title: Maximum Profit By Buying And Selling A Share At Most Twice
signature: def 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: import array
  import bisect
  import collections
  import datetime
  import functools
  import heapq
  import itertools
  import math
  import queue
  import re
  import string
  import sys
  from typing import Any, Dict, List, Optional, Set
  
  
  # SOLUTION CODE
  # ============================================
  PLACEHOLDER_CODE_BODY
  
  # TESTING CODE 
  # ============================================
  def validate_solution(actual, expected):
      return actual == expected
  
  def driver(price, n, expected):
      try:
          if validate_solution(PLACEHOLDER_FN_NAME(
              price, n),
              expected
          ):
              return "PASSED"
          return "FAILED"
      except Exception as exception_obj:
          return type(exception_obj).__name__
      
  if __name__ == "__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(f"TEST-0...{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(f"TEST-1...{result}")
  
      result = driver([0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 13, 1)
      print(f"TEST-2...{result}")
  
      result = driver([2, 67, 50, 8, 20, 42, 37, 69, 86, 74, 85, 96, 78, 89, 91], 8, 126)
      print(f"TEST-3...{result}")
  
      result = driver([-68, -52, -14, -2, 18, 22, 30, 34, 64, 64, 70], 9, 132)
      print(f"TEST-4...{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(f"TEST-5...{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(f"TEST-6...{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(f"TEST-7...{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(f"TEST-8...{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(f"TEST-9...{result}")
  
      sys.exit(0)
question_info.test_case_ids: ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
question_info.entry_fn_name: maximum_profit_by_buying_and_selling_a_share_at_most_twice
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.entry_cls_name: Solution