- By Vasudev Ram - Online Python training / SQL training / Linux training
Stock reduction image attribution
Hi, readers,
I subscribed to the mailing list of the Daily Coding Problem site site a while ago. It's a useful site. Their modus operandi is to send you one programming problem per day, described in English. You try to solve them, in any programming language of your choice. (They say that some of the questions were asked by companies like Google, Facebook, Amazon, Microsoft, Netflix, etc.) Something like Rosetta Code.
The idea is that you can use this to practice and improve your programming and algorithm development skills.
I haven't been attempting to solve every problem I get in email from them, as of now. I just try one now and then. Hope to attempt more later.
Daily Coding Problem #69 is one that I tried, and solved, using a functional programming approach.
This is the problem statement (taken from the email I got from them):
Daily Coding Problem: Problem #69
To: vasudevram@gmail.com
Good morning! Here's your coding interview problem for today.
This problem was asked by Facebook.
Given a list of integers, return the largest product that can be made by multiplying any three integers.
For example, if the list is [-10, -10, 5, 2], we should return 500, since that's -10 * -10 * 5.
You can assume the list has at least three integers.
And here is my functional-style solution below (actually, two variants on a solution). For this post, I've used a slightly different format than what I usually use - instead of alternating code and (text) explanations, I've put all the explanations in the code, as comments - sort of like literate programming.
# daily_coding_problem_069.py
# Problem source: https://dailycodingproblem.com
# Solution created by Vasudev Ram
# Website: https://vasudevram.github.io
# Copyright 2019 Vasudev Ram
# Blog: https://jugad2.blogspot.com
# Python posts: https://jugad2.blogspot.com/search/label/python
# Product store: https://gumroad.com/vasudevram
# Twitter: https://mobile.twitter.com/vasudevram
# LinkedIn: https://linkedin.com/in.vasudevram
"""
Daily Coding Problem: Problem #69
This problem was asked by Facebook.
Given a list of integers, return the largest product that can be made
by multiplying any three integers.
For example, if the list is [-10, -10, 5, 2], we should return 500,
since that's -10 * -10 * 5.
You can assume the list has at least three integers.
"""
from __future__ import print_function
try:
reduce
except NameError as ne:
from functools import reduce
from itertools import combinations
# Create a list with a few numbers.
lis = range(1, 6)
print()
print("lis:", lis)
# First, print the combinations iterator object.
print("combinations(lis, 3):", combinations(lis, 3))
# Next, print the combinations themselves.
print("list(combinations(lis, 3)):\n" + \
"\n".join(str(item) for item in list(combinations(lis, 3))))
print()
# Then define a function that takes an iterable and returns
# the product of all the numbers in it.
def product(iterable):
p = 1
for i in iterable:
p *= i
return p
# Test the product function a few times:
print("product(range(10)):", product(range(10)))
print("product(range(1, 11)):", product(range(1, 11)))
print("product(range(1, 6, 2)):", product(range(1, 6, 2)))
print("product(range(1, 10, 2)):", product(range(1, 10, 2)))
print()
# Now use the product function with the combinations function
# to solve Daily Coding Problem #69:
print("max(map(product, combinations(lis, 3)):", \
max(map(product, combinations(lis, 3))))
# Now let's solve the same problem with reduce and operator.mul
# instead of the product function above:
# Here is the docstring for reduce:
print("reduce.__doc__:", reduce.__doc__)
print
from operator import mul
# Here is the docstring for mul:
print("operator.mul.__doc__:", mul.__doc__)
print()
# Show how reduce works with mul with a few examples:
print("reduce(mul, range(1, 5)):", reduce(mul, range(1, 5)))
print("reduce(mul, range(3, 7)):", reduce(mul, range(3, 7)))
print()
