Coding the Matrix

Coding the Matrix

How to test the solutions


Lab 1: Introduction to Python—sets, lists, dictionaries, and comprehensions

Python provides some simple data structures for grouping together multiple values, and integrates them with the rest of the language. These data structures are called collections.


A set is an unordered collection in which each value occurs at most once. You can use curly braces to give an expression whose value is a set. Python prints sets using curly braces.

>>> {2, 1, 3}
{1, 2, 3}

Set comprehensions

Python provides for expressions called comprehensions that let you build collections out of other collections. We will be using comprehensions a lot because they are useful in constructing an expression whose value is a collection, and they mimic traditional mathematical notation. Here’s an example:

>>> {2*x for x in {1,2,3} }
{2, 4, 6}


Python represents sequences of values using lists. In a list, order is significant and repeated elements are allowed. The notation for lists uses square brackets instead of curly braces. The empy list is represented by [].

>>> [1,1+1,3,2,3]
[1, 2, 3, 2, 3]


Slices: A slice of a list is a new list consisting of a consecutive subsequence of elements of the old list, namely those indexed by a range of integers. The range is specified by a colon-separated pair i : j consisting of the index i as the first element and j as one past the index of the last element. Thus mylist[1:3] is the list consisting of elements 1 and 2 of mylist.

Prefixes: If the first element i of the pair is 0, it can be omitted, so mylist[:2] consists of the first 2 elements of mylist. This notation is useful for obtaining a prefix of a list.

Suffixes: If the second element j of the pair is the length of the list, it can be omitted, so mylist[1:] consists of all elements of mylist except element 0.

Slices that skip:You can use a colon-separated triple a:b:c if you want the slice to include every cth element. For example, here is how you can extract from L the list consisting of even-indexed elements and the list consisting of odd-indexed elements:


Like a list, a tuple is an ordered sequence of elements. However, tuples are immutable so they can be elements of sets. The notation for tuples is the same as that for lists except that ordinary parentheses are used instead of square brackets.


Another collection that can be iterated over is a zip. A zip is constructed from other collections all of the same length. Each element of the zip is a tuple consisting of one element from each of the input collections.

>>> list(zip([1,3,5],[2,4,6]))
[(1, 2), (3, 4), (5, 6)]


We will often have occasion to use functions with finite domains. Python provides collections, called dic- tionaries, that are suitable for representing such functions. Conceptually, a dictionary is a set of key-value pairs. The syntax for specifying a dictionary in terms of its key-value pairs therefore resembles the syntax for sets—it uses curly braces—except that instead of listing the elements of the set, one lists the key-value pairs. In this syntax, each key-value pair is written using colon notation: an expression for the key, followed by the colon, followed by an expression for the value:

$$key : value$$

The identity function on a set D is the function with the following spec: - input: an element x of D - output: x That is, the identity function simply outputs its input.


expression if condition else expression