Recurrence Solving

Recurrence Solving - Solving Recurrences 1 Solving...

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

View Full Document Right Arrow Icon
Solving Recurrences 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 3

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

View Full DocumentRight Arrow Icon
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
Background image of page 4
Hence,
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

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 Right Arrow Icon
Ask a homework question - tutors are online