[Leetcode] Triangle

最新推荐文章于 2020-05-23 10:06:18 发布

最新推荐文章于 2020-05-23 10:06:18 发布 · 108 阅读

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本文介绍了一个算法问题：在给定的三角形结构中找到从顶部到底部的最小路径总和。每一步可以移动到下一行相邻的数字。通过示例说明了如何实现这一算法，并提供了一种使用O(n)额外空间的解决方案。

TriangleOct 30 '126503 / 17796

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.

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