title: Count Palindromic Subsequence Given String
signature: function count_palindromic_subsequence_given_string(str)
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(str, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(str) 
      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("R", 1)
      print(string.format("TEST-0...%s",result))
  
      result = driver("2956350", 10)
      print(string.format("TEST-1...%s",result))
  
      result = driver("11100111110101", 2798)
      print(string.format("TEST-2...%s",result))
  
      result = driver("TZTDLIIfAD", 20)
      print(string.format("TEST-3...%s",result))
  
      result = driver("98", 2)
      print(string.format("TEST-4...%s",result))
  
      result = driver("1100100001", 270)
      print(string.format("TEST-5...%s",result))
  
      result = driver("oKwGeatf", 8)
      print(string.format("TEST-6...%s",result))
  
      result = driver("19", 2)
      print(string.format("TEST-7...%s",result))
  
      result = driver("00010110100", 563)
      print(string.format("TEST-8...%s",result))
  
      result = driver("Cyq", 3)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
source_py: def count_palindromic_subsequence_given_string(str):
      N = len(str)
      cps = [[0 for i in range((N + 2))] for j in range((N + 2))]
      for i in range(N):
          cps[i][i] = 1
      for L in range(2, (N + 1)):
          for i in range(N):
              k = ((L + i) - 1)
              if (k < N):
                  if (str[i] == str[k]):
                      cps[i][k] = ((cps[i][(k - 1)] + cps[(i + 1)][k]) + 1)
                  else:
                      cps[i][k] = ((cps[i][(k - 1)] + cps[(i + 1)][k]) - cps[(i + 1)][(k - 1)])
      return cps[0][(N - 1)]
source_cpp: int count_palindromic_subsequence_given_string(string str) {
    int N = str . length ( );
    int cps [ N + 1 ] [ N + 1 ];
    memset ( cps, 0, sizeof ( cps ) );
    for ( int i = 0;
    i < N;
    i ++ ) cps [ i ] [ i ] = 1;
    for ( int L = 2;
    L <= N;
    L ++ ) {
      for ( int i = 0;
      i < N;
      i ++ ) {
        int k = L + i - 1;
        if ( str [ i ] == str [ k ] ) cps [ i ] [ k ] = cps [ i ] [ k - 1 ] + cps [ i + 1 ] [ k ] + 1;
        else cps [ i ] [ k ] = cps [ i ] [ k - 1 ] + cps [ i + 1 ] [ k ] - cps [ i + 1 ] [ k - 1 ];
      }
    }
    return cps [ 0 ] [ N - 1 ];
  }