title: Maximum Profit By Buying And Selling A Share At Most Twice
signature: function maximum_profit_by_buying_and_selling_a_share_at_most_twice(price, n)
source_py: def maximum_profit_by_buying_and_selling_a_share_at_most_twice(price, n):
      profit = ([0] * n)
      max_price = price[(n - 1)]
      for i in range((n - 2), 0, (- 1)):
          if (price[i] > max_price):
              max_price = price[i]
          profit[i] = max(profit[(i + 1)], (max_price - price[i]))
      min_price = price[0]
      for i in range(1, n):
          if (price[i] < min_price):
              min_price = price[i]
          profit[i] = max(profit[(i - 1)], (profit[i] + (price[i] - min_price)))
      result = profit[(n - 1)]
      return result
source_cpp: int maximum_profit_by_buying_and_selling_a_share_at_most_twice(vector<int> price, int n) {
    int * profit = new int [ n ];
    for ( int i = 0;
    i < n;
    i ++ ) profit [ i ] = 0;
    int max_price = price [ n - 1 ];
    for ( int i = n - 2;
    i >= 0;
    i -- ) {
      if ( price [ i ] > max_price ) max_price = price [ i ];
      profit [ i ] = max ( profit [ i + 1 ], max_price - price [ i ] );
    }
    int min_price = price [ 0 ];
    for ( int i = 1;
    i < n;
    i ++ ) {
      if ( price [ i ] < min_price ) min_price = price [ i ];
      profit [ i ] = max ( profit [ i - 1 ], profit [ i ] + ( price [ i ] - min_price ) );
    }
    int result = profit [ n - 1 ];
    delete [ ] profit;
    return result;
  }
question_info.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(price, n, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(price, 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({9, 10, 10, 12, 17, 18, 23, 32, 41, 44, 47, 50, 59, 69, 69, 75, 82, 84, 87, 89, 97, 99}, 20, 80)
      print(string.format("TEST-0...%s",result))
  
      result = driver({6, 6, 60, 40, 32, -70, -92, 88, 10, -8, -54, 4, 16, 8, -44, 80, -70, 36, 36, -74, -94, 18, -64, -66, -46, 0, -54, -84, 16, -88, -34, -24, 92, 84, 62}, 34, 366)
      print(string.format("TEST-1...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 13, 1)
      print(string.format("TEST-2...%s",result))
  
      result = driver({2, 67, 50, 8, 20, 42, 37, 69, 86, 74, 85, 96, 78, 89, 91}, 8, 126)
      print(string.format("TEST-3...%s",result))
  
      result = driver({-68, -52, -14, -2, 18, 22, 30, 34, 64, 64, 70}, 9, 132)
      print(string.format("TEST-4...%s",result))
  
      result = driver({1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1}, 21, 2)
      print(string.format("TEST-5...%s",result))
  
      result = driver({4, 17, 19, 28, 29, 30, 30, 30, 35, 36, 36, 38, 40, 40, 42, 43, 45, 51, 55, 57, 58, 59, 64, 65, 66, 82, 84, 85, 87, 91, 92, 94, 98, 98}, 25, 62)
      print(string.format("TEST-6...%s",result))
  
      result = driver({52, 88, -40, 60, 30, 8, -96, 66, -96, -28, -56, -14, 76, -92, 56, 58, 64, -60, -90, 26, 64, -2, 54, -24, 54, -46, -44}, 14, 334)
      print(string.format("TEST-7...%s",result))
  
      result = driver({0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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}, 22, 0)
      print(string.format("TEST-8...%s",result))
  
      result = driver({82, 14, 51, 12, 5, 15, 50, 88, 91, 82, 16, 98, 23, 58, 86, 91, 30, 81, 7, 73, 67, 47, 10, 50, 43, 31, 19, 2, 22}, 18, 168)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
question_info.entry_cls_name: Solution
question_info.test_list: [{"idx": 0, "outputs": 80, "inputs": {"price": [9, 10, 10, 12, 17, 18, 23, 32, 41, 44, 47, 50, 59, 69, 69, 75, 82, 84, 87, 89, 97, 99], "n": 20}}, {"idx": 1, "outputs": 366, "inputs": {"price": [6, 6, 60, 40, 32, -70, -92, 88, 10, -8, -54, 4, 16, 8, -44, 80, -70, 36, 36, -74, -94, 18, -64, -66, -46, 0, -54, -84, 16, -88, -34, -24, 92, 84, 62], "n": 34}}, {"idx": 2, "outputs": 1, "inputs": {"price": [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "n": 13}}, {"idx": 3, "outputs": 126, "inputs": {"price": [2, 67, 50, 8, 20, 42, 37, 69, 86, 74, 85, 96, 78, 89, 91], "n": 8}}, {"idx": 4, "outputs": 132, "inputs": {"price": [-68, -52, -14, -2, 18, 22, 30, 34, 64, 64, 70], "n": 9}}, {"idx": 5, "outputs": 2, "inputs": {"price": [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1], "n": 21}}, {"idx": 6, "outputs": 62, "inputs": {"price": [4, 17, 19, 28, 29, 30, 30, 30, 35, 36, 36, 38, 40, 40, 42, 43, 45, 51, 55, 57, 58, 59, 64, 65, 66, 82, 84, 85, 87, 91, 92, 94, 98, 98], "n": 25}}, {"idx": 7, "outputs": 334, "inputs": {"price": [52, 88, -40, 60, 30, 8, -96, 66, -96, -28, -56, -14, 76, -92, 56, 58, 64, -60, -90, 26, 64, -2, 54, -24, 54, -46, -44], "n": 14}}, {"idx": 8, "outputs": 0, "inputs": {"price": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], "n": 22}}, {"idx": 9, "outputs": 168, "inputs": {"price": [82, 14, 51, 12, 5, 15, 50, 88, 91, 82, 16, 98, 23, 58, 86, 91, 30, 81, 7, 73, 67, 47, 10, 50, 43, 31, 19, 2, 22], "n": 18}}]
question_info.extension: lua
question_info.entry_fn_name: maximum_profit_by_buying_and_selling_a_share_at_most_twice
question_info.test_case_ids: 0 1 2 3 4 5 6 7 8 9
question_info.commands: lua __FILENAME__