title: Longest Palindrome Subsequence Space
signature: def longestPalindromeSubsequenceSpace(s: String) = {
test_code: import scala.collection.mutable.HashMap
  import scala.collection.immutable.HashSet
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  
  // TESTING CODE 
  // ============================================
  def validateSolution(actual: Int , expected: Int): Boolean = {
      actual.toString == expected.toString
  }
  
  def driver(s: String, expected: Int): String = {
      try {
          if (validateSolution(PLACEHOLDER_FN_NAME(s),expected)) {
              "PASSED"
          } else{
              "FAILED"
          }
      }catch{
          case e: Exception => {e.getClass.getName}
      }
  
  }
  object QuestionEvaluator extends App {
  
      println(s"TEST-0...${driver(
        " E", 
        1    
      )}")   
  
  
      println(s"TEST-1...${driver(
        "0845591950", 
        7    
      )}")   
  
  
      println(s"TEST-2...${driver(
        "00101011", 
        5    
      )}")   
  
  
      println(s"TEST-3...${driver(
        "pLSvlwrACvFaoT", 
        3    
      )}")   
  
  
      println(s"TEST-4...${driver(
        "7246", 
        1    
      )}")   
  
  
      println(s"TEST-5...${driver(
        "1010101100000", 
        8    
      )}")   
  
  
      println(s"TEST-6...${driver(
        "obPkcLSFp", 
        1    
      )}")   
  
  
      println(s"TEST-7...${driver(
        "914757557818", 
        7    
      )}")   
  
  
      println(s"TEST-8...${driver(
        "1", 
        1    
      )}")   
  
  
      println(s"TEST-9...${driver(
        "PKvUWIQ", 
        1    
      )}")   
  
  }
  
source_py: def longest_palindrome_subsequence_space(s):
      n = len(s)
      a = ([0] * n)
      for i in range((n - 1), (- 1), (- 1)):
          back_up = 0
          for j in range(i, n):
              if (j == i):
                  a[j] = 1
              elif (s[i] == s[j]):
                  temp = a[j]
                  a[j] = (back_up + 2)
                  back_up = temp
              else:
                  back_up = a[j]
                  a[j] = max(a[(j - 1)], a[j])
      return a[(n - 1)]
source_cpp: int longest_palindrome_subsequence_space(string & s) {
    int n = s . length ( );
    int a [ n ];
    for ( int i = n - 1;
    i >= 0;
    i -- ) {
      int back_up = 0;
      for ( int j = i;
      j < n;
      j ++ ) {
        if ( j == i ) a [ j ] = 1;
        else if ( s [ i ] == s [ j ] ) {
          int temp = a [ j ];
          a [ j ] = back_up + 2;
          back_up = temp;
        }
        else {
          back_up = a [ j ];
          a [ j ] = max ( a [ j - 1 ], a [ j ] );
        }
      }
    }
    return a [ n - 1 ];
  }