TreeMap navigation methods

Key points

• TreeMap and TreeSet are sorted, so they can answer questions a hash table cannot.
• Nearest key: floorKey is the largest key not above yours, ceilingKey the smallest not below.
• lowerKey and higherKey are the same idea but strict — they never return your own key.
• Ranges come back as live views: headMap, tailMap, subMap. Writing to a view writes to the map.
• Ends: firstEntry, lastEntry, plus pollFirstEntry and pollLastEntry which also remove.
• Perfect for lookup tables — grade bands, price tiers, time buckets. Lookups and range queries are O(log n).

Example

import java.util.*;

public class Main {
    public static void main(String[] args) {
        TreeMap<Integer, String> grades = new TreeMap<>();
        grades.put(60, "D");
        grades.put(70, "C");
        grades.put(80, "B");
        grades.put(90, "A");
        System.out.println("map               : " + grades);

        System.out.println("floorEntry(85)    : " + grades.floorEntry(85) + "   (largest key <= 85)");
        System.out.println("ceilingKey(85)    : " + grades.ceilingKey(85) + "   (smallest key >= 85)");
        System.out.println("lowerKey(80)      : " + grades.lowerKey(80) + "   (strictly less)");
        System.out.println("higherKey(80)     : " + grades.higherKey(80) + "   (strictly greater)");
        System.out.println("firstKey/lastKey  : " + grades.firstKey() + " / " + grades.lastKey());

        System.out.println("headMap(80)       : " + grades.headMap(80));
        System.out.println("tailMap(80)       : " + grades.tailMap(80));
        System.out.println("subMap(70, 90)    : " + grades.subMap(70, 90));
        System.out.println("descendingMap     : " + grades.descendingMap());

        System.out.println("pollFirstEntry    : " + grades.pollFirstEntry() + "  leaves " + grades);

        TreeSet<String> words = new TreeSet<>(List.of("apple", "fig", "kiwi", "pear"));
        System.out.println("ceiling(grape)    : " + words.ceiling("grape"));
        System.out.println("headSet(kiwi)     : " + words.headSet("kiwi"));
        System.out.println("descendingSet     : " + words.descendingSet());
    }
}

When the question is "nearest" or "between", only a sorted map can answer it cheaply.