Create TSL.py

Fixes #11938

Author: singhvibhanshu

dynamic_programming/TSL.py

@@ -0,0 +1,44 @@
+from itertools import combinations
+
+def tsp_dynamic_programming(dist_matrix):
+    n = len(dist_matrix) # number of cities
+
+    # Initialize a dictionary to store the costs of visiting a subset of cities ending at city i
+    # dp[subset][i] will store the minimum cost to visit all cities in 'subset' and end at city i
+    dp = {}
+
+    # Base case: Starting from the first city, i.e., only city 0 is visited
+    for i in range(1, n):
+        dp[(1 << i, i)] = dist_matrix[0][i]  # Subset contains city 0 and city i
+
+    # Iterate through subsets of cities (of increasing size)
+    for subset_size in range(2, n):
+        for subset in combinations(range(1, n), subset_size):
+            # Create the subset bitmask
+            subset_mask = 0
+            for city in subset:
+                subset_mask |= 1 << city
+
+            # Try ending at each city 'j' in the subset
+            for j in subset:
+                prev_mask = subset_mask & ~(1 << j)  # Remove city j from the subset
+                dp[(subset_mask, j)] = min(
+                    dp[(prev_mask, k)] + dist_matrix[k][j] for k in subset if k != j
+                )
+
+    # Final step: Consider returning to the start (city 0) from each possible city
+    final_mask = (1 << n) - 2  # All cities visited except city 0
+    return min(dp[(final_mask, i)] + dist_matrix[i][0] for i in range(1, n))
+
+# Example usage
+if __name__ == "__main__":
+    # Example distance matrix (symmetric matrix where dist_matrix[i][j] is the distance between city i and city j)
+    dist_matrix = [
+        [0, 10, 15, 20],
+        [10, 0, 35, 25],
+        [15, 35, 0, 30],
+        [20, 25, 30, 0]
+    ]
+
+    result = tsp_dynamic_programming(dist_matrix)
+    print(f"The minimum travel cost is: {result}")