120. 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).

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.

一，动态规划解法：

 

class Solution{
public:
    int minimumTotal(vector<vector<int>>& triangle){
        int n = triangle.size();
        vector<vector<int>> memo(n,vector<int>(n,-1));
        for(int j = 0; j < n; j++){
            memo[n-1][j] = triangle[n-1][j];
        }

        for(int i = n - 2; i >= 0; i--){
            for(int j = 0; j <= i; j++){
                memo[i][j] = min(memo[i+1][j], memo[i+1][j+1]) + triangle[i][j];
            }
        }
        return memo[0][0];
    }
};

class Solution{
public:
    int minimumTotal(vector<vector<int> > &triangle){
        int n = triangle.size();
        vector<int> memo(n,-1);
        for(int j = 0; j < n; j++){
            memo[j] = triangle[n-1][j];
        }

        for(int i = n - 2; i >= 0; i--){
            for(int j = 0; j <= i; j++){
                memo[j] = min(memo[j],memo[j+1]) + triangle[i][j];
            }
        }
        return memo[0];
    }
};

 

参考：

1，https://blog.csdn.net/u013250416/article/details/80558542