# Use reduce-with-mul instead of product.
print("max(map(lambda s: reduce(mul, s), combinations(lis, 3))):", \
max(map(lambda s: reduce(mul, s), combinations(lis, 3))))
# Here's the call using product again for comparison:
print("max(map(product, combinations(lis, 3))):", \
max(map(product, combinations(lis, 3))))
print()
# A few more calls to the reduce-with-mul version:
lis4 = range(1, 5)
print("lis4:", lis4)
print("max(map(lambda s: reduce(mul, s), combinations(lis4, 3))):", \
max(map(lambda s: reduce(mul, s), combinations(lis4, 3))))
print()
lis6 = range(1, 7)
print("lis6:", lis6)
print("max(map(lambda s: reduce(mul, s), combinations(lis6, 3))):", \
max(map(lambda s: reduce(mul, s), combinations(lis6, 3))))
print()
lis7 = range(1, 8)
print("lis7:", lis7)
print("max(map(lambda s: reduce(mul, s), combinations(lis7, 3))):", \
max(map(lambda s: reduce(mul, s), combinations(lis7, 3))))
print()
# And finally, here is the solution run again with the example
# input given in the Facebook problem mentioned above:
lis_fb = [-10, -10, 5, 2]
print("lis_fb:", lis_fb)
print("max(map(lambda s: reduce(mul, s), combinations(lis_fb, 3))):", \
max(map(lambda s: reduce(mul, s), combinations(lis_fb, 3))))
print()
# The result matches the given answer, 500.
# Now let's modify the Faceboook input and run the code again:
lis_fb2 = [-10, 8, -10, 9, 5, 7, 2]
# (Added values 8, 9 and 7 to the list.)
print("lis_fb2:", lis_fb2)
print("max(map(lambda s: reduce(mul, s), combinations(lis_fb2, 3))):", \
max(map(lambda s: reduce(mul, s), combinations(lis_fb2, 3))))
print()
# The result is right again, since -10 * -10 * 9 = 900 is
# the largest product.
Here is the output of a run of the program using Python 3:
lis: range(1, 6) combinations(lis, 3): <itertools.combinations object at 0x0000000001DA9598> list(combinations(lis, 3)): (1, 2, 3) (1, 2, 4) (1, 2, 5) (1, 3, 4) (1, 3, 5) (1, 4, 5) (2, 3, 4) (2, 3, 5) (2, 4, 5) (3, 4, 5) product(range(10)): 0 product(range(1, 11)): 3628800 product(range(1, 6, 2)): 15 product(range(1, 10, 2)): 945 max(map(product, combinations(lis, 3)): 60 reduce.__doc__: reduce(function, sequence[, initial]) -> value Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates ((((1+2)+3)+4)+5). If initial is present, it is placed before the items of the sequence in the calculation, and serves as a default when the sequence is empty. operator.mul.__doc__: Same as a * b. reduce(mul, range(1, 5)): 24 reduce(mul, range(3, 7)): 360 max(map(lambda s: reduce(mul, s), combinations(lis, 3))): 60 max(map(product, combinations(lis, 3))): 60 lis4: range(1, 5) max(map(lambda s: reduce(mul, s), combinations(lis4, 3))): 24 lis6: range(1, 7) max(map(lambda s: reduce(mul, s), combinations(lis6, 3))): 120 lis7: range(1, 8) max(map(lambda s: reduce(mul, s), combinations(lis7, 3))): 210 lis_fb: [-10, -10, 5, 2] max(map(lambda s: reduce(mul, s), combinations(lis_fb, 3))): 500 lis_fb2: [-10, 8, -10, 9, 5, 7, 2] max(map(lambda s: reduce(mul, s), combinations(lis_fb2, 3))): 900 I also tested it with Python 2 and it gave basically the same output, maybe with the exception of some minor message differences between 2 and 3. So I'm not showing the 2 output here.
The image at the top of the post is of stock with bay leaf and thyme being reduced in a pan.
Here is the Wikipedia article about reduction in cooking.
The functional programming meaning of reduce sort of matches the cooking meaning, right? Heh.
Enjoy.
- Vasudev Ram - Online Python training and consulting
I conduct online courses on Python programming, Unix / Linux commands and shell scripting and SQL programming and database design, with course material and personal coaching sessions.
The course details and testimonials are here.
Contact me for details of course content, terms and schedule.
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