[LeetCode] Triangle 解题记录

题目描述：

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.

考察动态规划，可以想象为一棵树，在构造路径的时候，到达当前节点的路径长度为当前节点的值加上相邻的上层较小值。最直观的是构造一个二维矩阵，自顶向下构造路径，空间复杂度为 O(N^2)；为了减少空间复杂度，可以自底向上构造，这样每一次的迭代结果覆盖前一次，最终0号元素就是最短路径值。

思考：自底向上的方法有点归并的感觉，总是将较小的和聚集到一个点。如果要求输出路径上的节点呢？如果底层的存储结果是树呢？

思维导图：

时间： 2024-11-01 01:40:56

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