title: Longest Palindrome Subsequence Space
signature: function longest_palindrome_subsequence_space(s)
test_code: 
  
  -- SOLUTION CODE
  -- ============================================
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  function isCorrect(actual, expected)
      if type(expected) ~= type(actual) then
          return false
      end
      
      if type(expected) == 'table' then
          for k,v_expected in pairs(expected) do
              
              if actual[k] == nil then
                  return false
              end
              local v_actual = actual[k]
              if not isCorrect(v_actual, v_expected) then
                  return false
              end
              actual[k]=nil
          end
      
          if next(actual) then 
              return false
          end
          return true
      else
          return actual == expected
      end
  end
  
  function validateSolution(actual, expected)
      return isCorrect(actual,expected)
  end
  
  function driver(s, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(s) 
      end)
      if status then
          if validateSolution(exec_result,expected) then
              return "PASSED"
          end
          return "FAILED"
      else
          return string.format("ERROR=%s",string.gsub(error_msg,".*:[%d]+: ",""))
      end
  end
      
  function main()
      result = driver(" E", 1)
      print(string.format("TEST-0...%s",result))
  
      result = driver("0845591950", 7)
      print(string.format("TEST-1...%s",result))
  
      result = driver("00101011", 5)
      print(string.format("TEST-2...%s",result))
  
      result = driver("pLSvlwrACvFaoT", 3)
      print(string.format("TEST-3...%s",result))
  
      result = driver("7246", 1)
      print(string.format("TEST-4...%s",result))
  
      result = driver("1010101100000", 8)
      print(string.format("TEST-5...%s",result))
  
      result = driver("obPkcLSFp", 1)
      print(string.format("TEST-6...%s",result))
  
      result = driver("914757557818", 7)
      print(string.format("TEST-7...%s",result))
  
      result = driver("1", 1)
      print(string.format("TEST-8...%s",result))
  
      result = driver("PKvUWIQ", 1)
      print(string.format("TEST-9...%s",result))
  
  end
  
  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 ];
  }