120. Triangle

https://leetcode.com/problems/triangle/

Problem

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

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        if (triangle.empty()) return 0;
        for (int i = 1 ;i < triangle.size(); ++i) {
            triangle[i].front() += triangle[i - 1].front();
            for (int j = 1; j < triangle[i].size() - 1; ++j) {
                triangle[i][j] += min(triangle[i - 1][j - 1], triangle[i - 1][j]);
            }
            triangle[i].back() += triangle[i - 1].back();
        }
        return *min_element(triangle.back().begin(), triangle.back().end());
    }
};

• #dp