From c05dfce66756d0d20258e57d6fa138b134291c18 Mon Sep 17 00:00:00 2001 From: Wenru Dong Date: Sun, 30 Dec 2018 22:07:06 +0000 Subject: [PATCH] minimum distance dynamic programming in python --- python/41_dynamic_programming/min_dist.py | 39 +++++++++++++++++++++++ 1 file changed, 39 insertions(+) create mode 100644 python/41_dynamic_programming/min_dist.py diff --git a/python/41_dynamic_programming/min_dist.py b/python/41_dynamic_programming/min_dist.py new file mode 100644 index 0000000..2b8e60a --- /dev/null +++ b/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))