Ultraviolet A 10246-Asterix and Obelix (Shortest Path)

Ultraviolet A 10246-Asterix and Obelix

Question Link

Question: Given a graph, each vertex has a price and a price. Now there are Q queries. The minimum cost of each query from u to V is calculated in the following way, the cost of the path plus the cost of the maximum cost node on the path

Train of Thought: enumerate the most costly nodes, and then perform Dijkstra. During the process, ignore the points that are more costly than the enumeration points, and then update all the answers, after preprocessing, each query can be completed within O (1 ).

Code:

#include <cstdio>#include <cstring>#include <vector>#include <queue>using namespace std;const int MAXNODE = 85;const int MAXEDGE = 10005;typedef int Type;const Type INF = 0x3f3f3f3f;struct Edge {int u, v;Type dist;Edge() {}Edge(int u, int v, Type dist) {this->u = u;this->v = v;this->dist = dist;}};struct HeapNode {Type d;int u;HeapNode() {}HeapNode(Type d, int u) {this->d = d;this->u = u;}bool operator < (const HeapNode& c) const {return d > c.d;}};int n, m, q, cost[MAXNODE], ans[MAXNODE][MAXNODE];struct Dijkstra {int n, m;Edge edges[MAXEDGE];int first[MAXNODE];int next[MAXEDGE];bool done[MAXNODE];Type d[MAXNODE];int p[MAXNODE];void init(int n) {this->n = n;memset(first, -1, sizeof(first));m = 0;}void add_Edge(int u, int v, Type dist) {edges[m] = Edge(u, v, dist);next[m] = first[u];first[u] = m++;}void dijkstra(int s) {priority_queue<HeapNode> Q;for (int i = 0; i < n; i++) d[i] = INF;d[s] = 0;p[s] = -1;memset(done, false, sizeof(done));Q.push(HeapNode(0, s));while (!Q.empty()) {HeapNode x = Q.top(); Q.pop();int u = x.u;if (done[u]) continue;done[u] = true;for (int i = first[u]; i != -1; i = next[i]) {Edge& e = edges[i];if (cost[e.v] > cost[s]) continue;if (d[e.v] > d[u] + e.dist) {d[e.v] = d[u] + e.dist;p[e.v] = i;Q.push(HeapNode(d[e.v], e.v));}}}for (int i = 0; i < n; i++) {for (int j = 0; j < n; j++) {ans[i][j] = min(ans[i][j], d[i] + d[j] + cost[s]);}}}} gao;int main() {int cas = 0;int bo = 0;while (~scanf("%d%d%d", &n, &m, &q) && n) {if (bo) printf("\n");else bo = 1;gao.init(n);for (int i = 0; i < n; i++) scanf("%d", &cost[i]);int u, v, d;while (m--) {scanf("%d%d%d", &u, &v, &d);u--; v--;gao.add_Edge(u, v, d);gao.add_Edge(v, u, d);}memset(ans, INF, sizeof(ans));for (int i = 0; i < n; i++) gao.dijkstra(i);for (int i = 0; i < n; i++)for (int j = 0; j < n; j++)if (ans[i][j] == INF) ans[i][j] = -1;printf("Case #%d\n", ++cas);while (q--) {scanf("%d%d", &u, &v);u--; v--;printf("%d\n", ans[u][v]);}}return 0;}

Ultraviolet A 10246-Asterix and Obelix (Shortest Path)