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This approach utilizes hash maps (dictionaries in Python) to achieve optimal time and space complexity for operations such as insertion, deletion, and lookup. By storing elements as keys in a hash map, we benefit from average-case O(1) time complexity for these operations.
Time Complexity: O(1) on average for search, insert, and delete due to the hash map.
Space Complexity: O(n), where n is the number of elements stored.
1import java.util.HashMap;
2
3public class MySet {
4 private HashMap<Integer, Boolean> hashMap;
5
6 public MySet() {
7 hashMap = new HashMap<>();
8 }
9
10 public void insert(int key) {
11 hashMap.put(key, true);
12 }
13
14 public boolean search(int key) {
15 return hashMap.containsKey(key);
16 }
17
18 public static void main(String[] args) {
19 MySet mySet = new MySet();
20 mySet.insert(10);
21 System.out.println("Search for 10: " + mySet.search(10)); // Output: true
22 System.out.println("Search for 20: " + mySet.search(20)); // Output: false
23 }
24}
25In Java, the HashMap is used to efficiently manage insertion and lookup operations. We use the presence of a key to indicate its inclusion.
This approach leverages sorted arrays to perform efficient binary searches. Operations are optimized for scenarios requiring sorted data, such as when frequent minimum/maximum queries are performed.
Time Complexity: O(n log n) for insertion (due to sorting), O(log n) for search (binary search).
Space Complexity: O(n).
1
In C, we maintain sorted arrays using qsort after each insertion. Searches are performed with a custom binary search function for efficiency.