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Problem solution · Java

Path with Maximum Probability

Path with Maximum Probability: a Java solution using breadth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Breadth-first search
Source
walkccc LeetCode Solutions
Length
41 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Breadth-first search

For Path with Maximum Probability, the implementation explores reachable states in layers, which is the standard shape for unweighted shortest paths and minimum-step transitions.

  1. Model each valid configuration as a state and each legal move as an edge.
  2. Seed the queue with the starting state and mark it immediately.
  3. Expand each state once, recording distance or reachability for unseen neighbours.

Code notes

  • 41 lines of Java from the credited upstream file 1514.java.
  • The implementation visibly relies on sequence storage, work queue.
  • 3 loop blocks detected.

Complexity

Verify that each state and transition is processed only a bounded number of times; that determines the traversal cost.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codePath with Maximum Probability · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public double maxProbability(int n, int[][] edges, double[] succProb, int start, int end) {    // {a: [(b, probability_ab)]}    List<Pair<Integer, Double>>[] graph = new List[n];    // (the probability to reach u, u)    Queue<Pair<Double, Integer>> maxHeap =        new PriorityQueue<>((a, b) -> Double.compare(b.getKey(), a.getKey())) {          { offer(new Pair<>(1.0, start)); }        };    boolean[] seen = new boolean[n];    Arrays.setAll(graph, i -> new ArrayList<>());     for (int i = 0; i < edges.length; ++i) {      final int u = edges[i][0];      final int v = edges[i][1];      final double prob = succProb[i];      graph[u].add(new Pair<>(v, prob));      graph[v].add(new Pair<>(u, prob));    }     while (!maxHeap.isEmpty()) {      final double prob = maxHeap.peek().getKey();      final int u = maxHeap.poll().getValue();      if (u == end)        return prob;      if (seen[u])        continue;      seen[u] = true;      for (Pair<Integer, Double> node : graph[u]) {        final int nextNode = node.getKey();        final double edgeProb = node.getValue();        if (seen[nextNode])          continue;        maxHeap.add(new Pair<>(prob * edgeProb, nextNode));      }    }     return 0;  }}

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