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).

思路：这道题主要使用动态规划的来解决问题。

 

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        int nSize=triangle.size();
        if(nSize<=0)
            return 0;
        int dp[1000];
        memset(dp,INT_MAX,sizeof(dp));
        dp[0]=triangle[0][0];
        for(int i=1;i<nSize;i++)
        {
            int m=triangle[i].size()-1;
            for(int j=m;j>=0;j--)
            {
                if(j==0)
                    dp[j]=dp[j]+triangle[i][j];
                else if(j==m)
                    dp[j]=dp[j-1]+triangle[i][j];
                else
                    dp[j]=min(dp[j],dp[j-1])+triangle[i][j];
            }
        }
        int sum=INT_MAX;
        for(int i=0;i<nSize;i++)
        {
            sum=((sum>dp[i])?dp[i]:sum);
        }
        return sum;
    }
};