Sunday, December 5, 2010

USACO - Palindromic Squares

Palindromic Squares
Rob Kolstad
Palindromes are numbers that read the same forwards as backwards. The number 12321 is a typical palindrome.
Given a number base B (2 <= B <= 20 base 10), print all the integers N (1 <= N <= 300 base 10) such that the square of N is palindromic when expressed in base B; also print the value of that palindromic square. Use the letters 'A', 'B', and so on to represent the digits 10, 11, and so on.
Print both the number and its square in base B.

PROGRAM NAME: palsquare

INPUT FORMAT

A single line with B, the base (specified in base 10).

SAMPLE INPUT (file palsquare.in)

10

OUTPUT FORMAT

Lines with two integers represented in base B. The first integer is the number whose square is palindromic; the second integer is the square itself.

SAMPLE OUTPUT (file palsquare.out)

1 1
2 4
3 9
11 121
22 484
26 676
101 10201
111 12321
121 14641
202 40804
212 44944
264 69696

Brute force - base conversion - palindrome checking

Produce all the squares of numbers from 1 to 300, convert them to base b and check whether they are palindrome or not, if they are, convert the number to base b too and print both the number and it's square that has been converted to base b.
I have two functions in my solution, toBase( int, int ) and isPal( string ). In toBase() function I convert the given number to base b, and in function isPal() I check whether the given string is palindrome or not with two iterators to the beginning and to the end of the string.

4 comments:

  1. There's no another solution more eficient?

    ReplyDelete
    Replies
    1. This comment has been removed by the author.

      Delete
  2. A better approach would be to generate palindrome for respective bases and check if they are squares. For example, for a base 2 we only need to do it for 32 such values.

    ReplyDelete
  3. This will not work, try base 5, 6 (base 10), will be 11 in base (5), and the square (36) is 121 in base 10, and therefore you are wrong.

    ReplyDelete

USACO - Prime Palindromes

I just skimmed the problem statement and panicked of the high boundary of the input, but something inside told me don't worry everyth...