Intro to Robots

Conditionals and Recursion

Intro to Robots

Modulus

• Two integer division operators - / and %.

• When dividing an integer by an integer we throw away the remainder.

• To capture the remainder (before we lose it) we use the modulus (%) operator.

• then

7 / 3 = 27 % 3 = 1

n % d = rn / d = q

n = q * d + r

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Use of Modulus

• Some numbers, like credit card or identification numbers, are encoded so that the last digit can be “calculated” from the previous digits.

• Suppose a 16-digit number has its first 15 digits as

• and that the 16th digit is calculated by • adding the digits as eight 2-digit numbers

• Repeat until there are only two digits

• the larger of the last two digits is the 16th digit

4591-3295-6843-256_

04 + 59 + 13 + 29 + 56 + 84 + 32 + 56 = 333

03 + 33 = 36

4591-3295-6843-2566

Intro to Robots

Exercise

• Which if these two 16-digit numbers is “valid”?

Or

• In a short while we’ll see an algorithm for verifying that a 16 digit number is valid using this method of calculating the last digit.

5291-4528-7426-6539

5291-4582-7426-6539

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Boolean Expressions:

• A boolean expression is one that is either true or false.• In Python, true and false are represented as 1 and 0.• The operator == compares two numbers and decides if

they are equal

• Other such operators for numbers are

>>> 5 == 60>>> 5 == 51

x != y -- x is not equal to yx > y -- x is greater than yx < y -- x is less than yx >= y -- x is greater than or equal to yx <= y -- x is less than or equal to yx == y -- x is equal to y

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BE CAREFUL!!

• The operator = is the “assignment operator” not the “comparison operator”.

x = y -- the variable x takes on the value of the variable yx == y -- returns 1 of x and y have the same value; 0 otherwise

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Exercise

• What does the following do?

• We can use a function definition to capture this logic without any mistakes

print ‘even’*(a%2==0) + ‘odd’*(a%2==1)

def parity(a):

return print ‘even’*(a%2==0) + ‘odd’*(a%2==1)

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Boolean or Logical Operators:

• There are three logical operators – and, or and not.• Their meaning (semantics) are the same as in English.

x > 2 and x < 10 -- true (1) if x is greater than 2 and less than 10not (x > 2 and x < 10) -- false(0) if x is greater than 2 and less than 10 -- true (1) is x is less than or equal to 2 or x is greater than or equal to 10x <= 2 or x >= 10 -- same as above

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Conditional Execution:

if x > 0: print ‘x is positive’

condition; if true, everything indentedis executed

HEADER: STATEMENT 1 STATEMENT 2 . . . STATEMENT n

HEADER: starts a new line, ends in a :

BODY: sometimes called a program block. Everything indented after the header.

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Alternative Execution:

• This can be encapsulated in a function to hide the code details:

• Or using the function we wrote earlier

if x %2 == 0: print x, ‘is even’else: print x, ‘is odd’

executed if condition is true

executed if condition is false

def printParity(x): if x %2 == 0: print x, ‘is even’ else: print x, ‘is odd’

print x, “is” + parity(x)

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Chained Conditionals:

• What happens if you need to choose from among three or more things (instead of just two):

if x > 0: print x, ‘is positive’elif (x == 0): print x, ‘is zero’else: print x, ‘is negative’

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Exercise:

• Write a function called compare(x,y) that does the following:– Returns 1 if x > y– Returns 0 if x == y– Returns -1 if x < y

def compare(x,y): if x > y: return 1 elif x == 0: return 0 else: return -1

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Exercise:

• Verify a 16-digit number.

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Nested Conditions:

Decision Tree

x == ‘A’

x == ‘B’

y == 0

y == 1

y == 0

y == 1

Do A0

Do A1

Do B0

Do B1

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Nested Conditions

if x == ‘A’ and y == 0: Do A0elif x == ‘A’ and y == 1: Do A1elif x == ‘B’ and y == 0: Do B0else: Do B1

if x == ‘A’: if y == 0: Do A0 else: Do A1else: if y == 0: Do B0 else: Do B1

if x == ‘A’ and y == 0: Do A0elif x == ‘A’ and y == 1: Do A1elif x == ‘B’ and y == 0: Do B0elif x == ‘B’ and y == 1: Do B1

if x == ‘A’: if y == 0: Do A0 elif y == 1: Do A1elif x == ‘B’: if y == 0: Do B0 elif y == 1: Do B1

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Return Statement:

• The classic reason for a function is to calculate a value (y) for a given value (x).

• In Python, the value returned by a function is expressed in a return statement.

y = f(x)

def min(a,b): # returns the smallest of two numbers if a < b: return a else: return b

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More than one return type:

The built-in math function sqrt() fails on a negative number

This version of square root “gently” avoids an error message if you try to calculate the square root of a negative number

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Recursion: def countDown(n): if n == 0: print “Blast Off!” else: print n countDown(n-1)

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Definition:

• A recursive definition is one that has two properties:– A trivial (base) case with a trivial definition– The definition describes something of a certain

size (n) in terms of the same thing but of a smaller size (n-1).

• Problems can have non-recursive and recursive definitions/descriptions.

• Not all problems can be described recursively

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Towers of Hanoi

A B C

Move one disk from A to BMove one disk from A to CMove one disk from B to CMove one disk from A to BMove one disk from C to AMove one disk from C to BMove one disk from A to B

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Towers of Hanoi Problem:

• Problem: Move n disks from ‘A’ to ‘B’ Using ‘C’

• Solution: Move the disks using the following rules:– You may only move one

disk at a time– You may never put a big

disk on top of a small disk

• Problem: Move n disks from ‘A’ to ‘B’ Using ‘C’

• Solution:

1. Move n-1 disks from ‘A’ to ‘C’ using ‘B’

2. Move 1 disk from ‘A’ to ‘B’

3. Move n-1 disks from ‘C’ to ‘B’ using ‘A’

Non-recursive Definition Recursive Definition

How! What!same problem;smaller size

problem size

base case

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Recursion and the Stack:

• Remember that each time a function is called space is reserved for its variables and parameters on “the Stack”.

• We saw this by introducing an error in the base case of the definition of the Towers of Hanoi program (divide by 0) and when the error occurred, the Python environment prints out the stack.

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n = (3-1) = 2

n = (2-1) = 1

n = (1-1) = 0

Error: division by 0

_toplevel_

hanoi n = 3

hanoi n = 2

hanoi n = 1

hanoi n = 0

also called main

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Infinite Recursion:

• What happens if there is no base case.

def countDown(n): countDown(n-1)

stack gets to be too big_toplevel_

countDown n = 3

countDown n = 2

countDown n = 1

countDown n = 0

countDown n = -1

countDown n = -2

countDown n = -3

countDown n = -4

.

.

.

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Keyboard Input:

• Python has several built-in keyboard read functions.

• raw_input() reads keyboard input into a string until you hit return.

raw_input()

you can supply a prompt

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Keyboard Input:

• You can use the input() function if the input is integer type.

• Just make sure you enter an integer and not something else.

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Keyboard Input:

• The myro system also comes with its own keyboard input environment; a separate dialog box that is invoked by calling

ask(“A Prompt”)

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Exercise: