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+// 1514. Path with Maximum Probability
+#include "leetcode.h"
+
+/*
+ * given an undirected weighted graph of 'n' nodes (0-indexed). represented by
+ * an edge list where 'edges[i] = [a, b]' is an undirected edge connecting the
+ * nodes 'a' and 'b' with a probability of success of traversing that edge
+ * 'succ_prob[i]'. given two nodes 'start, end', find the path with the maximum
+ * probability of success to go from 'start' to 'end' and return its success
+ * probability. if there is no path from 'start' to 'end', return 0. your answer
+ * will be accepted if it differs from the correct answer by at most '1e-5'
+ */
+
+class Solution {
+public:
+ double maxProbability(int n, vvd(int) & edges, vector<double> &succ_prob,
+ int start, int end) {
+ vector<vector<pair<int, double>>> vvp(n);
+ for (int i = 0; i < edges.size(); i++) {
+ vvp[edges[i][0]].push_back({edges[i][1], succ_prob[i]});
+ vvp[edges[i][1]].push_back({edges[i][0], succ_prob[i]});
+ }
+ vector<int> seen(n, 0);
+ priority_queue<pair<double, int>> pqp;
+ pqp.push({(double)1.0, start});
+ vector<double> mx(n, (double)0.0);
+ mx[start] = 1.0;
+ while (!pqp.empty()) {
+ auto top = pqp.top();
+ pqp.pop();
+ double prob_a = top.first;
+ int node = top.second;
+ if (!seen[node]) {
+ seen[node]++;
+ for (auto to : vvp[node]) {
+ if (mx[to.first] < to.second * prob_a) {
+ mx[to.first] = to.second * prob_a;
+ pqp.push({mx[to.first], to.first});
+ }
+ }
+ }
+ }
+ return mx[end];
+ }
+};
+
+int main() {
+ Solution obj;
+ vvd(int) e = {{0, 1}, {1, 2}, {0, 2}};
+ vector<double> sp1 = {0.5, 0.5, 0.2}, sp2 = {0.5, 0.5, 0.3};
+ printf("%f\n", obj.maxProbability(3, e, sp1, 0, 2)); // expect: 0.25000
+ printf("%f\n", obj.maxProbability(3, e, sp2, 0, 2)); // expect: 0.30000
+}