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.

难度：medium

题目：给定一三角形数组，找出从上到下最小的路径和。每步只可以向下一行的相邻元素移动。

思路：动态规划

Runtime: 4 ms, faster than 87.60% of Java online submissions for Triangle.
Memory Usage: 38.5 MB, less than 100.00% of Java online submissions for Triangle.

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