This is a continuation of
exercise 12 b (A function that returns a value)
We have discussed how to create a function, how to pass an argument to a function and then how to call a function. We have done a lot. It will pay us well if we take breaks frequently.
Kindly take a break to revise what we learnt so far and also take a long break away from PC.
In this exercise, we would discuss more on function. A recursive function calls itself. It does so until the base case becomes false.
Let's implement a factorial function. Our function will take in an integer input. If the input is less than 1, the function returns 1, else we proceed.
Let the integer input be,
n factorial is,
n * (n - 1) * (n - 2) * (n - 3) * ... * 1. Our base case is 1. When we get to
1, we break or terminate the recursive function.
factorial = 1 n = int(input("Enter n: ")) if n < 1: print(1) else: for i in range(1, n+1): factorial *= i print(factorial) # input output # 3 6 # 5 720 # 15 1307674368000
Now we shall implement the above using a recursive function.
def factorial(n): if n < 1: return 1 else: return n * factorial(n-1)
def factorial(n): we define a function called factorial that take an integer argument,
if n < 1: return 1: we check the base case and return 1. The function returns 1 and the execution stops.
else: return n * factorial(n-1): if
n > 1, we return
n=5, we would have that:
factorial(5) = 5 * factorial(4)
factorial(5) = 5 * 4 * factorial(3)
factorial(5) = 5 * 4 * 3 * factorial(2)
factorial(5) = 5 * 4 * 3 * 2 * factorial(1)
factorial(5) = 5 * 4 * 3 * 2 * 1
factorial(5) = 720
Implementation of Euclid GCD algorithm. We are interested in the greatest common divisor of two numbers,
bbe the two numbers
rbe the remainder of
a % b
- check if
a, if so, return
- else assign
band repeat the second step
a = int(input("Enter a: ")) b = int(input("Enter b: ")) while True: r = a % b if r == 0: print(b) break else: a = b b = r # a = 72 # b = 96 # gcd(a, b) = 24
def gcd(a, b): r = a % b if r == 0: return b else: return gcd(b, r) print(gcd(72, 96)) # 24
Let us shorten this code
def gcd(a, b): if a % b == 0: return b return gcd(b, a % b)
Lambda function is also known as anonymous function - a function without a name. We can say it is a one-time-function. We create a lambda function using the
lambda keyword. Simply,
(lambda comma-separated-args: body)
Let's consider a function that increments a given integer by one and returns the value.
def inc(n): return n + 1 print(inc(2)) # 3
The snippet above uses the
def keyword to create the function. Now let's see how we would use the
lambda keyword to create the same function.
print((lambda x: x+1)(2)) # 3
So the structure of a lambda function is similar to that of normal function. We use the
lambda keyword instead of
def, the function has no name. Any parameters are space comma-separated from the lambda keyword. The function body is separated by a colon,
From example 5, we passed the argument, 2, to the lambda function. Notice how it was passed.
We can pass multiple arguments into a lambda function. Note that we can not use
return lambda function. Let's use a lambda function to compare two numbers and return the lesser number.
print((lambda a, b: a if a < b else b)(2, 4)) # 2
Normally we would have written,
def min_val(a, b): return a if a < b else b print(min_val(2, 4)) # 2
This is the same as :
def min_val(a, b): if a < b: return a else: # we can comment out the else: return b
example 5 where we increment a given number by one, we can pass the lambda function to a variable and call the variable like a function later.
inc = (lambda n: n + 1) print(inc(2)) # 3
Can you tell the difference between these two snippets below?
# first func inc = (lambda x: x + 1) print(inc(4)) # second func inc = (lambda x: x + 1)(4) print(inc)
first func, the lambda function was assigned to
incwas called and an argument of value,
4was passed. So we can say that
incis a function.
second func, an argument of value
4was passed to the lambda function. The result was assigned to
incis just another variable of value,
4 + 1 = 5and not a function.
- Write a function to sort this list,
[[47, 3, 1, 34], [0. - 3, 4], [7, 21, 13, 37, 8]]
- Write a function that returns the temperature from degree Fahrenheit to degree Celsius
- Write a function that returns the sum of numbers between a given range inclusive. If the range is
1 to 5, return
- Write a function the prints the squares between a given range inclusive
- Write a function that sums up the individual digits in a given integer. Given,
- Write a function that verifies if a given year is a leap year. For a given input to be a leap year, it must be divisible by 4 but(and) not divisible by 100, or the input is divisible by 400.
- A function is a block of code that performs a specific task
- A function can take at least zero arguments
- function definition
def function_name(some_args): # some code
- we can call the function by doing
- A function allows reuse of code
- A function can be used in any part of our code
- parameters are passed into the function when creating the function
- argument is what we pass to the function when we are calling it
returnexits a function and returns a value from the function
- use the *arg - tuple argument to collect more arguments
- A function may be called as many times as possible
- A recursive function calls itself
- A lambda function is a nameless function, usually required on the fly