lc2714
带状态的Dijkstra算法求解允许最多跳过k条边权重的最短路径
状态为(节点, 剩余跳过次数)，每次转移可选择走边或跳过
typedef pair<int, int> PII;
typedef tuple<int, int, int> TIII;
class Solution {
public:
int shortestPathWithHops(int n, vector<vector<int>>& edges, int s, int d, int k) {
vector<vector<PII>> g(n);
for (auto& edge : edges) {
int a = edge[0], b = edge[1], c = edge[2];
g[a].emplace_back(b, c);
g[b].emplace_back(a, c);
}
vector<vector<int>> dist(n, vector<int>(k + 1, INT_MAX));
dist[s][0] = 0;
vector<vector<bool>> seen(n, vector<bool>(k + 1, false));
priority_queue<TIII, vector<TIII>, greater<TIII>> pq;
pq.emplace(0, s, 0);
while (!pq.empty()) {
auto [td, u, tk] = pq.top();
pq.pop();
if (seen[u][tk]) continue;
seen[u][tk] = true;
for (auto& [v, nd] : g[u]) {
if (dist[v][tk] > td + nd) {
dist[v][tk] = td + nd;
pq.emplace(td + nd, v, tk);
}
if (tk < k and dist[v][tk + 1] > td) {
dist[v][tk + 1] = td;
pq.emplace(td, v, tk + 1);
}
}
}
return *min_element(dist[d].begin(), dist[d].end());
}
};