Solved TravelingSalesManProblem Using DynamicProgramming(memoization)

In the above code, we implement a solution to the Traveling Salesman Problem (TSP) using dynamic programming with memoization. The algorithm calculates the shortest possible route that visits a set of cities exactly once and returns to the starting city by recursively exploring all possible paths and storing the results of subproblems to avoid redundant calculations. The program outputs both the minimum cost of the tour and the optimal path taken.

Author: Sujal1804

src/main/java/com/thealgorithms/dynamicprogramming/TravelingSalesManProblem

@@ -0,0 +1,67 @@
+import java.util.Arrays;
+
+public class TSP {
+    static int n; 
+    static int MAX = 1000000; 
+    static int[][] dist; 
+    static int[][] memo; 
+    static int[][] parent; 
+
+    static int tsp(int i, int mask) {
+        if (mask == (1 << n) - 1) {
+            return dist[i][0]; 
+        }
+
+        if (memo[i][mask] != -1) {
+            return memo[i][mask];
+        }
+
+        int res = MAX; 
+
+        for (int j = 0; j < n; j++) {
+            if ((mask & (1 << j)) == 0) { 
+                int newRes = dist[i][j] + tsp(j, mask | (1 << j)); 
+                if (newRes < res) {
+                    res = newRes;
+                    parent[i][mask] = j; 
+                }
+            }
+        }
+
+        return memo[i][mask] = res;
+    }
+
+    static void printPath(int i, int mask) {
+        System.out.print(i + " → ");
+        if (mask == (1 << n) - 1) { 
+            System.out.println(0); 
+            return;
+        }
+        int nextCity = parent[i][mask];
+        printPath(nextCity, mask | (1 << nextCity));
+    }
+
+    public static void main(String[] args) {
+        n = 4;
+        dist = new int[][] {
+            { 0, 10, 15, 20 },
+            { 10, 0, 35, 25 },
+            { 15, 35, 0, 30 },
+            { 20, 25, 30, 0 }
+        };
+
+        memo = new int[n][1 << n];
+        parent = new int[n][1 << n];
+
+        for (int[] row : memo) {
+            Arrays.fill(row, -1);
+        }
+
+        int minCost = tsp(0, 1);
+
+        System.out.println("The minimum cost of the tour is: " + minCost);
+
+        System.out.print("The optimal path is: ");
+        printPath(0, 1);
+    }
+}