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)