Merge pull request #143 from iko1133/add-floyd-warshall-graphs

Added implementation of Floyd-Warshall algorithm

Author: 0xbrayo

DIRECTORY.md

@@ -29,6 +29,9 @@
   * [Matrix-Multiplication](https://github.com/TheAlgorithms/Go/blob/master/dynamic-programming/matrix-multiplication.go)
   * [Rod-Cutting](https://github.com/TheAlgorithms/Go/blob/master/dynamic-programming/rod-cutting.go)
 
+## Graphs
+  * [Floyd-Warshall algorithm](https://github.com/TheAlgorithms/Go/blob/master/graphs/floyd_warshall.go)
+
 ## Other
   * [Maxsubarraysum](https://github.com/TheAlgorithms/Go/blob/master/other/maxSubarraySum.go)
   * [Nestedbrackets](https://github.com/TheAlgorithms/Go/blob/master/other/NestedBrackets.go)

graphs/floyd_warshall.go

@@ -0,0 +1,63 @@
+// Floyd-Warshall algorithm
+// https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm
+
+package graph
+
+import (
+	"math"
+)
+
+// Defining matrix to use 2d array easier
+type Matrix [][]float64
+
+// Defining maximum value. If two vertices share this value, it means they are not connected
+var maxValue = math.Inf(1)
+
+// Returns all pair's shortest path using Floyd Warshall algorithm
+func FloydWarshall(graph Matrix) Matrix {
+	// If graph is empty or width != height, returns nil
+	if len(graph) == 0 || len(graph) != len(graph[0]) {
+		return nil
+	}
+
+	numVertecies := len(graph)
+
+	// Initializing result matrix and filling it up with same values as given graph
+	result := make(Matrix, numVertecies)
+
+	for i := 0; i < numVertecies; i++ {
+		result[i] = make([]float64, numVertecies)
+		for j := 0; j < numVertecies; j++ {
+			result[i][j] = graph[i][j]
+		}
+	}
+
+	// Running over the result matrix and following the algorithm
+	for k := 0; k < numVertecies; k++ {
+		for i := 0; i < numVertecies; i++ {
+			for j := 0; j < numVertecies; j++ {
+				// If there is a less costly path from i to j node, remembering it
+				if result[i][j] > result[i][k]+result[k][j] {
+					result[i][j] = result[i][k] + result[k][j]
+				}
+			}
+		}
+	}
+
+	return result
+}
+
+// func main() {
+// 	var graph Matrix
+// 	graph = Matrix{{0, maxValue, -2, maxValue},
+// 		{4, 0, 3, maxValue},
+// 		{maxValue, maxValue, 0, 2},
+// 		{maxValue, -1, maxValue, 0}}
+
+// 	result := FloydWarshall(graph)
+
+// 	// Print result
+// 	for i := 0; i < len(result); i++ {
+// 		fmt.Printf("%4g\n", result[i])
+// 	}
+// }