Palindromes using Scala

Question

I came across this problem from CodeChef. The problem states the following:

A positive integer is called a palindrome if its representation in the decimal system is the same when read from left to right and from right to left. For a given positive integer K of not more than 1000000 digits, write the value of the smallest palindrome larger than K to output.

I can define a isPalindrome method as follows:

def isPalindrome(someNumber:String):Boolean = someNumber.reverse.mkString == someNumber

The problem that I am facing is how do I loop from the initial given number and break and return the first palindrome when the integer satisfies the isPalindrome method? Also, is there a better(efficient) way to write the isPalindrome method?

It will be great to get some guidance here

Answer 1

If you have a number like 123xxx you know, that either xxx has to be below 321 - then the next palindrom is 123321.

Or xxx is above, then the 3 can't be kept, and 124421 has to be the next one.

Here is some code without guarantees, not very elegant, but the case of (multiple) Nines in the middle is a bit hairy (19992):

object Palindrome extends App {

def nextPalindrome (inNumber: String): String = {
  val len = inNumber.length ()
  if (len == 1 && inNumber (0) != '9') 
    "" + (inNumber.toInt + 1) else {
    val head = inNumber.substring (0, len/2)
    val tail = inNumber.reverse.substring (0, len/2)
    val h = if (head.length > 0) BigInt (head) else BigInt (0)
    val t = if (tail.length > 0) BigInt (tail) else BigInt (0)

    if (t < h) {
      if (len % 2 == 0) head + (head.reverse)
      else inNumber.substring (0, len/2 + 1) + (head.reverse)
    } else {
     if (len % 2 == 1) {
       val s2 = inNumber.substring (0, len/2 + 1) // 4=> 4
       val h2 = BigInt (s2) + 1  // 5 
       nextPalindrome (h2 + (List.fill (len/2) ('0').mkString)) // 5 + "" 
     } else {
       val h = BigInt (head) + 1
       h.toString + (h.toString.reverse)
     }
    }
  }
}

def check (in: String, expected: String) = {
  if (nextPalindrome (in) == expected) 
    println ("ok: " + in) else 
    println (" - fail: " + nextPalindrome (in) + " != " + expected + " for: " + in)
}
//
val nums = List (("12345", "12421"), // f
  ("123456", "124421"), 
  ("54321", "54345"), 
  ("654321", "654456"), 
  ("19992", "20002"),
  ("29991", "29992"),
  ("999", "1001"),
  ("31", "33"),
  ("13", "22"),
  ("9", "11"),
  ("99", "101"),
  ("131", "141"),
  ("3", "4")
)
nums.foreach (n => check (n._1, n._2))
println (nextPalindrome ("123456678901234564579898989891254392051039410809512345667890123456457989898989125439205103941080951234566789012345645798989898912543920510394108095"))

}

I guess it will handle the case of a one-million-digit-Int too.

Answer 2

Doing reverse is not the greatest idea. It's better to start at the beginning and end of the string and iterate and compare element by element. You're wasting time copying the entire String and reversing it even in cases where the first and last element don't match. On something with a million digits, that's going to be a huge waste.

This is a few orders of magnitude faster than reverse for bigger numbers:

def isPalindrome2(someNumber:String):Boolean = {
  val len = someNumber.length;
  for(i <- 0 until len/2) {
    if(someNumber(i) != someNumber(len-i-1)) return false; 
  }
  return true;
}

There's probably even a faster method, based on mirroring the first half of the string. I'll see if I can get that now...

update So this should find the next palindrome in almost constant time. No loops. I just sort of scratched it out, so I'm sure it can be cleaned up.

def nextPalindrome(someNumber:String):String = {
  val len = someNumber.length;
  if(len==1) return "11";
  val half = scala.math.floor(len/2).toInt;
  var firstHalf = someNumber.substring(0,half);
  var secondHalf = if(len % 2 == 1) {
    someNumber.substring(half+1,len);
  } else {
    someNumber.substring(half,len);
  }

  if(BigInt(secondHalf) > BigInt(firstHalf.reverse)) {
    if(len % 2 == 1) {
      firstHalf += someNumber.substring(half, half+1);
      firstHalf = (BigInt(firstHalf)+1).toString;
      firstHalf + firstHalf.substring(0,firstHalf.length-1).reverse
    } else {
      firstHalf = (BigInt(firstHalf)+1).toString;
      firstHalf + firstHalf.reverse;
    }
  } else {
    if(len % 2 == 1) {
      firstHalf + someNumber.substring(half,half+1) + firstHalf.reverse;
    } else {
      firstHalf + firstHalf.reverse;
    }
  }
}

Answer 3

This is most general and clear solution that I can achieve:
Edit: got rid of BigInt's, now it takes less than a second to calculate million digits number.

