Leetcode: 368. Largest Divisible Subset

最新推荐文章于 2018-10-12 15:00:15 发布

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最新推荐文章于 2018-10-12 15:00:15 发布

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分类专栏：算法文章标签： leetcode

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本文介绍了一种使用动态规划解决寻找最大整除子集问题的方法。通过具体实例展示了如何找到一个整数集合中最大的子集，使得该子集中任意两个元素都能相互整除。附带提供了完整的C++代码实现。

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]

解法：
动态规划

class Solution {
public:
    vector<int> largestDivisibleSubset(vector<int>& nums) {
        vector<int> result;
        vector<int> table(nums.size(), 1);
        vector<int> pre(nums.size(), -1);

        if (nums.empty()) return result;

        sort(nums.begin(), nums.end());

        for (int i = 1; i < table.size(); ++i) {
            for (int j = i-1; j >= 0; --j) {
                if ((nums[i] % nums[j]) == 0) {
                    if (table[j] + 1 > table[i]) {
                        table[i] = table[j] + 1;
                        pre[i] = j;
                    }
                }
            }
        }

        int max = 0;
        int idx = 0;
        for (int i = 0; i < table.size(); ++i) {
            if (table[i] > max) {
                idx = i;
                max = table[i];
            }
        }

        do {
            result.push_back(nums[idx]);
            idx = pre[idx];
        } while(idx >= 0);

        return result;
    }
};