Triangle

 

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).

 

 

 

 

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        int r = triangle.size();
		//注意边界条件，写代码之前都先判断一下边界条件
		if(!r || !triangle[0].size())return 0;
		int len = triangle[r - 1].size();

		int *rst = new int[len];
		//从最后一行开始，先用最后一行为结果赋值
		//因为每次计算第[ij]的结果是之和rst[j]及[j+1]相关，更新的是rst[j]，
		//不会影响下次计算相关的额rst[j+1]及rst[j+2]所以可以再远rst数组的基础上计算，不用再开额外辅助空间
		for(int i = 0; i < len; i++)rst[i] = triangle[r - 1][i];
		for(int row = r - 1; row >= 1; row--)
		{
			int col_len = triangle[row - 1].size();
			for(int col = 0; col < col_len; col++)
				rst[col] = triangle[row - 1][col] + min(rst[col], rst[col + 1]);
		}
		int rtv = rst[0];
		delete[] rst;
		return rtv;



    }
};