Transcript Lecture 12 - cda college

Chapter 13:
Recursion
Starting Out with Programming Logic & Design
Second Edition
by Tony Gaddis
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Chapter Topics
13.1 Introduction to Recursion
13.2 Problem Solving with Recursion
13.3 Examples of Recursive Algorithms
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13.1 Introduction to Recursion
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
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13.1 Introduction to Recursion
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13.2 Problem Solving with Recursion
A problem can be solved with recursion if it can
be broken down into successive smaller
problems that are identical to the overall
problems
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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)
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13.2 Problem Solving with Recursion
How it works
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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
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13.2 Problem Solving with Recursion
Using recursion to calculate the factorial of a
number
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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
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13.2 Problem Solving with Recursion
Continued…
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13.2 Problem Solving with Recursion
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13.2 Problem Solving with Recursion
Inside Program 13-3
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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
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13.2 Problem Solving with Recursion
Figure 13-4 The value of n and the return value during
each call of the function
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13.3 Examples of Recursive Algorithms
Summing a Range of Array Elements with Recursion
Continued…
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13.3 Examples of Recursive Algorithms
Summing a Range of Array Elements with Recursion
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13.3 Examples of Recursive Algorithms
Inside Program 13-4
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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
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13.3 Examples of Recursive Algorithms
The Fibonacci Series
Continued…
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13.3 Examples of Recursive Algorithms
The Fibonacci Series
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13.3 Examples of Recursive Algorithms
Inside Program 13-5
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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
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13.3 Examples of Recursive Algorithms
Additional examples that can be solved with
recursion
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The Greatest Common Divisor
A Recursive Binary Search
The Towers of Hanoi
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13.3 Examples of Recursive Algorithms
Recursion vs. Looping
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Reasons not to use recursion
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Why use recursion
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They are certainly less efficient than iterative
algorithms because of the overhead
Harder to discern what is going on with recursion
The speed and amount of memory available to modern
computers diminishes the overhead factor
The decision is primarily a design choice
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