Add Traveling Salesman Problem implementation

Author: aydinomer00

dynamic_programming/travelling_salesman.py

@@ -0,0 +1,72 @@
+from typing import List, Tuple
+
+
+def tsp_dp(distances: List[List[float]]) -> Tuple[float, List[int]]:
+    """
+    Solves Traveling Salesman Problem using dynamic programming.
+
+    >>> distances = [[0, 10, 15, 20], [10, 0, 35, 25], [15, 35, 0, 30], [20, 25, 30, 0]]
+    >>> cost, path = tsp_dp(distances)
+    >>> float(cost)
+    80.0
+    >>> path[0]
+    0
+
+    >>> distances = [[0, 5], [5, 0]]
+    >>> cost, path = tsp_dp(distances)
+    >>> float(cost)
+    10.0
+    >>> path
+    [0, 1]
+    """
+    if not distances:
+        raise ValueError("Empty distance matrix")
+
+    n = len(distances)
+    all_points = (1 << n) - 1
+    dp = {}
+    parent = {}
+
+    def solve(mask: int, pos: int) -> float:
+        if mask == all_points:
+            return distances[pos][0]
+
+        state = (mask, pos)
+        if state in dp:
+            return dp[state]
+
+        minimum = float('inf')
+        min_next = -1
+
+        for next_city in range(n):
+            if mask & (1 << next_city) == 0:
+                new_mask = mask | (1 << next_city)
+                new_dist = distances[pos][next_city] + solve(new_mask, next_city)
+
+                if new_dist < minimum:
+                    minimum = new_dist
+                    min_next = next_city
+
+        dp[state] = minimum
+        parent[state] = min_next
+        return minimum
+
+    optimal_cost = solve(1, 0)
+
+    path = [0]
+    mask = 1
+    pos = 0
+
+    for _ in range(n - 1):
+        next_pos = parent[(mask, pos)]
+        path.append(next_pos)
+        mask |= (1 << next_pos)
+        pos = next_pos
+
+    return optimal_cost, path
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()