【leetcode】368. Largest Divisible Subset【M】【65】

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:

nums: [1,2,3]

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

Example 2:

nums: [1,2,4,8]

Result: [1,2,4,8]

Credits:

Special thanks to @Stomach_ache for adding this problem and creating all test cases.

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动态规划

首先对数组进行排序，这样保证小的在前面

地推公式是

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

然后使用ind数组，记录数组

ind[i] = j, if dp[j] is the max

class Solution(object):
def largestDivisibleSubset(self, nums):
if nums == []:
return []
nums.sort()
# print nums

dp = [1] * len(nums)
ind = [-1] * len(nums)

for i in xrange(len(nums)):
t = 1
for j in xrange(i):
if nums[i] % nums[j] == 0 and dp[j] + 1 >= t:
t = dp[j]+1
ind[i] = j
dp[i] = t

maxx = max(dp)

i = dp.index(maxx)#len(nums) - 1
res = []
while i >= 0:
res += nums[ind[i]],
i = ind[i]

return res