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.

动态规划

class Solution {
private:
    int sum;
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        int n = triangle.size();
        if(n==0) return 0;
        int f[n];
        f[0] = triangle[0][0];
        
        for(int i = 1;i < n;i++)
            for(int j = triangle[i].size()-1;j>=0;j--)
            {
                if(j==triangle[i].size()-1)
                    f[j] = f[j-1] + triangle[i][j];
                else if(j==0)
                    f[j] = f[j] + triangle[i][j];
                else
                    f[j] = min(f[j],f[j-1]) + triangle[i][j];
            }
        int ans = INT_MAX;
        for(int i = 0;i<n;i++)
            if(ans>f[i])
                ans = f[i];
        
        return ans;
    }
};