【Leetcode】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).

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        int size = triangle.size();
        vector<int> table(size, 0);
        for (int i = 0; i < size; ++i) {
            table[i] = triangle[size - 1][i];
        }
        for (int i = size - 2; i >= 0; --i) {
            for (int j = 0; j <= i; ++j) {
                table[j] = min(table[j], table[j + 1]) + triangle[i][j];
            }
        }
        return table[0];
    }
};

自底向上dp. 如果允许改变三角形本身，直接利用其本身空间即可。