Recurrence Solving

# Recurrence Solving - Solving Recurrences 1 Solving...

This preview shows pages 1–6. Sign up to view the full content.

Solving Recurrences 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Solving recurrences Solving recurrences means the asymptotic evaluation of their efficiency The recurrence can be solved using some mathematical tools and then bounds (big-O, big- Ω , and big- Θ ) on the performance of the algorithm should be found according to the corresponding criteria 2
Composing recurrences A recurrence for the running time of a divide-and-conquer algorithm is based on the three steps: 1) Let T ( n ) be the running time of a problem of size n . If the problem size is small enough ( n c ) for some constant c , the straightforward solution takes constant time, which we write as Θ (1) 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Composing recurrences 2) Suppose that our division of the problem yields a subproblems, each of which is 1/ b size of the original. 3) If we take D ( n ) time to divide the problem into subproblems and C ( n ) time to combine the solutions to the subproblems to the original problem, we got the recurrence 4
Hence,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/13/2011 for the course 332 351 taught by Professor Staff during the Fall '08 term at Rutgers.

### Page1 / 13

Recurrence Solving - Solving Recurrences 1 Solving...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online