go: add «1514. Path with Maximum Probability»

Signed-off-by: Matej Focko <me@mfocko.xyz>

go/path-with-maximum-probability.go

@@ -0,0 +1,59 @@
+package main
+
+import (
+	"cmp"
+
+	pq "github.com/emirpasic/gods/v2/queues/priorityqueue"
+)
+
+func maxProbability(n int, edges [][]int, succProb []float64, start int, end int) float64 {
+	type Edge struct {
+		v int
+		p float64
+	}
+
+	makeGraph := func() [][]Edge {
+		g := make([][]Edge, n)
+
+		for i, edge := range edges {
+			u, v, p := edge[0], edge[1], succProb[i]
+
+			g[u] = append(g[u], Edge{v: v, p: p})
+			g[v] = append(g[v], Edge{v: u, p: p})
+		}
+
+		return g
+	}
+	g := makeGraph()
+
+	type Entry struct {
+		probability float64
+		u           int
+	}
+	byProbability := func(a, b Entry) int {
+		return -cmp.Compare(a.probability, b.probability)
+	}
+
+	maxP := make([]float64, n)
+	q := pq.NewWith(byProbability)
+
+	maxP[start] = 1
+	q.Enqueue(Entry{probability: maxP[start], u: start})
+
+	for candidate, ok := q.Dequeue(); ok; candidate, ok = q.Dequeue() {
+		if candidate.u == end {
+			return candidate.probability
+		}
+
+		for _, edge := range g[candidate.u] {
+			p := candidate.probability * edge.p
+
+			if p > maxP[edge.v] {
+				maxP[edge.v] = p
+				q.Enqueue(Entry{probability: p, u: edge.v})
+			}
+		}
+	}
+
+	return 0
+}