LeetCode120 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.（Medium）

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.

 

分析：

经典的动态规划题，可以有自顶向下，自底向上的解法，是自己学动态规划的第一道题，就不分析了，写一个自底向上的解法。

代码：

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