title: Maximum Profit By Buying And Selling A Share At Most Twice
signature: maximumProfitByBuyingAndSellingAShareAtMostTwice :: [Integer] -> Integer -> Integer
  maximumProfitByBuyingAndSellingAShareAtMostTwice price n = 
test_code: import Text.Printf
  import Control.Exception (catch, SomeException)
  import Data.Typeable
  import qualified Data.List as List
  import qualified Data.Map as Map
  import qualified Data.Set as Set
  
  -- SOLUTION CODE
  -- ============================================
  
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  validateSolution :: Integer -> Integer -> Bool
  validateSolution actual expected = do
      actual == expected
  
  
  driver :: [Integer] -> Integer -> Integer -> String
  driver price n expected = do
      if (validateSolution (PLACEHOLDER_FN_NAME price n) expected)
          then "PASSED"
      else "FAILED"
  
  main = do
      printf "TEST-0...%s\n" (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) )
  
      printf "TEST-1...%s\n" (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) )
  
      printf "TEST-2...%s\n" (driver ([0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) (13) (1) )
  
      printf "TEST-3...%s\n" (driver ([2, 67, 50, 8, 20, 42, 37, 69, 86, 74, 85, 96, 78, 89, 91]) (8) (126) )
  
      printf "TEST-4...%s\n" (driver ([-68, -52, -14, -2, 18, 22, 30, 34, 64, 64, 70]) (9) (132) )
  
      printf "TEST-5...%s\n" (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) )
  
      printf "TEST-6...%s\n" (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) )
  
      printf "TEST-7...%s\n" (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) )
  
      printf "TEST-8...%s\n" (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) )
  
      printf "TEST-9...%s\n" (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) )
  
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;
  }