Merge pull request Pradeepsingh61#613 from tanmay-dev-001/main

Added Floyd–Warshall Algorithm implementation in Go

Author: Pradeepsingh61

go/FloydWarshall.go

@@ -0,0 +1,80 @@
+// FloydWarshall.go
+//
+// Floyd–Warshall Algorithm - All-Pairs Shortest Path
+//
+// Description:
+//   The Floyd–Warshall algorithm computes the shortest paths between
+//   all pairs of vertices in a weighted directed graph. It can handle
+//   negative edge weights (but not negative cycles).
+//
+// Purpose / Use cases:
+//   - Network routing, transitive closure, and distance computation.
+//   - Detect negative cycles in graphs.
+//
+// Approach / Methodology:
+//   - Dynamic Programming approach.
+//   - Initialize a distance matrix with given edge weights.
+//   - Iteratively relax edges by trying all intermediate vertices.
+//
+// Complexity Analysis:
+//   - Time: O(V³)
+//   - Space: O(V²)
+//
+// File contents:
+//   - FloydWarshall() function.
+//   - PrintDistanceMatrix() utility.
+//   - Example test in main().
+
+package main
+
+import (
+	"fmt"
+	"math"
+)
+
+// FloydWarshall computes all-pairs shortest paths.
+// It modifies and returns the distance matrix.
+func FloydWarshall(dist [][]float64) [][]float64 {
+	n := len(dist)
+	for k := 0; k < n; k++ {
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if dist[i][k]+dist[k][j] < dist[i][j] {
+					dist[i][j] = dist[i][k] + dist[k][j]
+				}
+			}
+		}
+	}
+	return dist
+}
+
+// PrintDistanceMatrix prints a formatted distance matrix.
+func PrintDistanceMatrix(dist [][]float64) {
+	fmt.Println("All-Pairs Shortest Path Matrix:")
+	for _, row := range dist {
+		for _, val := range row {
+			if val == math.Inf(1) {
+				fmt.Printf("%4s ", "INF")
+			} else {
+				fmt.Printf("%4.0f ", val)
+			}
+		}
+		fmt.Println()
+	}
+}
+
+// main runs an example directed graph for Floyd–Warshall.
+func main() {
+	fmt.Println("Floyd–Warshall Algorithm Demo")
+
+	const INF = math.Inf(1)
+	dist := [][]float64{
+		{0, 3, INF, 7},
+		{8, 0, 2, INF},
+		{5, INF, 0, 1},
+		{2, INF, INF, 0},
+	}
+
+	result := FloydWarshall(dist)
+	PrintDistanceMatrix(result)
+}