Merge pull request #217 from jerryderry/dp-theory-python

minimum distance dynamic programming in python

python/41_dynamic_programming/min_dist.py

@@ -0,0 +1,39 @@
+"""
+    Author: Wenru Dong
+"""
+
+from typing import List
+from itertools import accumulate
+
+def min_dist(weights: List[List[int]]) -> int:
+    """Find the minimum weight path from the weights matrix."""
+    m, n = len(weights), len(weights[0])
+    table = [[0] * n for _ in range(m)]
+    # table[i][j] is the minimum distance (weight) when
+    # there are i vertical moves and j horizontal moves
+    # left.
+    table[0] = list(accumulate(reversed(weights[-1])))
+    for i, v in enumerate(accumulate(row[-1] for row in reversed(weights))):
+        table[i][0] = v
+    for i in range(1, m):
+        for j in range(1, n):
+            table[i][j] = weights[~i][~j] + min(table[i - 1][j], table[i][j - 1])
+    return table[-1][-1]
+
+
+def min_dist_recur(weights: List[List[int]]) -> int:
+    m, n = len(weights), len(weights[0])
+    table = [[0] * n for _ in range(m)]
+    def min_dist_to(i: int, j: int) -> int:
+        if i == j == 0: return weights[0][0]
+        if table[i][j]: return table[i][j]
+        min_left = float("inf") if j - 1 < 0 else min_dist_to(i, j - 1)
+        min_up = float("inf") if i - 1 < 0 else min_dist_to(i - 1, j)
+        return weights[i][j] + min(min_left, min_up)
+    return min_dist_to(m - 1, n - 1)
+
+
+if __name__ == "__main__":
+    weights = [[1, 3, 5, 9], [2, 1, 3, 4], [5, 2, 6, 7], [6, 8, 4, 3]]
+    print(min_dist(weights))
+    print(min_dist_recur(weights))