Question

8.3 (7.3) a) Problem: Find whether an interesting number is in a list Algorithm: If the list is size 1, do a comparison to determine if the number in the list is interesting For bigger lists, split into three roughly equally sized pieces, do 4 comparison to find the two best candidates, then run this algorithm on those two lists. Give a big-Theta estimate for the number of comparisons used for the algorithm. For the following three algorithms, give a big-Theta estimate for the number of multiplications used. b) procedure naïve-pow(a: integer, n: non-negative integer) if n = 0, return 1 else return a \cdot naïve-pow(a, n - 1) c) procedure better-pow(a: integer, n: non-negative integer, power of 2) if n = 0, return 1 else return (better-pow(a, n / 2))$^2$ d) procedure better-pow2(a: integer, n: non-negative integer, power of 2) if n = 0, return 1 else if n is even return better-pow(a, n / 2) \cdot better-pow(a, n / 2)

          8.3 (7.3)
a) Problem: Find whether an interesting number is in a list
Algorithm: If the list is size 1, do a comparison to determine if the number in the list is interesting
For bigger lists, split into three roughly equally sized pieces, do 4 comparison to find the two best
candidates, then run this algorithm on those two lists.
Give a big-Theta estimate for the number of comparisons used for the algorithm.
For the following three algorithms, give a big-Theta estimate for the number of multiplications used.
b) procedure naïve-pow(a: integer, n: non-negative integer)
if n = 0, return 1 else return a \cdot naïve-pow(a, n - 1)
c) procedure better-pow(a: integer, n: non-negative integer, power of 2)
if n = 0, return 1
else return (better-pow(a, n / 2))$^2$
d) procedure better-pow2(a: integer, n: non-negative integer, power of 2)
if n = 0, return 1
else if n is even return better-pow(a, n / 2) \cdot better-pow(a, n / 2)

8.3 (7.3)
a) Problem: Find whether an interesting number is in a list
Algorithm: If the list is size 1, do a comparison to determine if the number in the list is interesting
For bigger lists, split into three roughly equally sized pieces, do 4 comparison to find the two best
candidates, then run this algorithm on those two lists.
Give a big-Theta estimate for the number of comparisons used for the algorithm.
For the following three algorithms, give a big-Theta estimate for the number of multiplications used.
b) procedure naïve-pow(a: integer, n: non-negative integer)
if n = 0, return 1 else return a ·naïve-pow(a, n - 1)
c) procedure better-pow(a: integer, n: non-negative integer, power of 2)
if n = 0, return 1
else return (better-pow(a, n / 2))^2
d) procedure better-pow2(a: integer, n: non-negative integer, power of 2)
if n = 0, return 1
else if n is even return better-pow(a, n / 2) ·better-pow(a, n / 2)

Added by Sara S.

Question

Please give Ace some feedback