Python Foundations, Lab 3: Practice with Functions¶

Instructor: Wesley Beckner

In this lab we will continue to practice writing functions

✍🏽 L3 Q1: Basic Function Writing¶

Part A¶

Write a Python function to find the maximum of three numbers

# Cell for L3 Q1 A
def max_num(a, b, c):
  if (a > b) and (a > c):
    return a
  elif (b > a) and (b > c):
    return b
  else:
    return c

max_num(100, 20, 3)

Part B¶

Write a Python function to multiply all the numbers in a list

Example:

Sample List : (8, 2, 3, -1, 7)
Expected Output : -336

# Cell for L3 Q1 B
def mult_list(a):
  val = 1
  for i in a:
    val *= i
  return val

mult_list([8, 2, 3, -1, 7])

-336

Part C¶

Write a Python program to reverse a string

Example:

Sample String : "1234abcd"
Expected Output : "dcba4321"

# Cell for L3 Q1 C
def rev_string(a):
  return a[::-1]

rev_string("1234abcd")

'dcba4321'

❄️ L3 Q2: Finding Unique Elements¶

Write a Python function that takes a list and returns a new list with unique elements of the first list

Example:

Sample List : [1,2,3,3,3,3,4,5]
Unique List : [1, 2, 3, 4, 5]

# Cell for L3 Q2
def find_unique(a):
  b = []
  for i in a:
    if i not in b:
      b.append(i)
  return b

find_unique([1,2,3,3,3,3,4,5])

[1, 2, 3, 4, 5]

❗ L3 Q3: Computing Factorials¶

Write a Python function to calculate the factorial of a number (any non-negative integer). The function accepts the number as an argument

Example:

Input: 4                                                       
Output: 24

# Cell for L3 Q3
def fact(a):
  b = 1
  for i in range(1,a+1):
    b *= i
  return b

fact(4)

Practicing our hand at functions by implementing recursion¶

We will practice the last exercise we did yesterday, this time using what we've learned about functions to write a recursive function

A recursive function is a function that makes a call to itself. This is particularly well suited for tasks that would otherwise require a lot of memory to hold intermediary solutions (when they are combined with a strategy called memoization which we will shy away from here). The Fibonnaci sequence is a good place for such a problem. So is a factorial calculation. See here below

$3! = 3 * 2 * 1$

$4! = 4 * 3 * 2 * 1$

def factorial(x):
    """This is a recursive function
    to find the factorial of an integer"""

    if x == 1:
        return 1
    else:
        # one trick to note that is common with recursive functions
        # is that the incrementation in the key variable is done
        # in the call to the function itself (vs a for loop)
        return (x * factorial(x-1))

n = 3
factorial(n)

In the above, we have on lines 5 and 6, what we call the baseline solution. It is the answer to the simplest subset of the problem. When we build a recursive tree, it is useful to think of the smallest problem, and work upwards, providing this leaf solution to nodes further up on the recursive tree. Like so:

# 1! = 1
# 2! = 2 * 1!
# 3! = 3 * 2!
# N! = N * (N-1)! ... like ... like so

This problem is intended to be a fun way to wrap our heads around functions... don't stress. If you want to see a further breakdown of the factorial problem, check out this link

🛺 L3 Q4: Recursive Functions¶

Using recursion, complete the Fibonacci sequence up to the 10^th place using recursion and any or all of the following: * if elif else * range

The Fibonacci sequence with indices:

0. 0
1. 1
2. 1
3. 2
4. 3
5. 5
6. 8
7. etc..

Example input:

index = 9

Example output:

Index: 9
Value: 34

# Cell for L3 Q4
def fib(a):
  if a == 0:
    return 0
  elif a == 1:
    return 1
  else:
    return fib(a-1) + fib(a-2)

fib(9)