Week 6: Exercises

1. Local and Global

What will this program print?

a = 2
b = 3

def foo():
  a = b + 1
  a = a + 1
  return a

def bar():
  global b
  b = a + 3
  return b

def baz():
  return a + b

def thud():
  a = b + 1
  b = a + 1
  return a

print(foo())
print(bar())
print(baz())
print(thud())

2. Append

Write a function append() that takes a variable number of arguments. Each argument should be a sequence, such as a list. The function should return a sequence formed by concatenating all of the sequences. For example:

>>> append([1, 2], [5, 6], [8, 9])
[1, 2, 5, 6, 8, 9]
>>> append()
[]

3. Max

Write a function my_max() that takes one or more arguments. If there is just one argument, it should be a sequence, and my_max() should return the maximum value in the sequence. Otherwise, each argument should be a value, and my_max() should return the maximum of these values. For example:

>>> my_max([2, 4, 6])
6
>>> my_max(2, 4, 6)
6

4. Lots of References

Recall that a[:] makes a copy of the list a. It's the same as a[0:len(a)], or as a.copy().

What will this program print? Why?

def bar(a):
    for i in range(len(a)):
        a[i] += 1
        a = a[:]

def foo(a):
    for b in a + a[:]:
        bar(b)
        bar(b[:])

m = [[1, 2], [3, 4]]
foo(m)
print(m)

5. Rectangle Class

Write a class Rectangle representing a rectangle in 2 dimensions. The class should support these operations:

• Rectangle(p, q) – make a rectangle with corners at Points p and q

• r.area() - return the area of a rectangle

• r.perimeter() - return the perimeter of a rectangle

• r.contains(p) – return true if point p is inside the rectangle r

• r.intersects(s) – return true if rectangle r intersects rectangle s. (Be warned: this is a bit tricky. As a hint, you might first write a helper function that determines whether two line segments intersect.)

6. Circle Class

Write a class Circle representing a circle in 2 dimensions. The class should support these operations:

• Circle(p, r) – make a circle whose center is at p, with radius r

• c.area() - return the area of a circle

• c.circumference() – return the circumference of a circle

• c.contains(p) – return true if point p is inside the circle c

7. Vector Class

Write a class Vector that represents a vector in n-dimensional space. (We partially implemented this class in the lecture.)

• Provide an initializer that takes a list of numbers, yielding a vector with those components.

• v.add(w) should add two vectors.

• v.mul(w) should multiply a scalar times a vector, yielding a new vector.

• v.dot(w) method should compute the dot product of two vectors, yielding a scalar.

• v.length() should compute the length of a vector.

• v.angle(w) should computes the angle between two vectors in radians.

8. Date Class

Write a class Date representing a month and day. The class should support these operations:

• Date(m, d) – make a Date representing the given month (1 ≤ m ≤ 12) and day (1 ≤ d ≤ 31)

• d.next() - return the Date after d

• d.prev() - return the Date before d

• d.add(n) – add n days to the given Date, wrapping past Dec 31 to Jan 1 if necessary