Lecture 16: Searching and Sorting (Thursday)

CompSci 105 SS 2005 Principles of Computer Science Test Tomorrow. Lecture 16: Searching and Sorting (Thursday) Lecturer: Santokh Singh

Array Implementation 0 1 2 3 4 5 6 7 items: 3 5 1 front: 0 back: 2 Textbook, pp. 306ff

“Circular Array” 7 0 3 items: 6 1 5 front: 0 1 back: 2 5 2 4 3 Java Code, Textbook, pp. 310ff

Linked List Implementation 3 1 5 firstNode lastNode Textbook, pp. 302ff,

Circular Linked List 3 1 5 lastNode Java code, textbook, pp. 305ff,

ADT List Implementation • 1 • 5 • 3 Java Code, Textbook, pp. 263ff

Algorithm Efficiency Challenges in Measuring Efficiency Counting Operations Growth Rates of Functions Big O Notation Examples General Rules

Node curr = head; while (curr != null ) { System.out.println( curr.getItem() ); curr = curr.getNext(); } Textbook, p. 374

Rate of Growth x + ny time n

for ( i=1 to n ) { for ( j=1 to n ) { for ( k=1 to 5 ) { Task T } } }

Rate of Growth n2z time n

Rate of Growth n2z x + ny time n

Algorithm Efficiency Challenges in Measuring Efficiency Counting Operations Growth Rates of Functions Big O Notation Examples General Rules

Big O Notation “An Algorithm A is order f(n) – denoted O(f(n)) – if constants k and n0 exist such that A requires no more than k * f(n) time units to solve a problem of size n≥n0” - Textbook, p. 376

Big O Notation “An Algorithm A is order f(n) – denoted O(f(n)) – if constants k and n0 exist such that A requires no more than k * f(n) time units to solve a problem of size n≥n0” - Textbook, p. 376 Worst Case

Big O Notation “An Algorithm A is order f(n) – denoted O(f(n)) – if constants k and n0 exist such that A requires no more than k * f(n) time units to solve a problem of size n≥n0” - Textbook, p. 376 Worst Case Large Problems

Rate of Growth n2z “An Algorithm A is order f(n) – denoted O(f(n)) – if constants k and n0 exist such that A requires no more than k * f(n) time units to solve a problem of size n≥n0” x + ny time n Book Computes k and n0 exactly, p. 377

Rate of Growth n2z k n “An Algorithm A is order f(n) – denoted O(f(n)) – if constants k and n0 exist such that A requires no more than k * f(n) time units to solve a problem of size n≥n0” x + ny time n Book Computes k and n0 exactly, p. 377

for ( i=1 to n ) { for ( j=1 to n ) { for ( k=1 to 5 ) { Task T } } }

for ( i=1 to n ) { for ( j=1 to i ) { for ( k=1 to 5 ) { Task T } } } Textbook, p. 374-5, 377

O Notation Tricks • Ignore “low-order” terms • Ignore Constants • Can combine O()’s Textbook, p. 380

Comparing Growth Rates O(n2) Faster Growth Faster Code O(n) Textbook, p. 378

Comparing Growth Rates O(n2) Faster Growth Faster Code O(n) O(1) Textbook, p. 378

Comparing Growth Rates O(2n) O(n2) Faster Growth Faster Code O(n) O(log n) O(1) Textbook, p. 378

Comparing Growth Rates O(2n) O(n3) O(n2) Faster Growth O(n log n) Faster Code O(n) O(log n) O(1) Textbook, p. 378

Lecture 16: Searching and Sorting (Thursday)