Leetcode Triangle

题目：

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.

分析：

这道题属于动态规划问题中找最小值问题。用动态规划四步分析法分析：

1. 状态代表到这个位置的最小值

2. 每个状态都从下一行相邻的两个元素中较小的加上当前的值得到，状态转移方程：f[i][j] = min(f[i+1][j] + f[i+1][j+1]) + value[i][j]

3. 初始值为最后一行的值

4. 答案 f[0][0]

Java代码实现：

public class Solution {    public int minimumTotal(List<List<Integer>> triangle) {        if(triangle==null || triangle.size()==0)            return 0;                int size = triangle.size();            int[][] count = new int[size][size];                for(int i=0;i<size;i++)            count[size-1][i] = triangle.get(size-1).get(i);                    for(int i=size-2;i>=0;i--)        {            for(int j=0;j<=i;j++)            {                count[i][j] = Math.min(count[i+1][j], count[i+1][j+1])+triangle.get(i).get(j);            }        }                return count[0][0];    }}