LeetCode Daily: Path with Maximum Probability Solution in Java | August 27, 2024
🔍 LeetCode Problem of the Day: Path with Maximum Probability
Today, we're solving the "Path with Maximum Probability" problem in Java as part of the LeetCode daily challenge. This problem involves finding the path between two nodes in a graph that maximizes the probability of success.
👉 Problem Link: https://leetcode.com/problems/path-wi...
👉 Solution: Pinned on the comments
🌟 Problem Description:
Given a graph where each edge has an associated success probability, the goal is to find the path from the start node to the end node that maximizes the success probability. This problem can be solved using a variation of Dijkstra's algorithm, focusing on probabilities instead of distances.
🔑 Key Points:
Graph Representation: The graph is represented using an adjacency list, where each node points to its neighbors along with the probability of successfully traversing that edge.
Dijkstra's Algorithm: A priority queue is used to explore the nodes in a greedy manner, always expanding the node with the highest current probability.
Probability Update: As each node is explored, the algorithm checks if the probability of reaching a neighboring node through the current path is greater than the previously known probability.
📝 Code Explanation:
Graph Construction: The makeGraph method initializes the graph and populates it with nodes and their corresponding edges.
Dijkstra's Application: The djikstras method applies a modified Dijkstra’s algorithm, where the priority queue is used to track the highest probability paths.
Final Result: The maxProbability method returns the maximum probability of reaching the destination from the start node.
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