leetcode: 120. Triangle

最新推荐文章于 2022-08-23 00:04:42 发布

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本文介绍了一种解决三角形最小路径和问题的算法，该算法通过动态规划从上到下计算每一步的最小路径和，最终找到从顶点到底部的最小路径总和。示例中使用了一个四层的三角形数组，展示了如何通过优化空间复杂度至O(n)来求解此问题。

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Difficulty

Medium.

Problem

Given a triangle, find the minimum path sum from top to bottom. 
Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]
The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:

Bonus point if you are able to do this using only O(n) extra space, 
where n is the total number of rows in the triangle.

AC

class Solution():
	def minimumTotal(self, x):
		if not x:
			return 0
		way = [0] * len(x)
		way[0] = x[0][0]
		for i in range(1, len(x)):
			for j in range(len(x[i])-1, -1, -1):
				if j == len(x[i]) - 1:
					way[j] = way[j-1] + x[i][j]
				elif j == 0:
					way[j] = way[j] + x[i][j]
				else:
					way[j] = min(way[j-1], way[j]) + x[i][j]
		return min(way)