Magical Strings - Editorial




Author: Sumeet Verma

Tester: Aman Kedia

Editorialist: Sidhant Bansal

Prerequisites - Pigeon Hole Principle, Disjoint Set Union

Difficulty : Easy - Medium

Expected Complexity: O(N*N)

Editorial -

  1. Find the mid-point of each range (query) and if there are many queries having the same mid-point then only retain that query whose length is max, i.e (where r - l is maxm)
  2. This would have reduced the number of queries to 2*N at max, since there are 2*N number of mid-points in a string of length N.
  3. Now for each query do dsu union of element l with r, (l + 1) with (r - 1), (l + 2) with (r - 2) and so on. We do this because the character which would be put on the index l would be same as the one we put on index r. Extending this logic to all queries we need to maintain dsu. So basically all the elements of one component of dsu should have the same letter on them.
  4. After processing all the queries, let the number of dsu components be x, then the answer is 26x

Complexity Analysis: O(N * N) because we do an O(N) iteration for each query and total number of queries can be 2N, therefore O(2N*N). Here I have ignored the constant of union-find for simplicity.

1 Like

Can anyone explain how a string of length N can have 2*N midpoints ?

N for odd length ranges and N for even. :slight_smile:

Yeah !! Thats what I even thought of :slight_smile: Thanks a lot

Hi, the following is my code: (I couldn’t get the inline code function to work, sorry for the external link).

When I submit however, I’m getting TLE. Can you please point out any errors? My approach is basically DSU.

Thanks :slight_smile:

Can anyone please explain it in simple terms.