LeetCode-Triangle

最新推荐文章于 2020-04-21 23:43:52 发布

Yadoer

最新推荐文章于 2020-04-21 23:43:52 发布

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分类专栏： Algorithms 动态规划 LeetCode Java

本文链接：https://blog.youkuaiyun.com/My_Jobs/article/details/48027377

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本文介绍了一个经典的动态规划问题——寻找从三角形顶部到底部的最小路径和。通过使用仅O(n)额外空间的高效算法解决该问题，文章提供了一段Java代码实现，展示了如何在遍历过程中更新路径和。

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.

题比较简单，dp问题，并且要求空间复杂度了。

    public int minimumTotal(List<List<Integer>> triangle) {
        if (triangle == null || triangle.size() == 0) return 0;
        int[] dp = new int[triangle.size()];
        dp[0] = triangle.get(0).get(0);
        for (int i = 1; i < triangle.size(); i++) {
            List<Integer> list = triangle.get(i);
            dp[i] = list.get(i)+dp[i-1];
            for (int j = i-1; j > 0; j--) {
                dp[j] = Math.min(dp[j], dp[j-1])+list.get(j);
            }
            dp[0] += list.get(0); 
        }
        int min = dp[0];
        for (int n : dp) {
            min = Math.min(min, n);
        }
        return min;
    }