added problem 1514

Author: SHA65536

problems/problem1514/path_max_prob.go

@@ -0,0 +1,70 @@
+package problem1514
+
+/*
+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.
+*/
+
+type Pair struct {
+	Prob float64
+	Pos  int
+}
+
+func maxProbability(size int, edges [][]int, succProb []float64, start int, end int) float64 {
+	var res float64
+	// Building graph
+	var graph = make([][]Pair, size)
+	for i := range edges {
+		graph[edges[i][0]] = append(graph[edges[i][0]], Pair{succProb[i], edges[i][1]})
+		graph[edges[i][1]] = append(graph[edges[i][1]], Pair{succProb[i], edges[i][0]})
+	}
+	// Cache for probability
+	var seen = make([]float64, size)
+	// BFS buckets
+	var cur, nxt []Pair
+	cur = []Pair{{1, start}}
+	// Run BFS until we run out of paths
+	for len(cur) > 0 {
+		nxt = nxt[:0]
+		// For each node in our list
+		for _, c := range cur {
+			// Check if we already visited with higher probability
+			if seen[c.Pos] > c.Prob {
+				continue
+			}
+			// For each potential path from there
+			for _, n := range graph[c.Pos] {
+				temp := Pair{c.Prob * n.Prob, n.Pos}
+				if n.Pos == end {
+					// Check we reached the end
+					res = max(res, temp.Prob)
+				} else {
+					// Check if we're going to a visited node with higher
+					// probability
+					if seen[temp.Pos] >= temp.Prob {
+						continue
+					}
+					// Record the current probability
+					seen[temp.Pos] = temp.Prob
+					// Add next node to bucket
+					nxt = append(nxt, temp)
+				}
+			}
+		}
+		// Switch buckets
+		cur, nxt = nxt, cur
+	}
+	return res
+}
+
+func max(a, b float64) float64 {
+	if a > b {
+		return a
+	}
+	return b
+}

problems/problem1514/path_max_prob_test.go

@@ -0,0 +1,60 @@
+package problem1514
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+type TestCase struct {
+	N          int
+	Edges      [][]int
+	Prob       []float64
+	Start, End int
+	Expected   float64
+}
+
+var TestCases = []TestCase{
+	{
+		N:     3,
+		Edges: [][]int{{0, 1}, {1, 2}, {0, 2}},
+		Prob:  []float64{0.5, 0.5, 0.2},
+		Start: 0, End: 2,
+		Expected: 0.25,
+	},
+	{
+		N:     3,
+		Edges: [][]int{{0, 1}, {1, 2}, {0, 2}},
+		Prob:  []float64{0.5, 0.5, 0.3},
+		Start: 0, End: 2,
+		Expected: 0.3,
+	},
+	{
+		N:     3,
+		Edges: [][]int{{0, 1}},
+		Prob:  []float64{0.5},
+		Start: 0, End: 2,
+		Expected: 0,
+	},
+}
+
+const precision float64 = 0.00001
+
+func TestMaxProbabilityPath(t *testing.T) {
+	assert := assert.New(t)
+
+	for _, tc := range TestCases {
+		want := tc.Expected
+		got := maxProbability(tc.N, tc.Edges, tc.Prob, tc.Start, tc.End)
+		assert.InDelta(want, got, precision, fmt.Sprintf("%+v", tc))
+	}
+}
+
+func BenchmarkMaxProbabilityPath(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		for _, tc := range TestCases {
+			maxProbability(tc.N, tc.Edges, tc.Prob, tc.Start, tc.End)
+		}
+	}
+}

readme.md

@@ -426,6 +426,7 @@ Each problem is in it's own directory, with test files. There are helper package
 | 1496 | [Path Crossing](https://leetcode.com/problems/path-crossing) | [My Solution](./problems/problem1496) | ✅ |
 | 1498 | [Number of Subsequences That Satisfy the Given Sum Condition](https://leetcode.com/problems/number-of-subsequences-that-satisfy-the-given-sum-condition) | [My Solution](./problems/problem1498) | ✅ |
 | 1502 | [Can Make Arithmetic Progression From Sequence](https://leetcode.com/problems/can-make-arithmetic-progression-from-sequence) | [My Solution](./problems/problem1502) | ✅ |
+| 1514 | [Path with Maximum Probability](https://leetcode.com/problems/path-with-maximum-probability) | [My Solution](./problems/problem1514) | ✅ |
 | 1519 | [Number of Nodes in the Sub-Tree With the Same Label](https://leetcode.com/problems/number-of-nodes-in-the-sub-tree-with-the-same-label) | [My Solution](./problems/problem1519) | ✅ |
 | 1523 | [Count Odd Numbers in an Interval Range](https://leetcode.com/problems/count-odd-numbers-in-an-interval-range) | [My Solution](./problems/problem1523) | ✅ |
 | 1539 | [Kth Missing Positive Number](https://leetcode.com/problems/kth-missing-positive-number) | [My Solution](./problems/problem1539) | ✅ |