Check the ordering of 2 different keys in LinkedHashMap in O(1)

In a LinkedHashMap, the keys are ordered by when they were inserted into the map.

For example, consider the following map.

LinkedHashMap<Integer,Integer> map = new LinkedHashMap<>();
map.put(1, 1);
map.put(2, 3);
map.put(7, 4);
map.put(5, 6);

So, my understanding of LinkedHashMap is that the keys are stored in the form a Doubly Linked List.

So, in this example, the keys would be ordered as 1<->2<->7<->5

Now, my requirement is this. Given 2 keys from this map, is it possible to check which one came first or last?

For example, a function like the following

public boolean isFirst(int key1,int key2){
// logic to compute if key1 is first
}

Now, the above function can be done in O(n) easily by maintaining another map to get the order and compare it.

I want to do this operation in O(1). If it is possible, then should I maintain some other data structure to handle insertion, removal and updation of keys in the map ?

You can create a custom class that extends LinkedHashMap and add the custom method isFirst. Internally, we keep a separate map as you already analyzed with a timestamp variable which acts like a timestamp for us(the second at which the key was added).

If the first key's timestamp is less than the second ones, we return true , else we return false.

Class Snippet:

class CustomMap<K,V> extends LinkedHashMap<K,V>{
    private Map<K,Integer> ord_map;
    private int timestamp = 0;
    CustomMap(){
        super();
        ord_map = new HashMap<>();
    }
    
    public V put(K key,V val){
        ord_map.put(key,timestamp++);
        return super.put(key,val);
    }
    
    public V remove(Object key){
        ord_map.remove(key);
        return super.remove(key);
    }
    
    public boolean isFirst(K key1,K key2) throws Exception{
        if(!ord_map.containsKey(key1)) throw new Exception(key1 + " does not exist.");
        if(!ord_map.containsKey(key2)) throw new Exception(key2 + " does not exist.");
        
        return ord_map.get(key1) < ord_map.get(key2);
    }
}

Driver Code:

public class Solution{
    public static void main(String[] args) {
        CustomMap<Integer,Integer> cmap = new CustomMap<>();
        try{
            cmap.put(1, 1);
            cmap.put(5, 6);
            cmap.put(2, 3);
            cmap.put(7, 4);
            System.out.println(cmap.isFirst(5,2));    
            cmap.remove(5);
            cmap.put(5,99);
            System.out.println(cmap.isFirst(5,2));  
        }catch(Exception e){
            System.out.println(e.getMessage());
        }
        
    }
}

There could be a solution based on HashMap for indexes, but it has O(N) complexity both in time and memory to populate the index map.

import java.util.*;
public class Solution {
static int index = 0;
static Map<Integer, Integer> indexMap = new HashMap<>();
static void initIndexes(LinkedHashMap<Integer, Integer> map) {
indexMap.clear();
index = 0;
map.keySet().forEach(x -> {indexMap.put(x, index++);});
}
static boolean isKeyBefore(int key1, int key2) {
return indexMap.getOrDefault(key1, Integer.MAX_VALUE) < 
indexMap.getOrDefault(key2, -1);
}
public static void main(String []args) {
LinkedHashMap<Integer,Integer> map = new LinkedHashMap<>();
map.put(1, 1);
map.put(2, 3);
map.put(7, 4);
map.put(5, 6);
initIndexes(map);
System.out.println(indexMap);
System.out.println(isKeyBefore(2, 5)); // true
System.out.println(isKeyBefore(7, 1)); // false
System.out.println(isKeyBefore(5, 3)); // key2 is not in the indexMap
System.out.println(isKeyBefore(4, 2)); // key1 is not in the indexMap
System.out.println(isKeyBefore(6, 8)); // both keys are not in the indexMap
}
}