Solved TravelingSalesManProblem Using DynamicProgramming(memoization)

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);
+    }
+}