def incStr(num: String) = {  // helper method to increment number as String
  val idx = num.lastIndexWhere('9'!=, num.length-1)
  num.take(idx) + (num.charAt(idx)+1).toChar + "0"*(num.length-idx-1)
}

def palindromeAfter(num: String) = {
  val lengthIsOdd = num.length % 2 
  val halfLength  = num.length / 2 + lengthIsOdd
  val leftHalf  = num.take(halfLength)               // first half of number (including central digit)
  val rightHalf = num.drop(halfLength - lengthIsOdd) // second half of number (also including central digit)      

  val (newLeftHalf, newLengthIsOdd) =  // we need to calculate first half of new palindrome and whether it's length is odd or even
    if (rightHalf.compareTo(leftHalf.reverse) < 0) // simplest case - input number is like 123xxx and xxx < 321
      (leftHalf, lengthIsOdd) 
    else if (leftHalf forall ('9'==))              // special case - if number is like '999...', then next palindrome will be like '10...01' and one digit longer
      ("1" + "0" * (halfLength - lengthIsOdd), 1 - lengthIsOdd)
    else                                           // other cases - increment first half of input number before making palindrome
      (incStr(leftHalf), lengthIsOdd)

  // now we can create palindrome itself
  newLeftHalf + newLeftHalf.dropRight(newLengthIsOdd).reverse
}   

Answer 4

According to your range-less proposal: the same thing but using Stream:

def isPalindrome(n:Int):Boolean = n.toString.reverse == n.toString
def ints(n: Int): Stream[Int] = Stream.cons(n, ints(n+1))
val result = ints(100).find(isPalindrome)

And with iterator (and different call method, the same thing you can do with Stream, actually):

val result = Iterator.from(100).find(isPalindrome)

But as @user unknown stated, it is direct bruteforce and not practical with large numbers.

Answer 5

To check if List of Any Type is palindrome using slice, without any Loops

def palindrome[T](list: List[T]): Boolean = {
if(list.length==1 || list.length==0 ){
  false
}else {
  val leftSlice: List[T] = list.slice(0, list.length / 2)
  var rightSlice :List[T]=Nil
  if (list.length % 2 != 0) {
    rightSlice = list.slice(list.length / 2 + 1, list.length).reverse
  } else {
    rightSlice = list.slice(list.length / 2, list.length).reverse
  }
  leftSlice ==rightSlice
}

}

Though the simplest solution would be

     def palindrome[T](list: List[T]): Boolean = {
      list == list.reverse
      }

Answer 6

You can simply use the find method on collections to find the first element matching a given predicate:

  def isPalindrome(n:Int):Boolean = n.toString.reverse == n.toString
  val (start, end) = (100, 1000)
  val result: Option[Int] = (start to end).find(isPalindrome)
  result foreach println

  >Some(101)

Answer 7

Solution to verify if a String is a palindrome

This solution doesn't reverse the String. However I am not sure that it will be faster.

def isPalindrome(s:String):Boolean = { 
  s.isEmpty ||   
  ((s.last == s.head) && isPalindrome(s.tail.dropRight(1)))
}

Solution to find next palindrome given a String

This solution is not the best for scala (pretty the same as Java solution) but it only deals with Strings and is suitable for large numbers

You just have to mirror the first half of the number you want, check if it is higher than the begin number, otherwise, increase by one the last digit of the first half and mirror it again.

First, a function to increment the string representation of an int by 1:

def incrementString(s:String):String = {
  if(s.nonEmpty){
    if (s.last == '9')
      incrementString(s.dropRight(1))+'0'
    else
      s.dropRight(1) + (s.last.toInt +1).toChar
  }else
    "1"
}

Then, a function to compare to string representation of ints: (the function 'compare' doesn't work for that case)

/* is less that 0 if x<y, is more than 0 if x<y, is equal to 0 if x==y */
def compareInts(x:String, y:String):Int = {
  if (x.length !=y.length)
    (x.length).compare(y.length)
  else
    x.compare(y)
}

Now the function to compute the next palindrome:

def nextPalindrome(origin_ :String):String = {
  /*Comment if you want to have a strictly bigger number, even if you already have a palindrome as input */
  val origin = origin_
  /* Uncomment if you want to have a strictly bigger number, even if you already have a palindrome as input */
  //val origin = incrementString(origin_)

  val length = origin.length
  if(length % 2 == 0){
    val (first, last) = origin.splitAt(length/2); 
    val reversed = first.reverse
    if (compareInts(reversed,last) > -1)
      first ++ reversed
    else{
      val firstIncr = incrementString(first)
      firstIncr ++ firstIncr.reverse
    }
  } else {
    val (first,last) = origin.splitAt((length+1)/2)
    val reversed = first.dropRight(1).reverse
    if (compareInts(reversed,last) != -1)
      first ++ reversed
    else{
      val firstIncr = incrementString(first)
      firstIncr ++ firstIncr.dropRight(1).reverse
    }
  }
}

Answer 8

You could try something like this, I'm using basic recursive:

 object Palindromo {
  def main(args: Array[String]): Unit = {

    var s: String = "arara"
    println(verificaPalindromo(s))
  }

  def verificaPalindromo(s: String): String = {
    if (s.length == 0 || s.length == 1)
      "true" 
    else
      if (s.charAt(0).toLower == s.charAt(s.length - 1).toLower)
        verificaPalindromo(s.substring(1, s.length - 1))
      else
        "false"
  }
}

Answer 9

  @tailrec
  def palindrome(str: String, start: Int, end: Int): Boolean = {
    if (start == end)
      true
    else if (str(start) != str(end))
      false
    else
      pali(str, start + 1, end - 1)
  }

  println(palindrome("arora", 0, str.length - 1))