(DP 入门) leetcode 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 nis the total number of rows in the triangle.

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这是一个入门题。。。。

C++代码：

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        int n = triangle.size();
        vector<vector<int> > dp(n,vector<int>(n,0));   //要掌握这个初始化代码。
        for(int i = 0; i < n; i++)
            dp[n-1][i] = triangle[n-1][i];
        for(int i = n - 2; i >= 0; i--){
            for(int j = 0; j <= i;j++){
                dp[i][j] = triangle[i][j] + min(dp[i+1][j],dp[i+1][j+1]);
            }
        }
        return dp[0][0];
    }
};