# Triangle

xiaoxiao2021-02-28  4

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

[ , [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)     {        int length=triangle.size();          if(length==0)            return 0;          if(length==1)            return triangle;          vector<int> temp(triangle.size(),0);             vector<vector<int>> MP(length,temp);          MP[length-1]=triangle[length-1];        for(int i=length-2;i>=0;i--)          {              for(int j=0;j<triangle[i].size();j++)              {                  MP[i][j]=min(MP[i+1][j],MP[i+1][j+1])+triangle[i][j];              }          }          return MP;     }};