title: Longest Palindrome Subsequence Space
signature: function longestPalindromeSubsequenceSpace($s) {
test_code: <?php
  
  
  // SOLUTION CODE 
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  function validateSolution($actual, $expected){
      return serialize($actual) == serialize($expected);
  }
  
  function driver($s, $expected){
      try{
        if (validateSolution(PLACEHOLDER_FN_NAME($s), $expected)){
          return "PASSED";
        }
        return "FAILED";
      }
      catch (Exception $exception_obj) {
        return get_class($exception_obj);
      }
  }
  
  function main(){
      printf("TEST-0...%s\n",driver(
        " E", 
        1));
      
      printf("TEST-1...%s\n",driver(
        "0845591950", 
        7));
      
      printf("TEST-2...%s\n",driver(
        "00101011", 
        5));
      
      printf("TEST-3...%s\n",driver(
        "pLSvlwrACvFaoT", 
        3));
      
      printf("TEST-4...%s\n",driver(
        "7246", 
        1));
      
      printf("TEST-5...%s\n",driver(
        "1010101100000", 
        8));
      
      printf("TEST-6...%s\n",driver(
        "obPkcLSFp", 
        1));
      
      printf("TEST-7...%s\n",driver(
        "914757557818", 
        7));
      
      printf("TEST-8...%s\n",driver(
        "1", 
        1));
      
      printf("TEST-9...%s\n",driver(
        "PKvUWIQ", 
        1));
      
  }
  
  main();
  ?>
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 ];
  }