CSCI-1101A Recursion Mohammad T . Irfan Roadmap Before After - - PDF document

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CSCI-1101A Recursion

Mohammad T . Irfan

Roadmap

• Recursion
• Object-oriented

programming

• Lab: relevant topics +

start final project of 2048 game

Before Thanksgiving

• Graph algorithms
• Google’s web search

algorithm

• Lab: Continue final

project, building website

After Thanksgiving

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Real world example of recursion

u Google Maps

Another real-world example

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Inception—Hollywood’s version of recursion

u Can we write a program to describe what

they were doing?

Code

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2 ways of understanding recursion

• 1. Tracing diagram: Cook a small example and

simulate the recursive function calls

• 2. Black box: Imagine the recursive function is

a magical black box

3 elements of recursion

• 1. Base case—the case where you don’t need

recursion to give an answer

• 2. Recursive case (forward flow)—the function

calls itself with a different argument

• 3. Kick (backward flow)—return the result

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Problem: compute factorial

u Factorial of a number

u factorial(4) = 4 * 3 * 2 * 1 u 4! = 4 * 3!

u if n == 0: # Base case

u n! = 1

u If n >= 1 # Recursive case

u n! = n * (n-1)!

Code

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Exercise 15.2

u Problem: Find the n-th number in the

Fibonacci sequence

u Fibonacci Sequence

u 0, 1, 1, 2, 3, 5, 8, 13, 21, ... u f0 = 0 u f1 = 1 u fn = fn-1 + fn-2 if n > 1

u What is the base case? u What is the recursive case?

Code

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Fibonacci numbers in nature

From: http://britton.disted.camosun.bc.ca/fibslide/jbfibslide.htm

Other examples (Wikipedia)

Yellow Chamomile head showing the arrangement in 21 (blue) and 13 (aqua) spirals.

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When there’s no formula...

u Main challenge

u Devise a recurrence relation first

Problem: Test for palindrome

u Recurrence relation?

u Do an example u Try to break the whole task into smaller tasks

u A string is a palindrome if

u its first and last letters match u the substring in between the first and last letters

is a palindrome

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Code Problem: find the max of a list

u Recurrence relation

u Work out an example

u The max of a list is the larger of two

numbers:

1.

The list’s first element and

2.

The max of the rest of the list (model the rest of the list as a smaller list)

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Code Problem: find the sum of a list

u What is the recurrence relation? u Sum of a list is the sum of two numbers

1.

The first number of the list

2.

The sum of the rest of the list (consider that as a smaller list)

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Video Lectures

u Counting the number of vowels in a string

(5 min)

u http://bit.ly/1qEIhsX

u Series sum (4 min)

u http://bit.ly/10Yz4Fc

u Binary Search (15 min) [Lab]

u http://bit.ly/1xj43dg

Exam 5 (December 9)

u Topics from recursion

u Recursion – Chapter 15.4 u Exercises 15.9—15.13: Draw the tracing diagrams

for very small examples to find what these functions are doing

u Binary search (lab) u Video lectures u Optional: Guttag’s Section 4.3