CS61A: Lecture 4

Designing Functions

• A function’s domain is the set of all inputs it might possibly take as arguments.
  • A function’s range is the set of output values it might possibly return
• A pure function’s behavior is the relationship it establishes between the input and output.
• Good programmer practice: Implement a process only once and do not repeat it many times.

# same_length.py
def digits(a, b):
    a_digits = 0
    while a > 0:
        a = a // 10
        a_digits = a_digits + 1
    return a_digits

def same_length(a,b):
    return digits(a) == digits(b)

Higher Order Functions

• Functions can be passed as parameters to another function.
• Summation Example

def cube(k):
    return pow(k, 3)

def summation(n, term):
    total, k = 0, 1
    while k <= n:
        total, k = total + term(k), k+1
    return total

summation(5, cube)

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Program Design

• Modularity: Simple objects can be combined to create more complex operations
• Abstraction: We can hide complex operations behind a name and trust that it works every time.
• Separation of Concerns (??)

Functions are Return values

• Locally Defined Functions
  • Functions that are defined within other function bodies are bound to names in a local frame

Twenty-One Game

• Example:

def play(strategy0, strategy1, goal=21):
    n = 0
    who = 0
    while n < goal:
        if who == 0:
            n = n + strategy0()
            who = 1
        elif who == 1:
            n = n + strategy1()
            who = 0
    return who

def three_strategy():
    return 3

play(three_strategy, three_strategy)

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