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| 1 | +# 368. Largest Divisible Subset |
| 2 | +Given a set of **distinct** positive integers `nums`, return the largest subset `answer` such that every pair `(answer[i], answer[j])` of elements in this subset satisfies: |
| 3 | + |
| 4 | +* `answer[i] % answer[j] == 0`, or |
| 5 | +* `answer[j] % answer[i] == 0` |
| 6 | + |
| 7 | +If there are multiple solutions, return any of them. |
| 8 | + |
| 9 | +#### Example 1: |
| 10 | +<pre> |
| 11 | +<strong>Input:</strong> nums = [1,2,3] |
| 12 | +<strong>Output:</strong> [1,2] |
| 13 | +<strong>Explanation:</strong> [1,3] is also accepted. |
| 14 | +</pre> |
| 15 | + |
| 16 | +#### Example 2: |
| 17 | +<pre> |
| 18 | +<strong>Input:</strong> nums = [1,2,4,8] |
| 19 | +<strong>Output:</strong> [1,2,4,8] |
| 20 | +</pre> |
| 21 | + |
| 22 | +#### Constraints: |
| 23 | +* `1 <= nums.length <= 1000` |
| 24 | +* <code>1 <= nums[i] <= 2 * 10<sup>9</sup></code> |
| 25 | +* All the integers in `nums` are **unique**. |
| 26 | + |
| 27 | +## Solutions (Rust) |
| 28 | + |
| 29 | +### 1. Solution |
| 30 | +```Rust |
| 31 | +impl Solution { |
| 32 | + pub fn largest_divisible_subset(nums: Vec<i32>) -> Vec<i32> { |
| 33 | + let mut nums = nums; |
| 34 | + let mut max_len = vec![1; nums.len()]; |
| 35 | + let mut prev_index = vec![None; nums.len()]; |
| 36 | + let mut answer = vec![]; |
| 37 | + |
| 38 | + nums.sort_unstable(); |
| 39 | + |
| 40 | + for i in 1..nums.len() { |
| 41 | + for j in 0..i { |
| 42 | + if nums[i] % nums[j] == 0 && max_len[i] < max_len[j] + 1 { |
| 43 | + max_len[i] = max_len[j] + 1; |
| 44 | + prev_index[i] = Some(j); |
| 45 | + } |
| 46 | + } |
| 47 | + } |
| 48 | + |
| 49 | + let mut curr = (0..nums.len()).max_by_key(|&i| max_len[i]).unwrap(); |
| 50 | + answer.push(nums[curr]); |
| 51 | + |
| 52 | + while let Some(i) = prev_index[curr] { |
| 53 | + curr = i; |
| 54 | + answer.push(nums[curr]); |
| 55 | + } |
| 56 | + |
| 57 | + answer |
| 58 | + } |
| 59 | +} |
| 60 | +``` |
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