Fist implementation for TSP using Dynamic Programming(Only returning …

…the cost)

README.md

@@ -19,6 +19,7 @@ This repository contains some of my first steps working with Go and implementing
 ### Graph Algoristhms
 - Depth first search
 - Dijkstra's algorithm
+- Travelling Salesman Problem: It is solved using a dynamic programming approach with O(n^2 * 2^n) time complexity. The code is capable to find the minimum cost but not the optimal path yet.
 
 ### Advanced Algoristhms
 - Hanoi's towers problem

graphs/travelling_salesman_problem/main.go

@@ -0,0 +1,101 @@
+package main
+
+import (
+	"fmt"
+	"math"
+)
+
+// N is the number of cities
+const N = 4
+
+// AllVisited is the mask used to represent when
+// all the cities have been visited
+const AllVisited = (1 << N) - 1
+
+// memoTable store the results already computed
+var memoTable [16][N]int
+
+func buildMatrix() [][]int {
+	var n int
+
+	fmt.Printf("Number of cities: ")
+	fmt.Scanf("%d", &n)
+
+	fmt.Println("Cities", n)
+
+	// allocate composed 2d array
+	matrix := make([][]int, n)
+	for i := range matrix {
+		matrix[i] = make([]int, n)
+	}
+
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			fmt.Printf("Position[%d][%d]: ", i+1, i+1)
+			fmt.Scanf("%d", &matrix[i][j])
+		}
+	}
+
+	return matrix
+}
+
+func tsp(m [][]int, mask int, pos uint) int {
+	if mask == AllVisited {
+		return m[pos][0]
+	}
+
+	if memoTable[mask][pos] != -1 {
+		return memoTable[mask][pos]
+	}
+	var city uint
+	var newCost int
+	minCost := math.MaxInt64 // Greatest possible value
+
+	// Let's go to an unvisited city
+	for city = 0; city < N; city++ {
+		cityAsBinary := (1 << city)
+
+		if (mask & cityAsBinary) == 0 {
+			newCost = m[pos][city] + tsp(m, mask|cityAsBinary, city)
+			minCost = min(minCost, newCost)
+			memoTable[mask][pos] = minCost
+		}
+
+	}
+
+	return minCost
+}
+
+func min(a int, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func main() {
+	// m := buildMatrix()
+	// m := [][]int{
+	// 	[]int{0, 20, 42, 25},
+	// 	[]int{20, 0, 30, 34},
+	// 	[]int{42, 30, 0, 10},
+	// 	[]int{25, 34, 10, 0},
+	// }
+
+	m := [][]int{
+		[]int{0, 10, 15, 20},
+		[]int{10, 0, 35, 25},
+		[]int{15, 35, 0, 30},
+		[]int{20, 25, 30, 0},
+	}
+
+	for i := 0; i < (1 << N); i++ {
+		for j := 0; j < N; j++ {
+			memoTable[i][j] = -1
+		}
+	}
+
+	cost := tsp(m, 1, 0)
+
+	fmt.Println("The minimum cost is:", cost)
+}