feat(1514): Medium

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.

internal/Leetcode/1514/1514.go

@@ -0,0 +1,55 @@
+package _1514
+
+import (
+	"container/heap"
+)
+
+func maxProbability(n int, edges [][]int, succProb []float64, start_node int, end_node int) float64 {
+	// 2 dim array with map
+	graph := make([]map[int]float64, n)
+	for i := range graph {
+		graph[i] = make(map[int]float64)
+	}
+	//maxHeap as priority queue
+	maxHeap := make(PriorityQueue, 0)
+	//init graph
+	maxHeap.Push(&Item{value: start_node, priority: 1})
+
+	seen := make([]bool, n)
+
+	for i := range edges {
+		u := edges[i][0]
+		v := edges[i][1]
+		prob := succProb[i]
+		//graph = append(graph, map[int]float64{v: prob})
+		//graph = append(graph, map[int]float64{u: prob})
+		graph[u][v] = prob
+		graph[v][u] = prob
+
+	}
+
+	for maxHeap.Len() > 0 {
+		item := heap.Pop(&maxHeap).(*Item)
+		prob := item.priority
+		u := item.value
+
+		if u == end_node {
+			return prob
+		}
+
+		if seen[u] {
+			continue
+		}
+
+		seen[u] = true
+
+		for nextNode, edgeProb := range graph[u] {
+			if seen[nextNode] {
+				continue
+			}
+			heap.Push(&maxHeap, &Item{value: nextNode, priority: prob * edgeProb})
+		}
+	}
+
+	return 0.0
+}

internal/Leetcode/1514/1514_test.go

@@ -0,0 +1,39 @@
+package _1514
+
+import (
+	"testing"
+)
+
+func Test_maxProbability(t *testing.T) {
+	type args struct {
+		n          int
+		edges      [][]int
+		succProb   []float64
+		start_node int
+		end_node   int
+	}
+	tests := []struct {
+		name string
+		args args
+		want float64
+	}{
+		{
+			name: "test case 1",
+			args: args{
+				n:          3,
+				edges:      [][]int{{0, 1}, {1, 2}, {0, 2}},
+				succProb:   []float64{0.5, 0.5, 0.2},
+				start_node: 0,
+				end_node:   2,
+			},
+			want: 0.25,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := maxProbability(tt.args.n, tt.args.edges, tt.args.succProb, tt.args.start_node, tt.args.end_node); got != tt.want {
+				t.Errorf("maxProbability() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}

internal/Leetcode/1514/PriorityQueue.go

@@ -0,0 +1,34 @@
+package _1514
+
+// An Item is something we manage in a priority queue.
+type Item struct {
+	value    int
+	priority float64
+}
+
+// A PriorityQueue implements heap.Interface and holds Items.
+type PriorityQueue []*Item
+
+func (pq PriorityQueue) Len() int { return len(pq) }
+
+func (pq PriorityQueue) Less(i, j int) bool {
+	// We want Pop to give us the highest, not lowest, priority so we use greater than here.
+	return pq[i].priority > pq[j].priority
+}
+
+func (pq PriorityQueue) Swap(i, j int) {
+	pq[i], pq[j] = pq[j], pq[i]
+}
+
+func (pq *PriorityQueue) Push(x interface{}) {
+	item := x.(*Item)
+	*pq = append(*pq, item)
+}
+
+func (pq *PriorityQueue) Pop() interface{} {
+	old := *pq
+	n := len(old)
+	item := old[n-1]
+	*pq = old[0 : n-1]
+	return item
+}