From 2c7df38aa7251fc8364ce73387a2a941187844dc Mon Sep 17 00:00:00 2001
From: chayan das <110921638+Chayandas07@users.noreply.github.com>
Date: Tue, 27 Aug 2024 17:32:36 +0530
Subject: [PATCH] Create 1514. Path with Maximum Probability1

---
 1514. Path with Maximum Probability1 | 29 ++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100644 1514. Path with Maximum Probability1

diff --git a/1514. Path with Maximum Probability1 b/1514. Path with Maximum Probability1
new file mode 100644
index 0000000..bccaa0b
--- /dev/null
+++ b/1514. Path with Maximum Probability1	
@@ -0,0 +1,29 @@
+class Solution {
+public:
+    double maxProbability(int n, vector<vector<int>>& edges, vector<double>& succProb, int start_node, int end_node) {
+        vector<vector<pair<int, double>>> adj(n);
+        vector<double> dist(n, 0);  // Initialize distance/probability array with 0
+        // Build the adjacency list
+        for (int i = 0; i < edges.size(); i++) {
+            int u = edges[i][0], v = edges[i][1];
+            adj[u].emplace_back(v, succProb[i]);
+            adj[v].emplace_back(u, succProb[i]);
+        }
+        priority_queue<pair<double, int>> pq;
+        pq.push({1, start_node});  // Start with probability 1 for the start node
+        dist[start_node] = 0;      // Probability to reach start node is 1
+        while (!pq.empty()) {
+            auto [prob, node] = pq.top(); pq.pop();
+            if (node == end_node)
+                return prob;
+            for (auto& [neighbor, cost] : adj[node]) {
+                double newProb = prob * cost;
+                if (newProb > dist[neighbor]) {
+                    dist[neighbor] = newProb;
+                    pq.push({newProb, neighbor});
+                }
+            }
+        }
+        return 0;
+    }
+};