# Homework 1 Solution

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## Description

1. Complete the function body.

def greatest difference(nums1, nums2):

• (list of number, list of number) -> number

Precondition: len(nums1) == len(nums2) and nums1 != []

Return the greatest absolute difference between numbers at corresponding positions in nums1 and nums2.

• greatest difference([1, 2, 3], [6, 8, 10])

7

• greatest difference([1, -2, 3], [-6, 8, 10])

10

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2. Complete the function body.

def can pay with two coins(denoms, amount):

“”” (list of int, int) -> bool

Return True if and only if it is possible to form amount, which is a number of cents, using exactly two coins, which can be of any of the denominations in denoms.

• can pay with two coins([1, 5, 10, 25], 35)

True

• can pay with two coins([1, 5, 10, 25], 20)

True

• can pay with two coins([1, 5, 10, 25], 12) False

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1

3. Complete the function body.

def all fluffy(s):

“”” (str) -> bool

Return True iff every character in s is fluffy. Fluffy characters are those that appear in the word ‘fluffy’.

• all fluffy(‘fullfly’)

True

• all fluffy(‘firefly’) False

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4. Complete the function body.

def digital sum(nums list):

“”” (list of str) -> int

Precondition: s.isdigit() holds for each string s in nums list.

Return the sum of all the digits in all strings in nums list.

• digital sum([‘64’, ‘128’, ‘256’])

34

• digital sum([‘12’, ‘3’])

6

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1. In math, the Collatz conjecture states that starting from any positive integer, you will eventually reach the number 1 by repeatedly applying the following two rules:

• if the number is even, divide it by 2 to get the next number in the sequence

• if the number is odd, multiply by 3 and add 1 to get the next number in the sequence

Repeatedly applying the rules generates a sequence of numbers. The Collatz step count is the number of applications of the rules required before the sequence reaches 1. For example, there are 8 Collatz steps in the Collatz sequence:

n = 6 -> n = 3 -> n = 10 -> n = 5 -> n = 16 -> n = 8 -> n = 4 -> n = 2 -> n = 1

Complete this function to count the Collatz steps for a particular number N.

2

def count collatz steps(n):

• (int) -> int Precondition: n >= 1

Return the number of steps it takes to reach 1 by applying the two rules of the Collatz conjecture beginning from the positive integer n.

• count collatz steps(6)

8

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Before 11:59:59 p.m., Friday, 19 April 2019 (3rd Friday), you must upload a .PY file with all your solutions of the above questions to the course Blackboard assignment for Homework 1.

3

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