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MSc/ICY Software Workshop
2016-17, Semester 2
Uday Reddy
University of Birmingham
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Semester 2 Outline
 Recursion and Recursive data structures
Lists, trees, binary search trees
 Mutable data structures

 Java Collections library
 Java type system and generic classes
 Graphical User Interfaces (GUI’s)
 Concurrent Threads & Network Sockets
 Software Engineering methods
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Organisation
 Assessment:
 4 Lab exercises (1-2 weeks each, part of 20%)
 2 short class tests (quizzes, part of 20%)
 Group project (5 weeks, 10%)
 Tutorial groups same as last semester
 Tue, 1-2pm, 2-3pm
 21 Lectures (3 per week for 7 weeks:
 No lectures after Week 8
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Class 1 - Recursion
 Recursion
Fundamentals of recursion
Number-theoretic functions
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Recursive methods
An alternative way to do repetitive actions.
More general than loops:
A recursive method is one
that calls itself.
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Why study recursion?
Used only occasionally in programming, but:
 Mathematically
useful - related to principle of
induction
 Used to specify programs (rather than write
them).
 Represents basic principle of computation.
 It is the most general method of repetitive
computation.
 Introduces functional programming style.
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What basic principle?
All computation is, in some sense, performed
in one of two ways:
 Directly
(e.g. addition)
 By solving a “simpler” version of the
computation and using this solution to get the
desired answer.
 Note that solving and using are mixed up.
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Recursive methods in Java
Recursive method f with argument x has the form
static typename f (typename x) {
if (x is simple enough)
solve directly
else
use f(value “smaller than” x)
to calculate f(x)
}
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Recursion on integers
On integers, this becomes
static int f (int x) {
if (x is a small enough number)
return expression using x;
else {
int y = f (number less than x);
return expression using x and y;
}
}
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Recursion example
Given n, calculate sum n+(n-1)+ ... +1 (for n  0)
static int sum (int n) {
if (n == 0)
return 0;
else {
int y = sum (n-1);
return n+y;
}
}
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Computing using sum
 The sum method, in mathematical style:
S(0) = 0
S(n) = n + S(n-1), if n  0
 Example computation
S(3) = 3 + S(2)
= 3 + (2 + S(1))
= 3 + (2 + (1 + S(0)))
=3+2+1+0
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Java computation for sum
 Java computation works the same way:
sum(3)
6
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sum(2)
3
sum(1)
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sum(0)
0
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Recursion example
Define f(i) to be the ith number in the sequence
5, 8, 11, 14, 17, … (counting from zero)
static int f (int i) {
if (i == 0)
return 5;
else {
int y = f(i-1);
return y+3;
}
}
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Recursion on integers
Methods returning void can also be defined by
recursion.
Basic principle: use computation on smaller
values to perform computation on larger
values.
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Recursion example
Given n, print numbers n, n-1, ..., 0
static void printnums (int n) {
if (n == 0) {
System.out.print(0);
}
else {
System.out.print(n);
printnums(n-1);
}
}
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Thinking recursively
Key ideas:
 Know
exactly what the method is supposed to
do.
 Assume the method works for smaller values.
Then just figure out how to use it to compute
the method for larger values.
 Don’t forget base cases - small values that can
be calculated directly.
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Example
Given n, print numbers 0, ..., n-1, n.
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Example
Given n, calculate n!, defined to be the nth
number in the list 1, 1, 2, 6, 24, 120, …
(counting from zero)
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Example
Given n >=0, print n asterisks.
> java stars
Input number: 4
****
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Example
Given n>=0, print a triangle out of asterisks.
> java triangle
Input number: 4
****
***
**
*
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Example
Given integers m, n >= 0, compute mn
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Example
Given integers m, n >= 0, compute mn more
efficiently, using this idea:
mn = 1,
if n=0
(mn/2)2, if n even
mmn-1, if n odd
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Why more efficient?
Count multiplications:
 pow(m,n): n-1 multiplications
 fastpow(m,n): log2 n multiplications
One advantage of recursion is that it sometimes
suggests much more efficient algorithms.
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Binomial coefficients
m
n
( ) (“m choose n”) = number of ways of selecting
n items from m>=n objects (disregarding order).
E.g. ( 4 )
2
= 6:
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Binomial coefficients (cont.)
m’
n’
Assume we can calculate ( ) for m’ <= m
and/or n’ <= n. How does this help us
m
calculate ( n ) ?
Select element e out of the m elements. To
choose the n elements, either:
 Include
e: choose n-1 out of remaining m-1
objects; or
 Exclude e: choose n out of remaining m-1 objects.
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Binomial coefficients (cont.)
Thus, binomial coefficient can be calculated
recursively:
m
m-1
m-1
( n ) = ( n-1 ) + ( n )
Base cases:
m
( 0 )= 1
0
( n )= 0
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