LeetCode 368. Largest Divisible Subset

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题目

Given a set of distinct positive integers, find the largest subset such that every pair (Si, Sj) of elements in this subset satisfies:

Si % Sj = 0 or Sj % Si = 0.

If there are multiple solutions, return any subset is fine.

Example 1:

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Input: [1,2,3]
Output: [1,2] (of course, [1,3] will also be ok)

Example 2:

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Input: [1,2,4,8]
Output: [1,2,4,8]

思路

DP.
状态转移方程: dp[x] = max(dp[x], dp[y] + 1) 其中： 0 <= y < x 且 nums[x] % nums[y] == 0
再通过一个辅助数组pre回溯。

代码

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class Solution(object):
    def largestDivisibleSubset(self, nums):
        """
        :type nums: List[int]
        :rtype: List[int]
        """
        if not nums:
            return []
        res = []
        nums = sorted(nums)
        dp = [1] * len(nums)
        pre = [None] * len(nums)
        for i in range(len(nums)):
            for j in range(i):
                if nums[i] % nums[j] == 0 and dp[j] + 1 > dp[i]:
                    dp[i] = dp[j] + 1
                    pre[i] = j
        index = dp.index(max(dp))
        while index is not None:
            res.append(nums[index]) 
            index = pre[index]
        return res[::-1]