Computing Science 1P

Large Group Tutorial 14

Simon GayDepartment of Computing Science

University of Glasgow

2006/07

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If d = { "John" : 5, "Helen" : 7 }, what do we call "John" ?

• A key• A value• Don't know

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Question

Suppose we define a dictionary by

d = { "Fred":10, "Joe":15, "Anne": 23, "Clare":14 }

and then run the following code:

for x in d.keys():print x

In which order will the keys of the dictionary appear?

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What is the order?

• Alphabetical order of keys• Numerical order of values• We can't tell; it looks random• The order in the definition• Don't know

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Calculating the mode

In statistics, the most frequently occurring element of a list of data is called the mode. It's a kind of average which does notrequire the data to have any structure at all.

e.g. mode([1,2,1,1,3,4,3,2]) should return 1.

We want to define a function to calculate the mode of a list ofnumbers.

We can do this by combining two ideas we already know:- frequency analysis- finding the largest value among data

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Calculating the mode

To calculate the mode, we need to calculate how many timeseach number occurs in the data.

How should we do this? (Example: [1,2,1,1,3,4,3,2] )

1. Use a list in which position i contains the number of occurrences of i

Example: [ 0,3,2,2,1 ]

2. Use a dictionary in which an item with key i has a valuewhich is the number of occurrences of i

Example: { 1:3, 2:2, 3:2, 4:1 }

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What is your preferred data structure for this problem?

• The list• The dictionary• Don't know

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Discussion

Think about what will happen in the following function call:

mode([1,2,1,1,3,4,3,2,1000000])

Do you still like your choice of data structure?

Discuss it with your neighbours.

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When a dictionary is better

When keys are integers and the set of keys is sparse (i.e. there is a large range of possible keys but relatively few are actually used), a dictionary is better than a list.

When keys are some other type (e.g. strings), so that we can'tuse positional lookup, a dictionary is better than a nested listbecause lookup is faster.

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Mode: counting occurrences

def mode(x):d = {}for n in x:

if d.has_key(n):d[n] = d[n] + 1

else:d[n] = 1

# now find the most common number

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What do you think of this code?

• It's correct: in fact, ideal• It's correct but can be simplified• It contains errors• Don't know

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Mode: counting occurrences

def mode(x):d = {}for n in x:

d[n] = d.get(n,0)+1# now find the most common number

The code is correct but it can be simplified a little by usingthe technique from page 76 of the book:

Exercise: complete the definition so that the most commonnumber is returned.

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Using nested lists to represent a matrix

A matrix (plural: matrices) is a rectangular grid of numbers.

1 2 32 4 53 1 2

Represent it by a list of lists:

[ [1,2,3], [2,4,5], [3,1,2] ]

Let's think about an n n matrix: n rows and n columns,represented by a list of n lists, each of n elements.

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Opposite diagonal of an n n matrix

Which of the following code fragments prints the "opposite"diagonal of an n n matrix m ? 1 3 2 5

4 1 0 2

2 2 3 4

5 1 2 3

n = len(m)for i in range(n):

print m[i][i]

n = len(m)for i in range(n):

print m[i][n-i]

n = len(m)for i in range(n):

print m[i][n-i-1]

n = len(m)for i in range(n):

print m[i][n-i+1]

1

2

3

4

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Which piece of code?

• 1• 2• 3• 4• None of them• Don't know