120. Triangle

Posted 2021-03-11 dysjtu1995

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.

思路：

Solution (C++):

int minimumTotal(vector<vector<int>>& triangle) {
    int n = triangle.size();
    vector<int> min_path(triangle.back());
    
    for (int layer = n-2; layer >= 0; --layer) {
        for (int i = 0; i <= layer; i++) {
            min_path[i] = min(min_path[i], min_path[i+1]) + triangle[layer][i];
        }
    }
    return min_path[0];
}

性能：

Runtime: 8 ms??Memory Usage: 9.8 MB