120. Triangle

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.

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

自底向上的DP算法

f(i,j)=min{f(i,j),f(i,j+1)}+(i,j)

来源：https://www.cnblogs.com/wentiliangkaihua/p/11595506.html