{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Final.sp10

# Final.sp10 - Signature Name Student ID Final CSE 21 Spring...

This preview shows pages 1–4. Sign up to view the full content.

0 Signature ___________________ Name ______________________ Student ID __________________ Final CSE 21 Spring 2010 Page 1 ___________ (30 points) Page 2 ___________ (18 points) Page 3 ___________ (11 points) Page 4 ___________ (12 points) Page 5 ___________ (13 points) Page 6 ___________ (34 points) Page 7 ___________ (10 points) Page 8 ___________ (11 points) Page 9 ___________ (5 points) SubTotal ___________ (144 points = 100%) Page 10 ___________ (10 points) Extra Credit (7%) Total ___________

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

View Full Document
1 { Calculate the first 6 terms for the triangular numbers ( n = 1, n = 2, n = 3, . .. , n = 6). Then to the right calculate the sequence of differences between these terms. 1 st triangular number is 1. n Sequences of differences 1 _______________________ = _____ _____ 2 _______________________ = _____ _____ _____ 3 _______________________ = _____ _____ _____ 4 _______________________ = _____ _____ _____ 5 _______________________ = _____ _____ _____ 6 _______________________ = _____ Write the recurrence relation for the triangular numbers T ( n ). ___________________________ if n ________ T ( n ) = ___________________________ if n ________ Based on the sequence of differences (above) what is a good guess for the closed-form solution to the recurrence relation above? f ( n ) = ____________ Why?: Verify this with a proof by induction. Prove T ( n ) = f ( n ) for all n ___________ . Proof (Induction on n ): _________________: If n = ____, the recurrence relation says T (__) = ____, and the closed-form solution says f (__) = ______ = ____, so T (__) = f (__). _________________: Suppose as inductive hypothesis that T ( k -1) = ____________________ for some k > ___. _________________: Using the recurrence relation, T ( k ) = ___________________________, by 2 nd part of RR = ___________________________, by IHOP = ___________________________ = ___________________________ So, by induction, T ( n ) = ____________ for all n >= 1 (as ______________). A) 4n – 2n B) n 3 – n C) n 4 – n 2 + 2 D) (n 2 + n)/2 E) 2n + n F) 2 n + n * * * * * * * * * * etc. n = 1 n = 2 n = 3 n = 4
2 What are the four general decompositions of recursive algorithms discussed in class? _______________________________ _______________________________ _______________________________ _______________________________ Which of the above general recursive decompositions are most appropriate for the following algorithms: Factorial ____________________________ Binary Search _______________________________ Palindrome ____________________________ Fractal graphic _______________________________ Check output (for example, Koch snowflake or tree fractal) List/String reversal ________________________ List/String reversal ____________________________ moving last element to front, recurse on rest exchanging first and last elements, recurse on rest (s a ) R a (s) R Which is true about proof by induction on k (IHOP on k and IS on k +1) vs proof by induction on k -1 (IHOP on k -1 and IS on k )? _____ A) Both the same

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.

{[ snackBarMessage ]}

### Page1 / 13

Final.sp10 - Signature Name Student ID Final CSE 21 Spring...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online