LeetCode-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.

 

使用动态规划 递推，时间复杂度为O(n)

public int minimumTotal(List<List<Integer>> triangle) {//dp my
        if(0==triangle.size()){
            return 0;
        }
        List<Integer> result = new ArrayList<>();
        result.addAll(triangle.get(triangle.size()-1));
        for(int i=triangle.size()-2;i>=0;i--){
            for(int j=0;j<=i;j++){
                int min = result.get(j)<result.get(j+1)?(result.get(j)+triangle.get(i).get(j)):(result.get(j+1)+triangle.get(i).get(j));
                result.set(j,min);
            }
        }
        return result.get(0);
    }

 可在原始数据上修改，这样空间复杂度为O(1)