title: Maximum Height Of Triangular Arrangement Of Array Values
signature: function maximum_height_of_triangular_arrangement_of_array_values(a, n)
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(a, n, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(a, n) 
      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({8, 10, 11, 14, 14, 17, 20, 20, 22, 22, 22, 23, 25, 30, 33, 39, 39, 41, 43, 45, 46, 46, 46, 50, 51, 53, 57, 59, 60, 64, 64, 66, 72, 72, 75, 77, 85, 85, 87, 88, 90, 91, 93, 94, 94, 95}, 38, 8)
      print(string.format("TEST-0...%s",result))
  
      result = driver({-44, -90, 20, 4, -56, -50, -80, 74, -82, 20, 62, -26, -10, -14, -76, 82, -88, 92, 30, 44, -62, -86, -20, -96, -60, -88, -78, -40, -48, -92, 62, 58, 94, 68, 68, 44, 80, 4, 48, -92, 30, -76, -46, -20, 4}, 36, 7)
      print(string.format("TEST-1...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 28, 6)
      print(string.format("TEST-2...%s",result))
  
      result = driver({8, 34, 48, 10, 5, 12, 80, 7, 67, 1, 79, 59, 63, 13, 16, 23, 62, 56, 99, 89, 7, 80}, 12, 4)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-88, -46, -40, -40, 38}, 3, 1)
      print(string.format("TEST-4...%s",result))
  
      result = driver({1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1}, 44, 8)
      print(string.format("TEST-5...%s",result))
  
      result = driver({8, 15, 35, 39, 49, 81, 86, 91}, 7, 3)
      print(string.format("TEST-6...%s",result))
  
      result = driver({-24, 56, -74, -76, -80, 86, 90, 0, -26, 18, 72, 78, -66, -28, 22, 22, 72, 78, -50, -12, 20, 12, -68, -2, -58, -44, 28, -58, 90, -28, 32, -70, -48, -66, -94, -50, 18, -12, 80, 12, 82, 56, -64, 10, -22}, 36, 7)
      print(string.format("TEST-7...%s",result))
  
      result = driver({0, 0}, 1, 1)
      print(string.format("TEST-8...%s",result))
  
      result = driver({62, 93, 69, 40, 26, 2, 29, 83, 66, 68, 67, 73, 12, 65, 89, 57, 38, 99, 42, 27, 38, 24, 43, 4, 4, 54, 72, 47, 52, 46, 53, 24, 3, 41, 64, 33, 88, 3, 1, 7, 17, 31, 20, 33, 69, 21, 9, 24, 59}, 26, 6)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
source_py: def maximum_height_of_triangular_arrangement_of_array_values(a, n):
      result = 1
      for i in range(1, n):
          y = ((i * (i + 1)) / 2)
          if (y < n):
              result = i
          else:
              break
      return result
source_cpp: int maximum_height_of_triangular_arrangement_of_array_values(vector<int> a, int n) {
    int result = 1;
    for ( int i = 1;
    i <= n;
    ++ i ) {
      long long y = ( i * ( i + 1 ) ) / 2;
      if ( y < n ) result = i;
      else break;
    }
    return result;
  }