What storage method and data structure are best suited for storing a large set of numbers not exceeding 30000 modulo, to ensure fast search and minimal memory usage?

To store a large set of numbers in the range from -30000 to 30000 for fast search and minimal memory usage, it is best to use data structures with compact representation and efficient access.

Options:

• Indexed array: if the numbers are integers and the range is known, a boolean array (bitset) of length 60001 (from -30000 to 30000) can be used, where each bit indicates the presence of a number. Search will be O(1), memory — about 7.5 KB (60001 bits).

• Sorted array with binary search: store numbers in a sorted array and search via binary search in O(log n). Memory is minimal, but search is slightly slower.

• HashSet or TreeSet: in Java, you can use HashSet<Integer> for quick search (O(1) on average), but with overhead for storing objects and hash table.

Example of using BitSet in Java:

import java.util.BitSet;

public class NumberSet {
    private static final int OFFSET = 30000;
    private BitSet bitSet = new BitSet(60001);

    public void add(int number) {
        bitSet.set(number + OFFSET);
    }

    public boolean contains(int number) {
        return bitSet.get(number + OFFSET);
    }
}

This approach ensures minimal memory usage and very fast search.