[LeetCode]368. Largest Divisible Subset（自学留存）-优快云博客

本文链接：https://blog.youkuaiyun.com/Ada_who/article/details/79362625

本文介绍了一种使用动态规划算法解决寻找最大整除子集问题的方法。通过将输入数组排序，并利用动态规划来确定满足特定整除条件的最大子集。文章提供了详细的实现步骤和示例代码。

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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.

Personal tips: DP算法。数组排序后，假设j大于i，nums[j]%nums[i]=0,利用a[i]=j储存位置关系并保存最长子串的最小位数pos。代码如下：

class Solution {
public:
	vector<int> largestDivisibleSubset(vector<int>& nums)
	{
		if (nums.empty()) return nums;
		sort(nums.begin(), nums.end());
		int m = nums.size();
		vector<int> subset{}; vector<int> length(m, 0); vector<int> a(m, m); int max = 0,pos=0;
		for (int i = m - 1; i >= 0; i--)
		{
			for (int j = i; j < m; j++)
			{
				if (nums[j] % nums[i] == 0 && length[i] < length[j] + 1)
				{
					length[i] = length[j] + 1;
					a[i] = j;
					if (max < length[i])
					{
						max = length[i];
						pos = i;
					}
				}
			}
		}
		int next;
		subset.push_back(nums[pos]);
		while (pos < m)
		{
			next = a[pos]; if (pos == next) break;
			subset.push_back(nums[next]);
			pos = next;
		}	
		return subset;
	}
};