A set of coins makes change for n if the sum of the values of the coins is n. For example, if you have 1- cent, 2-cent and 4-cent coins, the following sets make change for 7: . 71-cent coins 5 1-cent, 1 2-cent coins. 31-cent, 2 2-cent coins 31-cent, 1 4-cent coins 11-cent, 3 2-cent coins 11-cent, 1 2-cent, 1 4-cent coins Thus, there are 6 ways to make change for 7. Write a function count_change that takes a positive integer n and a list of the coin denominations and returns the number of ways to make change for n using these coins (Hint: You will need to use tree recursion):

C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter4: Selection Structures
Section: Chapter Questions
Problem 14PP
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A set of coins makes change for n if the sum of the values of the coins is n. For example, if you have 1-
cent, 2-cent and 4-cent coins, the following sets make change for 7:
• 7 1-cent coins
. 51-cent, 1 2-cent coins
3 1-cent, 2 2-cent coins
3 1-cent, 1 4-cent coins
.
11-cent, 3 2-cent coins
. 1 1-cent, 1 2-cent, 1 4-cent coins
Thus, there are 6 ways to make change for 7. Write a function count_change that takes a positive integer
n and a list of the coin denominations and returns the number of ways to make change for n using these
coins (Hint: You will need to use tree recursion):
def count_change (amount, denominations):
"""Returns the number of ways to make change for amount.
>>> denominations = [50, 25, 10, 5, 1]
>>> count_change (7, denominations).
2
>>> count_change (100, denominations)
292
>>> denominations = [16, 8, 4, 2, 11
>>> count_change (7, denominations)
6
>>> count_change (10, denominations)
14
>>> count_change (20, denominations)
60
||||||
"*** YOUR CODE HERE ***"
Ĵ
Transcribed Image Text:A set of coins makes change for n if the sum of the values of the coins is n. For example, if you have 1- cent, 2-cent and 4-cent coins, the following sets make change for 7: • 7 1-cent coins . 51-cent, 1 2-cent coins 3 1-cent, 2 2-cent coins 3 1-cent, 1 4-cent coins . 11-cent, 3 2-cent coins . 1 1-cent, 1 2-cent, 1 4-cent coins Thus, there are 6 ways to make change for 7. Write a function count_change that takes a positive integer n and a list of the coin denominations and returns the number of ways to make change for n using these coins (Hint: You will need to use tree recursion): def count_change (amount, denominations): """Returns the number of ways to make change for amount. >>> denominations = [50, 25, 10, 5, 1] >>> count_change (7, denominations). 2 >>> count_change (100, denominations) 292 >>> denominations = [16, 8, 4, 2, 11 >>> count_change (7, denominations) 6 >>> count_change (10, denominations) 14 >>> count_change (20, denominations) 60 |||||| "*** YOUR CODE HERE ***" Ĵ
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