分层图最短路

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 = edge0, b = edge1, c = edge2;

ga.emplace_back(b, c);

gb.emplace_back(a, c);

}

vector<vector<int>> dist(n, vector<int>(k + 1, INT_MAX));

dists0 = 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 (seenutk) continue;

seenutk = true;

for (auto& v, nd : gu) {

if (distvtk > td + nd) {

distvtk = td + nd;

pq.emplace(td + nd, v, tk);

}

if (tk < k and distvtk + 1 > td) {

distvtk + 1 = td;

pq.emplace(td, v, tk + 1);

}

}

}

return *min_element(distd.begin(), distd.end());

}

};