# How to find a missing element between two linked lists in O (n)?

I have two Singly Linked Lists of Integer. One of them is a subset of another (the order of numbers is different). What is the best way (regarding performance) to find a number which the first list does contain and the second one does not?

My thought is first to sort them (using merge sort) and then just compare element by element. So, it takes `O(nlogn+mlogm+n)`, but a better `O(n)` soltuion should exist.

This is O(n) solution both in Time and Space.

Logic

Lets say the original Linked List has size N we'll call it `LL1` and second Linked List as `LL2`.

=> Prepare a `Hasmap` of size N, `key` would be the `numbers` in the `LL1` and `value` would be frequency in `LL2`

`````` HashMap<Integer,Integer> map= new HashMap<Integer,Integer>();
```
```

=> Start traversing `LL1` and set the frequency to 0 for all the Numbers
By the time all values in `LL1` is iterated, you have all the Numbers present in `HashMap` with frequency = 0

`````` map.put(key, 0);
```
```

=> Now start looping through the `LL2`, pick the numbers using them as key and increment the value by `1`.
By the time all values in `LL2` is iterated, you have all the common numbers present in both `LL1` and `LL1` inside `HashMap` having`frequency > 0`

``````  map.put(key, map.get(key) + 1);
```
```

=> Now start traversing the `hasmap`, searching for `value = 0`, when found, print the `key` as this number present only in `LL1` and not in `LL2`

``````for (map.Entry<Integer,Integer> entry : map.entrySet())
{
if(entry.getValue() == 0)
System.out.println(entry.getKey());//This is a loner
}
```
```

2 Iterations and O(n) memory with O(n) time.