368. Largest Divisible Subset

class Solution:
    def largestDivisibleSubset(self, nums):
        """
        :type nums: List[int]
        :rtype: List[int]
        """
        if not nums:
            return []
        if len(nums) == 1:
            return nums
        # 排序
        # 排序之后对nums[i]看前面所有j < i是否nums[i] % nums[j] == 0
        nums.sort()
        dp = [1] * len(nums)    # dp[i]是包含当前nums[i]的最长整除序列长度
        pre = [0] * len(nums)   # pre[当前i] = 使个数增多1的j
        maxSize = maxi = 0
        
        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
                if dp[i] > maxSize:
                    maxSize = dp[i]
                    maxi = i
                    
        res = []
        i = maxi
        # 回溯
        for _ in range(maxSize):
            res.append(nums[i])
            i = pre[i]
        
        return res[::-1]