MapUtils.java

import java.util.*;
import java.util.Map.*;
import java.util.stream.*;

public class MapUtils {
    // Java 8 - Functional
    public static final <T, U> Map<U, List<T>> invertMap(Map<T, U> map) {
        HashMap<U, List<T>> invertedMap = new HashMap<>();

        for (T key : map.keySet()) {
            U newKey = map.get(key);

            invertedMap.computeIfAbsent(newKey, k -> new ArrayList<>());
            invertedMap.get(newKey).add(key);

        }

        return invertedMap;
    }

    // Java 8 - Streams
    public static final <T, U> Map<U, List<T>> invertMap2(Map<T, U> map) {
        return map.entrySet().stream().collect(Collectors.groupingBy(Entry::getValue,
                Collectors.mapping(Entry::getKey, Collectors.toList())));
    }

    // Java 5 - 7
    public static final <T, U> Map<U, List<T>> invertMap3(Map<T, U> map) {
        HashMap<U, List<T>> invertedMap = new HashMap<>();

        for (T key : map.keySet()) {
            U newKey = map.get(key);
            List<T> list = invertedMap.containsKey(newKey) ? invertedMap.get(newKey) : new ArrayList<T>();

            list.add(key);
            invertedMap.put(newKey, list);

        }

        return invertedMap;
    }

    public static void main(String[] args) {
        HashMap<Integer, String> original = new HashMap<Integer, String>() { {
            put(1, "A");
            put(2, "B");
            put(3, "C");
            put(4, "A");
        } };

        Map<String, List<Integer>> inverted = invertMap(original);

        System.out.println(original);
        System.out.println(inverted);
    }
}