Starting Out With Programming Logic & Design - Chapter13_Recursion

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Starting Out with Programming Logic & Design

Second Edition

by Tony Gaddis

Chapter 13:

Recursion

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 13-2

Chapter Topics

13.1 Introduction to Recursion

13.2 Problem Solving with Recursion

13.3 Examples of Recursive Algorithms



A recursive module is a module that calls itself– When this happens, it becomes like an infinite loop

because there may be no way to break out– Depth of Recursion is the number of times that a

module calls itself– Recursion should be written so that it can

eventually break away– This can be done with an If statement



A problem can be solved with recursion if it can be broken down into successive smaller problems that are identical to the overall problems

– This process is never required, as a loop can do the same thing

– It is generally less efficient to use than loops because it causes more overhead (use of system resources such as memory)


13.2 Problem Solving with RecursionHow it works

– If the problem can be solved now, then the module solves it and ends

– If not, then the module reduces it to a smaller but similar problem and calls itself to solve the smaller problem

– A Base Case is where a problem can be solved without recursion

– A Recursive Case is where recursion is used to solve the problem



Using recursion to calculate the factorial of a number

– A factorial is defined as n! whereas n is the number you want to solve

– 4! or “four factorial” mean 1*2*3*4 = 24– 5! or “five factorial” means 1*2*3*4*5 = 120– 0! is always 1

• Factorials are often solved using recursion



Continued…



Inside Program 13-3– Inside the function, if n is 0, then the function

returns a 1, as the problem is solved– Else, Return n * factorial(n-1) is processed and

the function is called again– While the Else does return a value, it does not do

that until the value of factorial(n-1) is solved


13.2 Problem Solving with RecursionFigure 13-4 The value of n and the return value during each call of the function


13.3 Examples of Recursive AlgorithmsSumming a Range of Array Elements with Recursion

Continued…

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley


13-13

Summing a Range of Array Elements with Recursion



Inside Program 13-4– start and end represent the array range– Return array[start] + rangeSum(array, start+1), end)

• This continuously returns the value of the first element in the range plus the sum of the rest of the elements in the range

• It only breaks out when start is greater than end• start must be incremented



The Fibonacci Series

Continued…



The Fibonacci Series



Inside Program 13-5– The Fibonacci numbers are 0,1,1,2,3,5,8,13,21…– After the second number, each number in the

series is the sum of the two previous numbers– The recursive function continuously processes

the calculation until the limit is reached as defined in the for loop in the main module



Additional examples that can be solved with recursion

– The Greatest Common Divisor– A Recursive Binary Search– The Towers of Hanoi



Recursion vs. Looping– Reasons not to use recursion

• They are certainly less efficient than iterative algorithms because of the overhead

• Harder to discern what is going on with recursion

– Why use recursion• The speed and amount of memory available to modern

computers diminishes the overhead factor

– The decision is primarily a design choice

Starting Out With Programming Logic & Design - Chapter13_Recursion

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