Data structures that can map a range of keys to a value

Question

I am trying to find a data structure that takes in a particular value from a range of values and map it to a key.

For example, I have the following conditions:

Answer 1

This seems like a natural situation to use a tree structure.

Unfortunately it won't be practical to implement the java.util.Map interface because it specifies a method to return all of the keys, and in your situation you theoretically have an impractically large number of keys.

Each node of your tree should have a minimum key, a maximum key, and a value associated with that range. You can then have links to the nodes representing the next higher and next lower range (if they exist). Something like:

public class RangeMap, V> {
    protected boolean empty;
    protected K lower, upper;
    protected V value;
    protected RangeMap left, right;

    public V get(K key) {
        if (empty) {
            return null;
        }

        if (key.compareTo(lower) < 0) {
            return left.get(key);
        }

        if (key.compareTo(upper) > 0) {
            return right.get(key);
        }

        /* if we get here it is in the range */
        return value;
    }

    public void put(K from, K to, V val) {
        if (empty) {
            lower = from;
            upper = to;
            value = val;
            empty = false;
            left = new RangeMap();
            right = new RangeMap();
            return;
        }

        if (from.compareTo(lower) < 0) {
            left.put(from, to, val);
            return;
        }

        if (to.compareTo(upper) > 0) {
            right.put(from, to, val);
            return;
        }

        /* here you'd have to put the code to deal with adding an overlapping range,
           however you want to handle that. */
    }

    public RangeMap() {
        empty = true;
    }
}

If you need faster lookups than the tree can provide, you may want to look into something like a skip list or developing your own hash function.