# 题目

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

• 最底层: $[4,1,8,3]$</br>
• 向上走:$[6+1,5+1,7+3] = [7,6,10]$</br>
• 继续:$[3+6,4+6] = [9,10]$</br>
• 最后:$[2+9] = [11]$</br>

# 代码

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