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Quicksort 4-18-2013
Quicksort
4-18-2013
Thursday, April 18th Barben Rooms A&B, Cheel
4:00 pm–4:45 pm Panel discussion on “Technical Career Opportunities”, Moderated by Bob Lockwood ‘86
5:00 pm–5:45 pm Roundtables:
How to Communicate with your Client – Differences in Internal vs. External Client Development with Chris Snelling ‘86 and Rich Bogart ‘86
Technology Trends in Industry with Ron Ayers ‘02 and Chris Fohlin ‘07
Tricks and Tips for the Job Seeker with Dan Dedrick ‘06 and Bob Lockwood ‘86
6:00 pm – 6:45 pm “Building Your Digital Presence”; Presentation by Chris Fohlin ’07
Employers and clients do their homework on you before you walk through the door. Does your online presence paint the right picture? Learn best practices for managing, and maximizing, your professional digital image.
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Sorting
Quicksort
OOP
inheritance
Reading: Maciel
Chapter 15, Sorting
Project#2: Evil Hangman, due Wed. 4/24
see the sample output
Selection Sort ϴ(n2)
if ( [start,stop) contains more than one element ) {
i_max = index of the largest element in [start,stop)
swap a[i_max] and a[stop - 1]
sort [start, stop-1)
}
Insertion Sort ϴ(n2)
if ( [start,stop) contains more than one element ) {
sort [start, stop-1)
insert a[stop-1] into [start, stop-1)
}
Mergesort
if ( the array contains more than one element ) {
sort the first half of the array
sort the second half of the array
merge the two sorted halves
}
Quicksort
find a “pivot point”
partition around the pivot
sort halves
example run: (top level of recursion)
[ 60 12 37 42 25 38 16 ]
[ 60 12 37 42 ] [ 25 38 16 ] 1. divide in half
[ 12 37 42 60 ] [ 16 25 38 ] 2. sort halves
[ 12 16 25 37 38 42 60 ] 3. merge
example run: trace
[ 60 12 37 42 25 38 16 ]
[ 60 12 37 42 ] [ 25 38 16 ]
[ 60 12 ] [ 37 42 ] [ 25 38 ] [ 16 ]
[ 60 ] [ 12 ] [ 37 ] [ 42 ] [ 25 ] [ 38 ] [ 16 ]
[ 12 60 ] [ 37 42 ] [ 25 38 ] [ 16 ]
[ 12 37 42 60 ] [ 16 25 38 ]
[ 12 16 25 37 38 42 60 ]
merging algorithm: array [ 60 12 37 42 25 38 16]
first second result
[ 12 37 42 60 ] [ 16 25 38 ] [ ]
[ 37 42 60 ] [ 16 25 38 ] [ 12 ]
[ 37 42 60 ] [ 25 38 ] [ 12 16 ]
[ 37 42 60 ] [ 38 ] [ 12 16 25 ]
[ 42 60 ] [ 38 ] [ 12 16 25 37 ]
[ 42 60 ] [ ] [ 12 16 25 37 38 ]
[ ] [ ] [ 12 16 25 37 38 42 60 ]
idea:
find a “pivot point”
partition around the pivot
sort halves
}
if ( the array contains more than one element ) {
choose a pivot element
partition the array around the pivot
sort each subarray
}
Partition must rearrange the array so that the following 3 conditions hold:
1. the element a[p] is in its final place in the array, for some p
2. all elements in a[first..p-1] are ≤ a[p]
3. all elements in a[p+1..last] are ≥ a[p]
example: [ 30 10 14 37 42 13 51 5 30 ]
pivot
1. select a pivot
2. partition around the pivot
[ 10 14 13 5 | 30 | 37 42 51 30 ]
3. sort the partitions
[ 5 10 13 14 30 30 37 42 51 ]
If the pivot point divides the list exactly in half, then the number of comparisons would be N log N
If the pivot point is chosen so that one partition is always empty, then the running time is N2
The performance of quicksort heavily depends on the pivot point
best case: pivot element is the median value in the array (divides the array in half)
worst case: the first element of the array is chosen to be the pivot point, but the array is already sorted
in practice, large parts of an input array can be already in sorted order
choose a random element to be the pivot (but then need a call to a pseudorandom number generator)
compromise: choose the median of the first, middle and last element of the array
example: [ 60 12 37 42 25 38 16 ]
pivot
1. select a pivot: median of [16 42 60] => 42
2. partition around the pivot
[ 12 37 25 38 16 ] 42 [ 60 ]
2. sort the partitions
[ 12 16 25 37 38 42 60 ]
[ 60 12 37 42 25 38 16 ]
[ 12 37 25 38 16 ] 42 [ 60 ]
[ 12 ] 16 [ 37 25 38 ] 42 [ 60 ]
[ 12 ] 16 [ 25 ] 37 [ 38 ] 42 [ 60 ]
[ 12 ] 16 [ 25 37 38 ] 42 [ 60 ]
[12 16 25 37 38 ] 42 [ 60 ]
[12 16 25 37 38 42 ] [ 60 ]
[ 12 16 25 37 38 42 60 ]
Quicksort
worst case: ϴ(n2)
best & average case: ϴ(n log n)
easy to write recursively
Mergesort
all cases: ϴ(n log n)
disadvantage: needs extra space proportional to n
good when sequential access is required (e.g. sort a linked list)
easy to write recursively
use a better partitioning element (pivot) to avoid the worst case
median-of-3 partitioning works well in practice
use a simple sort for small partitions (can reduce running time by 20%)
e.g. if size of array ≤ M then use insertion sort
The C++ standard library (in <algorithm>) provides the following functions: template<typename RI>
void sort(RI first, RI last);
template<typename RI, typename Compare>
void sort(RI first, RI last, Compare comp);
The template parameter RI is a random-access iterator.
