【LeedCode】120. Triangle

Description:

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.

题目分析：

一开始考虑用贪心算法，但后来发现贪心算法每一行找到的最小值不一定满足相邻的条件。故只有逐行查找，本题采用从下到上逐行查找的办法。

Solutions:

class Solution {  
public:  
        int minimumTotal(vector<vector<int> > &triangle) {  
        int  tri_size=(int)triangle.size();  
        if(tri_size==0)  
            return 0;  
        vector<int> sum_vec(triangle[tri_size-1]);  
        for(int i=tri_size-2;i>=0;i--){  
            for(int j=0;j<i+1;j++){  
                if(sum_vec[j]<sum_vec[j+1])  
                    sum_vec[j]+=triangle[i][j];  
                else  
                    sum_vec[j]=triangle[i][j]+sum_vec[j+1];  
            }  
        }  
        return sum_vec[0];  
    }  
};