Sync LeetCode submission Runtime - 56 ms (39.85%), Memory - 74.6 MB (21.30%)

Author: koralkulacoglu

LeetCode/1325-path-with-maximum-probability/README.md

@@ -0,0 +1,49 @@
+<p>You are given an undirected weighted graph of&nbsp;<code>n</code>&nbsp;nodes (0-indexed), represented by an edge list where&nbsp;<code>edges[i] = [a, b]</code>&nbsp;is an undirected edge connecting the nodes&nbsp;<code>a</code>&nbsp;and&nbsp;<code>b</code>&nbsp;with a probability of success of traversing that edge&nbsp;<code>succProb[i]</code>.</p>
+
+<p>Given two nodes&nbsp;<code>start</code>&nbsp;and&nbsp;<code>end</code>, find the path with the maximum probability of success to go from&nbsp;<code>start</code>&nbsp;to&nbsp;<code>end</code>&nbsp;and return its success probability.</p>
+
+<p>If there is no path from&nbsp;<code>start</code>&nbsp;to&nbsp;<code>end</code>, <strong>return&nbsp;0</strong>. Your answer will be accepted if it differs from the correct answer by at most <strong>1e-5</strong>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/20/1558_ex1.png" style="width: 187px; height: 186px;" /></strong></p>
+
+<pre>
+<strong>Input:</strong> n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.2], start = 0, end = 2
+<strong>Output:</strong> 0.25000
+<strong>Explanation:</strong>&nbsp;There are two paths from start to end, one having a probability of success = 0.2 and the other has 0.5 * 0.5 = 0.25.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/20/1558_ex2.png" style="width: 189px; height: 186px;" /></strong></p>
+
+<pre>
+<strong>Input:</strong> n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.3], start = 0, end = 2
+<strong>Output:</strong> 0.30000
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/09/20/1558_ex3.png" style="width: 215px; height: 191px;" /></strong></p>
+
+<pre>
+<strong>Input:</strong> n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2
+<strong>Output:</strong> 0.00000
+<strong>Explanation:</strong>&nbsp;There is no path between 0 and 2.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>2 &lt;= n &lt;= 10^4</code></li>
+	<li><code>0 &lt;= start, end &lt; n</code></li>
+	<li><code>start != end</code></li>
+	<li><code>0 &lt;= a, b &lt; n</code></li>
+	<li><code>a != b</code></li>
+	<li><code>0 &lt;= succProb.length == edges.length &lt;= 2*10^4</code></li>
+	<li><code>0 &lt;= succProb[i] &lt;= 1</code></li>
+	<li>There is at most one edge between every two nodes.</li>
+</ul>

LeetCode/1325-path-with-maximum-probability/solution.cpp

@@ -0,0 +1,35 @@
+class Solution {
+public:
+    double maxProbability(int n, vector<vector<int>>& edges, vector<double>& succProb, int start_node, int end_node) {
+        int m = edges.size();
+        unordered_map<int, vector<pair<int, double>>> graph;
+        for (int i=0; i<m; i++) {
+            graph[edges[i][0]].push_back({edges[i][1], succProb[i]});
+            graph[edges[i][1]].push_back({edges[i][0], succProb[i]});
+        }
+
+        vector<double> probs(n, 0);
+        priority_queue<pair<double, int>> pq;
+        probs[start_node] = 1;
+        pq.push({1, start_node});
+        while (!pq.empty()) {
+            auto [prob, node] = pq.top();
+            if (node == end_node) return prob;
+            pq.pop();
+
+            if (prob < probs[node]) continue;
+
+            for (auto& neigh : graph[node]) {
+                int newNode = neigh.first;
+                double newProb = prob * neigh.second;
+
+                if (newProb > probs[newNode]) {
+                    probs[newNode] = newProb;
+                    pq.push({newProb, newNode});
+                }
+            }
+        }
+
+        return probs[end_node];
+    }
+};