**Idea:**

Let’s define an array **RES**, where **RES[i][j]** represents the total number of eligible pair of strings which starts at index **i** and ends at index **j**. So at any time we will be able to answer any query in **O(1)**.

We need to build a data structure such that given any string s it can tell us how many inserted strings are already there which match with string **S** in **O(maximum length of S)** complexity. We can do this using trie data structure. For each of the suffix of a string we must build a trie.

If you are not familiar with trie then please check this links:

http://www.shafaetsplanet.com/planetcoding/?p=1679

http://www.geeksforgeeks.org/trie-insert-and-search/

Now sort all the names in increasing order of time and iterate through one by one. When a person enters the party we will insert his name in that data structure, and when he leaves we will delete him again.

Now let’s see how we can handle this **insert** and **delete** operation.

Let’s say a person **S** has entered the party. Now for each of the **substring S(u,v)** of string **S** insert this substring in **TRIE[u]**.

Here **u** is the starting position and **v** is the ending position of **substring S(u,v)**.

Now how this new insertion change the **RES[u][v]**?

Let’s take **K** = the number of string in **TRIE[u]** which match with **substring S(u,v)** before inserting it. So **C(K,2)** was included in **RES[u][v]** for this particular substring.

Here **C(K,2)** = no of ways to select any pair of items from **K** items.

But after the insertion of it the new count will be **(K+1)**, so the new result is supposed to be **C(K+1,2)** now.

So to adjust the result remove **C(K,2)** and add **C(K+1,2)** in **RES[u][v]**. Which is **RES[u][v]** = RES[u][v] - C(K,2) + C(K,+1,2).

The deleting process is similar to the insertion. As we are deleting now the new value of **K** will be **K-1**. We handle the other things accordingly.

**Complexity:** We can iterate through each of the suffix in **O(length of the suffix)** and then insert or delete each of the prefix of that suffix in **O(length of the suffix)**. Thus we will be able to insert or delete all the sub-string of a string in * O(N(length of the suffix)^2)** complexity.

**Note:** We could also handle the same operations using hashing and unordered_map. As unordered_map is supposed to work in **O(1)**. So the complexity would be same. But unordered_map works very slowly when there is huge amount of data. So this solution wouldn’t pass even in 3 seconds.

**Judge Solution:** http://ideone.com/yJ49A3

**Alternate Writer:** Labib Md Rashid

67%
Solution Ratio

imranziadEarliest,

Sourav1234Fastest, 0.5s

MorassLightest, 16 MB

Deshi_TouristShortest, 2022B

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