【leetcode】No.120：triangle

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.

思路

由于只能通过相邻的结点，就好像一棵完全二叉树，找到完全二叉树最小的路径我们用递归的方法可以这样做：选择左子节点和右子节点中最小的与当前值相加，再往上，层做同样的事。换成当前场景也是一样，我们可以从最底层自底向上去更新，最终到跟节点的值就是路径最小值，更新过程如下：

   [2],                 [2],              
  [3,4],              [3, 4],            [2],
 [6,5,7],     ==>   [7, 6, 10]     ==>  [9, 10]   ==>    [11]
[4,1,8,3]

代码

import java.util.ArrayList;

public class Solution {
    public int minimumTotal(ArrayList<ArrayList<Integer>> triangle) {
        int len = triangle.size();
        for (int i=len-2; i>=0; i--){
            for (int j=0; j<=i; j++){
                triangle.get(i).set(j, triangle.get(i).get(j) + Math.min(triangle.get(i+1).get(j), triangle.get(i+1).get(j+1)));
            }
        }
        return triangle.get(0).get(0);
    }
}