From 6e255f65f0ee20ac66b41c097a05a92b6a6bdfe2 Mon Sep 17 00:00:00 2001 From: AbodiDawood Date: Wed, 3 Jun 2026 16:41:57 +0200 Subject: [PATCH] Fix minimum partition for negative numbers --- dynamic_programming/minimum_partition.py | 46 +++++++----------------- 1 file changed, 12 insertions(+), 34 deletions(-) diff --git a/dynamic_programming/minimum_partition.py b/dynamic_programming/minimum_partition.py index 748c0599efb0..6458ba6364fa 100644 --- a/dynamic_programming/minimum_partition.py +++ b/dynamic_programming/minimum_partition.py @@ -2,8 +2,10 @@ Partition a set into two subsets such that the difference of subset sums is minimum """ +from collections.abc import Iterable -def find_min(numbers: list[int]) -> int: + +def find_min(numbers: Iterable[int]) -> int: """ >>> find_min([1, 2, 3, 4, 5]) 1 @@ -21,8 +23,6 @@ def find_min(numbers: list[int]) -> int: 0 >>> find_min([-1, -5, 5, 1]) 0 - >>> find_min([-1, -5, 5, 1]) - 0 >>> find_min([9, 9, 9, 9, 9]) 9 >>> find_min([1, 5, 10, 3]) @@ -32,42 +32,20 @@ def find_min(numbers: list[int]) -> int: >>> find_min(range(10, 0, -1)) 1 >>> find_min([-1]) - Traceback (most recent call last): - -- - IndexError: list assignment index out of range + 1 >>> find_min([0, 0, 0, 1, 2, -4]) - Traceback (most recent call last): - ... - IndexError: list assignment index out of range + 1 >>> find_min([-1, -5, -10, -3]) - Traceback (most recent call last): - ... - IndexError: list assignment index out of range + 1 """ - n = len(numbers) - s = sum(numbers) - - dp = [[False for x in range(s + 1)] for y in range(n + 1)] - - for i in range(n + 1): - dp[i][0] = True - - for i in range(1, s + 1): - dp[0][i] = False - - for i in range(1, n + 1): - for j in range(1, s + 1): - dp[i][j] = dp[i - 1][j] - - if numbers[i - 1] <= j: - dp[i][j] = dp[i][j] or dp[i - 1][j - numbers[i - 1]] + total_sum = 0 + reachable_sums = {0} - for j in range(int(s / 2), -1, -1): - if dp[n][j] is True: - diff = s - 2 * j - break + for number in numbers: + total_sum += number + reachable_sums |= {reachable_sum + number for reachable_sum in reachable_sums} - return diff + return min(abs(total_sum - 2 * reachable_sum) for reachable_sum in reachable_sums) if __name__ == "__main__":