LeetCode (Triangle)

最新推荐文章于 2023-10-24 19:12:47 发布

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本文介绍了一种求解从三角形顶部到底部的最小路径和的问题，通过动态规划的方法逐步计算每一层的最短路径，最终找出整体的最小路径总和。

Problem:

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.

Solution:

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