Problem

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.

Bottom-top DP

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

Non Extra Space DP

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