Editorial for DMOPC '17 Contest 2 P4 - Mimi and Dictionary

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Submitting an official solution before solving the problem yourself is a bannable offence.

Author: Kirito

For $10\%$ ~10\%~ of points, we can iterate over all prefixes, and check if they are a palindrome in $\mathcal O(N)$ ~\mathcal O(N)~ time, and see if the string exists in the remainder of the string in $\mathcal O(N^2)$ ~\mathcal O(N^2)~ time.

Time Complexity: $\mathcal O(N^3)$ ~\mathcal O(N^3)~

For $20\%$ ~20\%~ of points, we can iterate over all prefixes, and check if they are a palindrome in $\mathcal O(N)$ ~\mathcal O(N)~ time, and see if the string exists in the remainder of the string in $\mathcal O(N)$ ~\mathcal O(N)~ time, by using a linear time string finding algorithm, such as KMP or Rabin-Karp.

Time Complexity: $\mathcal O(N^2)$ ~\mathcal O(N^2)~

For the remaining $70\%$ ~70\%~ of points, we can run Manacher's Algorithm, and then run the Z-Algorithm, and then use either binary search or preprocessing to determine the answer.

Time Complexity: $\mathcal O(N)$ ~\mathcal O(N)~ or $\mathcal O(N \log N)$ ~\mathcal O(N \log N)~

Comments

0

Ninjaclasher commented on Nov. 15, 2017, 9:10 p.m. ← edited →

Time limit not strict enough. My $\mathcal{O}(N^2)$ ~\mathcal{O}(N^2)~ algorithm passes without a problem.

1

r3mark commented on Nov. 15, 2017, 9:23 p.m. ← edited →

Yea, unfortunately there are multiple $\mathcal{O}(N^2)$ ~\mathcal{O}(N^2)~ solutions which pass, some of which perform even better than $\mathcal{O}(N)$ ~\mathcal{O}(N)~ solutions even on specially crafted data.

-1

imaxblue commented on Nov. 15, 2017, 11:46 p.m.

wow its indcyc