[LeetCode 6.13] Largest Divisible Subset

原创于 2020-06-15 21:06:45 发布 · 161 阅读

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本文探讨了在一组独特正整数中寻找最大子集的问题，使得子集内的每对元素Si和Sj满足Si%Sj=0或Sj%Si=0。通过示例说明并提供Python3解决方案，采用动态规划思想，确保找到满足条件的最大子集。

Largest Divisible Subset

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:

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

Example 2:

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

Python3 Solution:

思路：如果一个数可以被subset中最大的数整除，那么它就可以被subset中的所有数整除。

class Solution:
    def largestDivisibleSubset(self, nums: List[int]) -> List[int]:
        if len(nums) == 0: return []
        nums.sort()
        sol = [[num] for num in nums]
        for i in range(len(nums)):
            for j in range(i):
                if nums[i] % nums[j] == 0 and len(sol[i]) < len(sol[j]) + 1:
                    sol[i] = sol[j] + [nums[i]]
        return max(sol, key=len)