CS 211:
Introduction to Computer Programming II

	Instructor: Brian M. Dennis
	Teaching Assistants:
	Tom Lechner, Bin Lin, Rachel Goldsborough
	http://www.cs.northwestern.edu/~bmd/cs211/

Binary Reping Sets

	int set = 0x5A; // Binary 0101 1010, decimal 90
	// Integers in the set, 1 3 4 6
	// Technically, can hold 32 integers
	// 0 to 31
	// 0000 0000 0000 0000 0000 0000 0101 1010
	// Another set
	int another_set = 0xdecafbad;
	// 1101 1110 1100 1010 1111 1011 1010 1101

Adding an Element

	int set = 0x5A; // Binary 0101 1010, decimal 90
	// Adding a an integer d to the set
	// Left shift, bitwise or
	int d = 7;
	int mask = 1 << d;
	set = set | mask;
	set |= mask;
	set |= 1 << d;

Membership Testing

	int set = 0x5A; // Binary 0101 1010, decimal 90
	// Testing membership of int d in the set
	// Left shift, bitwise and
	int d = 7;
	int mask = 1 << d;
	int test = set & mask;

Deleting a Member

	int set = 0x5A; // Binary 0101 1010, decimal 90
	// Deleting d from the set
	// Left shift, negate, bitwise and
	int d = 6;
	int mask = 1 << d;  // mask = 0100 0000
	mask = ~mask;       // mask = 1011 1111
	int test = set & mask;

Set Abstract Datatype

	#ifndef _SET_H_
	#define _SET_H_ 1
	class BitSet {
	public:
	BitSet();
	void add(int d);
	void del(int d);
	bool is_member(int d);
	public:
	int bits;
	};
	#endif

Set Abstract Datatype

	BitSet::BitSet() {
	bits = 0;
	}
	BitSet::add(int d) {
	int mask = 1 << d;
	bits |= mask;
	}

Set Abstract Datatype

	BitSet::del() {
	int mask = 1 << d;
	mask = ~mask;
	bits &= mask;
	}
	bool BitSet::is_member(int d) {
	int mask = 1 << d;
	int test = bits & mask;
	test ? true : false;
	}

Set Abstract Datatype

	#include <ctime>
	#include <cstdlib>
	#include "BitSet.h"
	int main() {
	BitSet bit_set;
	for(int i = 0; i < 10; i++) {
	int d = rand() % 32;
	bit_set.add(d);
	}
	return 0;
	}

Set Abstract Datatype

	#include <ctime>
	#include <cstdlib>
	#include "BitSet.h"
	using namespace std;
	int main() {
	BitSet bit_set;
	srand(time(0));
	for(int i = 0; i < 10; i++) {
	int d = rand() % 32;
	bit_set + d;  // Wouldn't it be nice if
	}
	}

Set Abstract Datatype

	// Stuff elided
	#include <iostream>
	using namespace std;
	int main() {
	BitSet bit_set;
	// Stuff elided
	// Let's print out a bitset
	cout << "BitSet[";
	for (int j = 0; j < 32; j++) {
	if (bit_set.is_member(j)) {
	cout << j;
	}
	}
	cout << "]";
	cout << endl;
	}

Set Abstract Datatype

	// Stuff elided
	#include <iostream>
	using namespace std;
	int main() {
	BitSet bit_set;
	// Stuff elided
	// Let's print out a bitset
	cout << bit_set << endl;  // Wouldn't it be nice
	}

Operator Overloading

	// Stuff elided
	BitSet& operator+(BitSet& bs, int d) {
	bs.add(d);
	return bs;
	}
	int main() {
	BitSet bit_set;
	for(int i = 0; i < 10; i++) {
	int d = rand() % 32;
	bit_set + d;  // Wouldn't it be nice if
	}
	}

Operator Overloading

	#ifndef _SET_H_
	#define _SET_H_ 1
	class BitSet {
	public:
	BitSet();
	void add(int d);
	void delete(int d);
	bool is_member(int d);
	// Let's hook into C++'s syntax
	BitSet& operator+(int d);
	private:
	int bits;
	};
	#endif

Operator Overloading

	BitSet::BitSet() {
	bits = 0;
	}
	BitSet::add(int d) {
	int mask = 1 << d;
	bits |= mask;
	}
	BitSet& BitSet::operator+(int d) {
	add(d)
	return *this;
	}

Operator Overloading

	// Has to be a standalone function not member function
	ostream& operator<<(ostream& os, BitSet& bs) {
	int foo = 10;
	cin >> foo;
	return os;
	}
	int main() {
	BitSet bit_set;
	// Stuff elided
	// Let's print out a bitset
	cout << bit_set << end;  // Wouldn't it be nice
	}

That’s a Wrap

	Takeaways
	Bits can represent sets
	Building an ADT on that representation
	Operator overloading
		Syntactic extension
	Reading 8.1 – 8.7