Problem Triangle

最新推荐文章于 2020-04-11 02:00:24 发布

转载最新推荐文章于 2020-04-11 02:00:24 发布 · 163 阅读

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原文链接：http://www.cnblogs.com/liew/p/3815132.html

本文介绍了一种求解从三角形顶部到底部的最小路径和的问题，通过动态规划的方法，自底向上更新每条边的累积权重，最终返回顶部元素即为最小路径和。

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Problem Description:

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

Solution:

 1     public int minimumTotal(List<List<Integer>> triangle) {
 2         for (int i = triangle.size()- 1; i >= 0; i--) {
 3             minimumTriangle(triangle, i);
 4         }
 5         return triangle.get(0).get(0);
 6     }
 7     
 8     public void minimumTriangle(List<List<Integer>> triangle, int row) {
 9         if (row == triangle.size() - 1)
10             return;
11         int min = Integer.MAX_VALUE;
12         for (int i = 0; i < triangle.get(row).size(); i++) {
13             triangle.get(row).set(i, triangle.get(row).get(i) + Math.min(triangle.get(row+1).get(i), triangle.get(row+1).get(i+1)));
14         }
15     }