Triangle, Leetcode 解题笔记

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.

一维DP题,total[i]存的是每行到达i元素的最小和,每遍历一行则更新total。一个窍门是从底向上遍历,可以省去不少麻烦。

public class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        int[] total = new int[triangle.size()];
    	int l = triangle.size() - 1;
     
    	for (int i = 0; i < triangle.get(l).size(); i++) {
    		total[i] = triangle.get(l).get(i);
    	}
     
    	// iterate from last second row
    	for (int i = triangle.size() - 2; i >= 0; i--) {
    		for (int j = 0; j < triangle.get(i + 1).size() - 1; j++) {
    			total[j] = triangle.get(i).get(j) + Math.min(total[j], total[j + 1]);
    		}
    	}
     
    	return total[0];
    }
}
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