[LeetCode]Largest Divisible Subset | NoobSky

[LeetCode]Largest Divisible Subset | NoobSky

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:

1 2 3

nums: [1,2,3] Result: [1,2] (of course, [1,3] will also be ok)

Example 2:

1 2 3

nums: [1,2,4,8] Result: [1,2,4,8]

这道题的DP思想跟LIS（最长递增子序列）的思想是一样的，详见Longest Increasing Subsequence，只是LIS只要求长度，这里要给出序列。
dp[n]表示最大元素为nums[n]的largest divisible subset的长度，则：

dp[i] = max{dp[j] + 1 if dp[i] % dp[j] == 0}, 0<= j < i

有了以上状态方程，我们可以写出O(n²)的算法。

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