Problem Statement   During tough times like these, investment becomes more uncertain with more dangers. To solve it, we might try to train a model to decide when to buy or sell. Therefore, to provide it with correct data, we plan to design an algorithm that answers: what is the perfect moment to buy and when to sell to maximize your profit? Assume you must buy Input: ???????: array listing ??????? ?? ??? ??????, where indices represent days; it has at least two valueschanges: array listing changes in the prices, where indices represent days; it has at least two values Output: ???????????:index of the change before which we buy:index of the change before which we sell:the profit of this intervali:index of the change before which we buyj:index of the change before which we sellmaxProfit:the profit of this interval Example: Assume the below table contains the prices of a particular stock over days   ??????prices ???????changes Day Value   0 50 - 1 63 13 2 70 7 3 40 -30 4 55 15 5 65 10 6 60 -5 7 72 12 8 79 7 9 68 -11 10 74 6 Therefore, the output of maxProfit([13,7,-30,15,10,-5,12,7,-11,6]) should be (3, 7, 39) . This is because our maximum profit would be 3939 when we buy the stock at day 4, index of 33, and sell after day 8, index of 77. Then, the total profit is 15+10−5+12+7=3915+10−5+12+7=39 We will try to solve the problem using various techniques: Brute-Force Divide-and-Conquer

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Problem Statement

 

During tough times like these, investment becomes more uncertain with more dangers. To solve it, we might try to train a model to decide when to buy or sell. Therefore, to provide it with correct data, we plan to design an algorithm that answers:

  • what is the perfect moment to buy and when to sell to maximize your profit?
    Assume you must buy

Input:

???????: array listing ??????? ?? ??? ??????, where indices represent days; it has at least two valueschanges: array listing changes in the prices, where indices represent days; it has at least two values
Output:
???????????:index of the change before which we buy:index of the change before which we sell:the profit of this intervali:index of the change before which we buyj:index of the change before which we sellmaxProfit:the profit of this interval
Example:
Assume the below table contains the prices of a particular stock over days

 

??????prices ???????changes
Day Value  
0 50 -
1 63 13
2 70 7
3 40 -30
4 55 15
5 65 10
6 60 -5
7 72 12
8 79 7
9 68 -11
10 74 6

Therefore, the output of maxProfit([13,7,-30,15,10,-5,12,7,-11,6]) should be (3, 7, 39) . This is because our maximum profit would be 3939 when we buy the stock at day 4, index of 33, and sell after day 8, index of 77. Then, the total profit is 15+10−5+12+7=3915+10−5+12+7=39

We will try to solve the problem using various techniques:

  • Brute-Force
  • Divide-and-Conquer
Divide and Conquer
Now, we would try to use a divide and conquer paradigm. Hint: try the three steps, and design multiple versions to master these steps
In [ ]: # write your implementation here
def maxProfit(changes):
This is just an interface for <maxProfitDivide>
it returns the indices of (i,j) indicating the day to buy and sell respectively
to have the maximum profit in a list of prices per day in <changes>.
Inputs:
- changes: the list holding the changes in prices; the value whose index is k represents
the change between day <k> and day <k+1>
<changes> has at least a single change [two days]
Output:
- i: the index of the change before which we buy
- j: the index of the change after which we sell
- maxProfit: the value of the maximum profit
return (0,0,0)
In [ ]: maxProfit([13,7,-30,15,10, -5,12,7,-11,6])
Transcribed Image Text:Divide and Conquer Now, we would try to use a divide and conquer paradigm. Hint: try the three steps, and design multiple versions to master these steps In [ ]: # write your implementation here def maxProfit(changes): This is just an interface for <maxProfitDivide> it returns the indices of (i,j) indicating the day to buy and sell respectively to have the maximum profit in a list of prices per day in <changes>. Inputs: - changes: the list holding the changes in prices; the value whose index is k represents the change between day <k> and day <k+1> <changes> has at least a single change [two days] Output: - i: the index of the change before which we buy - j: the index of the change after which we sell - maxProfit: the value of the maximum profit return (0,0,0) In [ ]: maxProfit([13,7,-30,15,10, -5,12,7,-11,6])
Brute Force
As we in general, try to solve the problem first; we start with a brute force algorithm: design it below
In [ ]: # write your implementation here
def maxProfitBrute(changes):
it returns the indices of (i,j) indicating the day to buy and sell respectively
to have the maximum profit in a list of prices per day in <changes>.
Inputs:
- changes: the list holding the changes in prices; the value whose index is k represents
the change between day <k> and day <k+1>
<changes> has at least a single change [two days]
Output:
- i: the index of the change before which we buy
- j: the index of the change after which we seli
maxProfit: the value of the maximum profit
Example:
changes = [1,2]
- that means the price started with <x>;
day 1: it became <x+1>
- day 2: it became <x+3>
In that case: (i,j) = (8,1) as we should buy at the first day, and sell after the third day
# return the values
return (e,0,0)
In [ ]: # Try your algorithm
maxProfitBrute([13,7,-30,15,1e, -5,12,7,-11,6])
Transcribed Image Text:Brute Force As we in general, try to solve the problem first; we start with a brute force algorithm: design it below In [ ]: # write your implementation here def maxProfitBrute(changes): it returns the indices of (i,j) indicating the day to buy and sell respectively to have the maximum profit in a list of prices per day in <changes>. Inputs: - changes: the list holding the changes in prices; the value whose index is k represents the change between day <k> and day <k+1> <changes> has at least a single change [two days] Output: - i: the index of the change before which we buy - j: the index of the change after which we seli maxProfit: the value of the maximum profit Example: changes = [1,2] - that means the price started with <x>; day 1: it became <x+1> - day 2: it became <x+3> In that case: (i,j) = (8,1) as we should buy at the first day, and sell after the third day # return the values return (e,0,0) In [ ]: # Try your algorithm maxProfitBrute([13,7,-30,15,1e, -5,12,7,-11,6])
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