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.

Solution: Note that there are n elements in the n-th row (n starts from 1).
1. DFS. (Time Limit Exceeded for large test data).
2. DP. Do not need additional spaces (happen in-place).
3. DP. O(n) space (If the input 'triangle' can not be changed).

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