3Basics

© 2010 David A Watt, University of Glasgow

Accelerated Programming 2

Part I: Python Programming

3-2

Data types (1)

Programs input, store, manipulate, and output values or data.

Values are classified according to their types and the operations that can be performed on them. E.g.:– It makes sense to subtract numbers but not booleans

or strings.

– It makes sense to concatenate strings but not subtract them.

3-3

Data types (2)

Basic data types in Python:– integer numbers

– floating-point numbers

– booleans

– strings.

21 1003 …integers

1.5 3.1416 9.9 …floats

False Truebooleans

‘’ ‘$’ ‘Hi’ ‘apple’ …strings

values

3-4

Data types (3)

Composite data types in Python:– tuples (§6)

– lists (§7)

– dictionaries (§9).

3-5

Integer numbers

The integer numbers are positive and negative whole numbers:…, –3, –2, –1, 0, +1, +2, +3, …

3-6

Integer operators

Integer operators:- y negation of y

x + y sum of x and y

x - y difference of x and y

x * y product of x and y

x // y quotient when x is divided by y

x % y remainder when x is divided by y

x ** y x raised to the power of y

3-7

Example: integer arithmetic

This function uses integer remainders: def gcd (m, n): # Return the greatest common divisor of m and n. p = m q = n r = p % q # remainder on dividing p by q while r != 0: # i.e., p is not a multiple of q p = q q = r r = p % q return q

3-8

Floating-point numbers

The floating-point numbers are positive and negative real numbers.

Floating-point numbers are represented approximately in a computer (unlike integers, booleans, etc.).

3-9

Floating-point operators

Floating-point operators:

- y negation of y

x + y sum of x and y

x - y difference of x and y

x * y product of x and y

x / y division of x by y

x ** y x raised to the power of y

3-10

Example: floating-point arithmetic (1)

This function uses floating-point arithmetic: def square_root (x): # Return the square root of the positive number x. r = 1.0 while abs(x/r**2 – 1) > 0.0001: r = 0.5 * (r + x/r) return r

This function assumes that its argument is positive.

– What will happen if its argument is negative?

3-11

Example: floating-point arithmetic (2)

Tracing the function call square_root(2.0):

Enter the function:

Test “abs(…) > 0.0001”:

Execute “r = 1.0”:

2.0x

r2.0 1.0

yields True 2.0 1.0

Execute “r = 0.5*(r+x/r)”: 2.0 1.5

Test “abs(…) > 0.0001”: yields True 2.0 1.5

Execute “r = 0.5*(r+x/r)”: 2.0 1.4167

Test “abs(…) > 0.0001”: yields True 2.0 1.4167

3-12

Example: floating-point arithmetic (3)

Tracing the function call (continued):

Execute “r = 0.5*(r+x/r)”:

rx2.0 1.4167

Test “abs(…) > 0.0001”:

Execute “return r”:

yields False 2.0 1.4142

2.0 1.4142returns 1.4142

3-13

Floating-point approximation

Floating-point numbers are represented in the form:± m x 2±e

where the mantissa m is a binary fraction (½ ≤ m < 1)

and the exponent e is a small binary integer.

Most real numbers (including all irrational numbers) can only be approximated in a computer.

It follows that floating-point computations are only approximate – beware!

3-14

Example: floating-point approximation

Consider the expression:1.0 + 0.2 – 1.0

On my computer, this expression yields 1.19999999999999996!

The problem is that the number 0.2, although it can be written exactly as a decimal fraction, cannot be represented exactly as a binary fraction.

3-15

Boolean values and operators

The boolean values are False and True.

Boolean operators:not y negation of y (i.e., True iff y is False)

x and y conjunction of x and y (i.e., True iff both x and y are True)

x or y disjunction of x and y (i.e., True iff either x or y is True)

3-16

Comparison operators

Comparison operators:x == y True iff x is equal to y

x != y True iff x is unequal to y

x < y True iff x is less than y

x <= y True iff x is less than or equal to y

x > y True iff x is greater than y

x >= y True iff x is greater than or equal to y

Comparison chaining:x < y < z True iff x is less than y and y is less than z

etc.

3-17

Example: booleans

Using boolean and comparison operations: def in_range (n, p, q): # Return True iff n is in the range p … q. return (p <= n and n <= q)

Alternatively, using comparison chaining:def in_range (n, p, q): # Return True iff n is in the range p … q. return (p <= n <= q)

Function call:d = input('Enter integer in range 0-9: ')if not in_range(d, 0, 9): print 'Invalid integer'

3-18

String values

A string is a sequence of characters.

The length of a string is the number of characters in it.

The empty string has length 0 (i.e., it consists of no characters at all).

The string values are character sequences of any length.

3-19

String operators

String operators:

s + t concatenation of strings s and t

n * s concatenation of n copies of s

s * n ditto

3-20

String comparison operators

String comparison operators:s == t True iff s is equal to t

s != t True iff s is unequal to t

s < t True iff s is lexicographically less than t

s <= t True iff s is lexicographically less than or equal to t

s > t True iff s is lexicographically greater than t

s >= t True iff s is lexicographically greater than or equal to t

Comparison chaining: as before.

3-21

Example: string operations

Program:place = 'Paris'season = 'spring'title = place + ' in ' + 2*'the ' + seasonprint title

Output:Paris in the the spring

3-22

Example: string comparisons (1)

Program:word1 = raw_input('Enter a word: ')word2 = raw_input('Enter another word: ')if word1 > word2: # Swap word1 and word2 … word1, word2 = word2, word1print 'Words in lexicographic order:'print word1print word2

3-23

Example: string comparisons (2)

Program’s output and input:Enter a word: mouseEnter another word: elephantWords in lexicographic order:elephantmouse