IOI '00 P1 - Palindrome

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Points: 10 (partial)
Time limit: 1.0s
Memory limit: 32M

Problem type
IOI '00 - Beijing, China

A palindrome is a symmetrical string, that is, a string read identically from left to right as well as from right to left. You are to write a program which, given a string, determines the minimal number of characters to be inserted into the string in order to obtain a palindrome.

As an example, by inserting 2 characters, the string Ab3bd can be transformed into a palindrome (dAb3bAd or Adb3bdA). However, inserting fewer than 2 characters does not produce a palindrome.

Input Specification

The first line contains one integer: the length of the input string N, 3 \le N \le 5\,000. The second line contains one string with length N. The string is formed from uppercase letters from A to Z, lowercase letters from a to z and digits from 0 to 9. Uppercase and lowercase letters are to be considered distinct.

Output Specification

The first line contains one integer, which is the desired minimal number.

Sample Input


Sample Output



  • 0
    Pheonix  commented on Oct. 3, 2023, 1:00 p.m.

    How to get rid of RTE here! (bad_alloc)?

    • 4
      volcano  commented on Oct. 4, 2023, 7:59 p.m.

      You've defined int as long long, so your DP vector uses up to 8 \times 5001 \times 5001 \approx 200MB, and even with 32-bit integers (64-bit integers are not required for this problem), it uses 100MB of memory. The memory limit is only 32 megabytes. The solution is to only store the current and previous rows, as you only need the previous row to calculate the answer for the current row. Hope this helps.