;
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const int N = 10010, M = N << 1, K = 110;
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// 链式前向星
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int e[M], h[N], idx, w[M], ne[M];
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void add(int a, int b, int c = 0) {
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e[idx] = b, ne[idx] = h[a], w[idx] = c, h[a] = idx++;
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}
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// 入队列的结构体
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struct Node {
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int id; // 节点号
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int r; // %k的余数
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};
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int dis[N][K]; // 最短路径
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int n, m, k; // n个节点，m条边，时间是k的整数倍，即 %k=0
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bool bfs(int mid) {
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memset(dis, -1, sizeof dis);
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queue<Node> q;
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dis[n][0] = mid * k;
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q.push({n, 0});
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while (q.size()) {
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int u = q.front().id;
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int r = q.front().r;
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q.pop();
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if (dis[u][r] == 0) continue; // 反着走，距离为0，就不需要继续走了,剪枝
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for (int i = h[u]; ~i; i = ne[i]) {
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int v = e[i]; // 前序节点
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int p = (r - 1 + k) % k; // 前序节点合法状态
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if (~dis[v][p]) continue; // 如果前序点的合法状态不等于-1，表示已经被宽搜走过了，根据宽搜的理论，就是已经取得了最短距离，不需要再走
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if (dis[u][r] - 1 < w[i]) continue; // 现在的最短距离是dis[u][r],那么前序的距离应该是dis[u][r]-1,那么，如果dis[u][r]-1<w[i],就是表示到达时，开放时间未到，无法能行
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// 修改合法前序点距离，为当前最小距离减1
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dis[v][p] = dis[u][r] - 1;
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// 入队列继续扩展
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q.push({v, p});
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}
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}
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if (dis[1][0] == -1)
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return false;
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else
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return true;
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}
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int main() {
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memset(h, -1, sizeof h);
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cin >> n >> m >> k;
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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(b, a, c);
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}
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int l = 0, r = (1e6 + 1e4) / k, ans = -1;
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while (l < r) {
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int mid = l + r >> 1;
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if (bfs(mid)) {
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ans = mid * k;
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r = mid;
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} else
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l = mid + 1;
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}
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cout << ans << endl;
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return 0;
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}
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