【LeetCode】119.Triangle

题目描述(Medium)

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

题目链接

https://leetcode.com/problems/triangle/description/

Example 1:

For example, given the following triangle

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

算法分析

设状态为，表示从出发，路径的最小和，则状态转移方程为，从上到下可以考虑递归搜寻，但是时间复杂度太高，因此采用动态规划从下往上查找。

提交代码：

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