LeetCode每日一题(1514. Path with Maximum Probability)

You are 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 succProb[i].

Given two nodes start and 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.

Example 1:

Input: n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.2], start = 0, end = 2
Output: 0.25000

Explanation: 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.

Example 2:

Input: n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.3], start = 0, end = 2
Output: 0.30000

Example 3:

Input: n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2
Output: 0.00000

Explanation: There is no path between 0 and 2.

Constraints:

• 2 <= n <= 10^4
• 0 <= start, end < n
• start != end
• 0 <= a, b < n
• a != b
• 0 <= succProb.length == edges.length <= 2*10^4
• 0 <= succProb[i] <= 1
• There is at most one edge between every two nodes.

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与计算最短路径的方法相同， 只不过把最短路径换成了最大概率， 广度优先更新每个节点的最大概率， 直到最后没有节点可更新为止

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use std::collections::HashMap;

impl Solution {
    
    pub fn max_probability(
        n: i32,
        edges: Vec<Vec<i32>>,
        succ_prob: Vec<f64>,
        start: i32,
        end: i32,
    ) -> f64 {
    
        let mut probs = vec![0f64; n as usize];
        let edges: HashMap<i32, Vec<(i32, f64)>> =
            edges
                .into_iter()
                .zip(succ_prob)
                .fold(HashMap::new(), |mut m, (l, p)| {
    
                    m.entry(l[0]).or_insert(Vec::new()).push((l[1], p));
                    m.entry(l[1]).or_insert(Vec::new()).push((l[0], p));
                    m
                });
        probs[start as usize] = 1f64;
        loop {
    
            let mut modified = false;
            for i in 0..n {
    
                if probs[i as usize] > 0f64 {
    
                    let cp = probs[i as usize];
                    if let Some(nexts) = edges.get(&i) {
    
                        for &(n, p) in nexts {
    
                            let np = cp * p;
                            if np > probs[n as usize] {
    
                                probs[n as usize] = np;
                                modified = true;
                            }
                        }
                    }
                }
            }
            if !modified {
    
                break;
            }
        }
        probs[end as usize]
    }
}