feat: Add Traveling Salesman Problem algorithm and tests

dynamic/travelingsalesman.go

@@ -0,0 +1,53 @@
+// filename: travelingsalesman.go
+// description: The TravelingSalesman function calculates the minimum cost to complete a round-trip through all cities, starting and ending at the first city, using dynamic programming with bitmasking to track visited cities.
+// details:
+// The code defines a Go function tsp that solves the Traveling Salesman Problem using dynamic programming and bitmasking to track the subsets of visited cities.
+// It initializes a DP table where dp[mask][i] holds the minimum cost to visit cities represented by mask and end at city i.
+// The function iterates through all possible city subsets to update the DP table.
+// Finally determining the least costly route to visit all cities and return to the starting point.
+// author [Harshith Sai (SAI)](https://github.com/harshithsaiv)
+
+package dynamic
+
+import (
+	"math"
+)
+
+const MAX = math.MaxInt32 / 2
+
+func TravelingSalesman(cost [][]int) int {
+	n := len(cost)
+	allVisited := (1 << n) - 1
+	dp := make([][]int, 1<<n)
+	for i := range dp {
+		dp[i] = make([]int, n)
+		for j := range dp[i] {
+			dp[i][j] = MAX
+		}
+	}
+	dp[1][0] = 0
+
+	for mask := 1; mask < (1 << n); mask += 2 {
+		for i := 0; i < n; i++ {
+			if (mask & (1 << i)) != 0 {
+				for j := 0; j < n; j++ {
+					if (mask & (1 << j)) == 0 {
+						newMask := mask | (1 << j)
+						if dp[mask][i]+cost[i][j] < dp[newMask][j] {
+							dp[newMask][j] = dp[mask][i] + cost[i][j]
+						}
+					}
+				}
+			}
+		}
+	}
+
+	res := MAX
+	for i := 1; i < n; i++ {
+		if dp[allVisited][i]+cost[i][0] < res {
+			res = dp[allVisited][i] + cost[i][0]
+		}
+	}
+
+	return res
+}

dynamic/travelingsalesman_test.go

@@ -0,0 +1,46 @@
+package dynamic_test
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/TheAlgorithms/Go/dynamic"
+)
+
+func TestTravelingSalesman(t *testing.T) {
+	costTables := [][][]int{
+		{
+			{0, 10, 15, 20},
+			{10, 0, 35, 25},
+			{15, 35, 0, 30},
+			{20, 25, 30, 0},
+		},
+		{
+			{0, 29, 20, 21},
+			{29, 0, 15, 17},
+			{20, 15, 0, 28},
+			{21, 17, 28, 0},
+		},
+		{
+			{0, 12, 10},
+			{12, 0, 15},
+			{10, 15, 0},
+		},
+	}
+
+	expectedResults := []int{
+		80,
+		73,
+		37,
+	}
+
+	for i, costTable := range costTables {
+		expected := expectedResults[i]
+		t.Run(fmt.Sprintf("TSP Case %d", i+1), func(t *testing.T) {
+			result := dynamic.TravelingSalesman(costTable)
+			if result != expected {
+				t.Errorf("Expected %d, but got %d", expected, result)
+			}
+		})
+	}
+}