python and algorithims.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
python and algorithims.
![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 [ ]: # urite 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 maximun profit
return (e,e,0)
In [ ]: maxProfit([13,7, -30,15, 18,-5,12,7,-11,6])
Empirical Analysis
Now, compare between the growth rate of the two algorithms
In [ ]: # feel free to import what you want
Snatplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import time
In [ ]: # recording the time for various calls
In [ ]: # the code to plot the curve
Theoretical Analysis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9e43f91-79e0-4e0e-b33b-f2930152e64c%2Fe5f915fe-b974-4793-b024-6c7a5dcbf2f2%2F5xs5xtr_processed.png&w=3840&q=75)
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 [ ]: # urite 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 maximun profit
return (e,e,0)
In [ ]: maxProfit([13,7, -30,15, 18,-5,12,7,-11,6])
Empirical Analysis
Now, compare between the growth rate of the two algorithms
In [ ]: # feel free to import what you want
Snatplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import time
In [ ]: # recording the time for various calls
In [ ]: # the code to plot the curve
Theoretical Analysis
![Simple Iterative
As we in general, try to solve the problem first; we start with a brute force, simple, algorithm: design it below
In [ ]: # urite 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 sell
- maxProfit: the value of the maximun 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,e,e)
In [ ]: # Try your algorithm
maxProfitBrute ([13,7,-30,15,10, -5,12,7,-11,6])](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9e43f91-79e0-4e0e-b33b-f2930152e64c%2Fe5f915fe-b974-4793-b024-6c7a5dcbf2f2%2F7zz1m76_processed.png&w=3840&q=75)
Transcribed Image Text:Simple Iterative
As we in general, try to solve the problem first; we start with a brute force, simple, algorithm: design it below
In [ ]: # urite 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 sell
- maxProfit: the value of the maximun 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,e,e)
In [ ]: # Try your algorithm
maxProfitBrute ([13,7,-30,15,10, -5,12,7,-11,6])
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