Triangle

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本文探讨了如何通过编程解决一个经典的路径优化问题——从三角形顶点到底部的最小路径和。利用迭代方法，我们逐步更新每个节点的最小路径值，最终得到从顶部到底部的最小总和。

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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.

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
   
        for(int i = triangle.size()-2;i >= 0;i--)
        {
             for(int j = 0;j < triangle[i].size();j++)
                 triangle[i][j] += min(triangle[i+1][j],triangle[i+1][j+1]); 
        }
        return triangle[0][0];
    }
};

48 milli secs

Time:O(n^2),space: no extra