The data to be sorted is in the range first .. last, where last is one past the last data value.
In practice you would tend to use these
Assume that array items contains 16 integers.
sort(items, items + 16);
● will sort the whole array.
sort(items, items + 8);
● will sort the first half.
sort(items, items + 16, greater<int>()); ● will sort in descending order.
Assume that v is a vector.
sort(v.begin(), v.end()); // sorts vector v
Objects, classes, and inheritance, plus
An object is a software entity that combines state and
behavior.
A class describes the state (member data) and services
(member functions) provided by objects that are
instances of that class.
Classes can be related by inheritance.
polymorphism and dynamic binding.
Goals of OO: abstraction, encapsulation,
comprehensibility, changeability, and reusability.
We’ve now looked at classes and objects.
What about inheritance, polymorphism and dynamic binding?
Object-oriented programming (OOP) is popular because:
It enables reuse of previous code saved as classes
Inheritance and hierarchical organization capture idea:
One thing is a refinement or extension of another
UML Class Diagram
class Arrow : public Line {...}
An Arrow “is a” Line
Arrow
IS-A (inheritance)
Line
important to
make this public
class Line {...}
FilledCircle Line Point
HAS-A
(composition)
2
UML Class Diagram
class Line {
private:
Point endpt1, endpt2;
A Line “has a” Point
Circle
FilledCircle
Point
IS-A (inheritance)
HAS-A
(composition)
1
base class or superclass
derived class or subclass
Confusing has-a and is-a leads to misusing inheritance
Model a has-a relationship with an attribute (data member/instance variable)
class C { ... private: B part; ...}
Model an is-a relationship with inheritance
If every C is-a B then model C as a derived class (also called subclass) of B
Show this: in C include : public B:
class C : public B { ... }
/** the Point class represents a 2D point */
class Point {
private:
int xcoord, ycoord;
public:
Point() : xcoord(0), ycoord(0) {}
Point(int newx, int newy) : xcoord(newx), ycoord(newy) {}
int getX() { return xcoord; }
int getY() { return ycoord; }
void display();
};
class Circle {
private:
Point center;
float radius:
public:
Circle(): center(Point()), radius(1.0f) {}
Circle(int x, int y, float newradius)
: center(Point(x,y)), radius(newradius) {}
float getRadius() { return radius; }
double computeArea();
void display();
};
class FilledCircle public Circle {
private:
string color;
public:
FilledCircle(): Circle(), color(“black”) {}
FilledCircle(int x, int y, float newradius, string newcolor)
: Circle(x, y, newradius), color(newcolor) {}
};
/** test program for shapes */
int main() {
/* Test the Point class, starting with constructors & accessors: */
Point p1;
Point p2(100, 200);
Point p3(50, 50);
cout << "Point 1: " << p1.getX() << ":" << p1.getY() << endl;
cout << "Point 2: " << p2.getX() << ":" << p2.getY() << endl;
cout << "Point 3: " << p3.getX() << ":" << p3.getY() << endl;
/* test Point's display method */
p2.display();
/* Next test the Circle class, starting with constructors: */
/* (continued on next slide) */
/* test program for shapes, continued */
Circle c1(100, 40, 2.5f);
Circle c2;
/* test Circle's accessors and method computeArea */
cout << "Circle c1 radius: " << c1.getRadius() << endl;
cout << “Area of circle c1 is: " << c1.computeArea() << endl;
/* test Circle's display method */
c1.display();
/* Test the FilledCircle class, starting with the constructors */
FilledCircle fc3;
FilledCircle fc4(20, 30, 2.5f, "red");
/* continued on next slide */
/* test program for shapes, continued */
/* Test the FilledCircle class, starting with the constructors */
FilledCircle fc3;
FilledCircle fc4(20, 30, 2.5f, "red");
/* Test the accessors and inherited method computeArea */
cout << "Filled Circle fc3 color is " << fc3.getColor() << endl;
cout << "fc3 area: " << fc3.computeArea() << endl;
cout << "Filled Circle fc4 color is " << fc4.getColor() << endl;
/* Test the FilledCircle's display method */
fc4.display();
/* Testing completed */
return 0;
}
Sorting
Maciel: Chapter 15
Software Life Cycle
Maciel: Chapter 11
Error Checking
Maciel, Chapter 4
