LeetCode 368. Largest Divisible Subset

最新推荐文章于 2021-07-30 09:29:42 发布

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本文介绍了一种算法，用于从一组不同的正整数中找到最大的子集，使得该子集中任意两个元素都能相互整除。通过动态规划的方法，文章详细解释了如何找到并返回这样一个子集。

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]

class Solution {
public:
    vector<int> largestDivisibleSubset(vector<int>& nums) {
        if (nums.empty()) {
            return vector<int>();
        }
        sort(nums.begin(), nums.end());
        int n = nums.size();
        vector<int> cur(n, 1);
        vector<int> index(n, 0);
        int max_ = 1;
        int pre = 0;
        for (int i = 1; i < n; ++i) {
            for (int j = i - 1; j >= 0; --j) {
                if ((nums[i] % nums[j] == 0) && (cur[i] < cur[j] + 1)){
                    cur[i] = cur[j] + 1;
                    index[i] = j;  
                }
            }
            if (cur[i] > max_) {
                max_ = cur[i];
                pre = i;
            }
        }
        vector<int> result(max_, 0);
        for (int i = max_ - 1; i >= 0; --i) {
            result[i] = nums[pre];
            pre = index[pre];
        }
        return result;
    }
};