【Leetcode】Triangle

题目链接：https://leetcode.com/problems/triangle/

题目：

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：

从下往上递推，d[i][j] 表示从下往上，到了trigle[i][j]这个点最小的路径和，状态转移方程：

d[i][j]=trigle[i][j]+min{d[i+1][j],d[i+1][j+1]}

算法：

public int minimumTotal(List<List<Integer>> triangle) {  
        int d[][] = new int[triangle.size()][triangle.size()];  
        List<Integer> l1 =  triangle.get(triangle.size() - 1);  
        for (int j = 0; j <triangle.size(); j++)  
            d[triangle.size() - 1][j] =l1.get(j);  
          
        for (int i = triangle.size() - 2; i >= 0; i--) {  
            List<Integer> list = triangle.get(i);  
            for (int j = 0; j < list.size(); j++) {  
                int min = Math.min(d[i + 1][j], d[i + 1][j + 1]);  
                d[i][j] = list.get(j) + min;  
            }  
        }  
  
        return d[0][0];  
    }