Big-O notation.
Let
T(n) be given using the recursive formula.
T(n) = T(n-1) + n,
T(1) = 1.
Prove that T(n) = O(n2).
T(n) = T(n-1) + n, T(1) = 1. using substitution method: --------------------------- T(n) = T(n-1) + n = T(n-2) + n-1 + n = T(n-3) + n-2 + n-1 + n = T(1) + 2 + ... + n-2 + n-1 + n = 1 + 2 + ... + n-2 + n-1 + n This is sum of first n natural numbers. It's formula is n(n+1)/2. = n(n+1)/2 = (n2+n)/2 we can ignore lower order terms(n) and constant factors(/2). so, time complexity is O(n2) T(n) = O(n2)
Big-O notation. Let T(n) be given using the recursive formula. T(n) = T(n-1) + n, T(1)...
Can I get help with this question? Problem 1. Solve the recursive equations with big-O notation. a) T(n)=167(n/2) + n° with T(1)=1. b) T(n) = T(vn+1 with T(1)=T(2)=T(3)=1, where (a) is the largest integer m less than or equal to a. For example [3.1]=3.
7. [4] (Big-O-Notation) What is the order of growth of the following functions in Big-o notation? a. f(N) = (N® + 100M2 + 10N + 50) b. f(N) = (10012 + 10N +50) /N2 c. f(N) = 10N + 50Nlog (N) d. f(N) = 50N2log (n)/N
6. Using big-oh notation, give the runtime for each of the following recursive functions. You do not need to justify your answers: a) Int nonesense (int n) if (n <0) return 1; return nonsense (n-2) 1; b) int no nonesense (int n) if (n <0) return 1; return no_nonsense (n-1)+ no nonsense (n-1)
What is the order of the following growth function expressed using Big-Oh notation: T(N)=7*N3 + N/2 + 2 * log N + 38 ? O(2N) O(N3) O(N/2) O(N3 + log N)
Q6) let T(n) be a running time function defined recursively as 0, n=0 n=1 3T(n - 1)- 2T(n - 2), n> 1 a) Find a non-recursive formula for T(n) b) Prove by induction that your answer in part (a) is correct. c) Find a tight bound for T(n).
Choose the equivalent Big Oh notation for the functions given below. If there is more than one option, circle the tightest asymptotic bound. function f(n) = 5n - 10 belongs to a) O(1) b) O(n) c) O(n2) d) O(log n) function f(n) = 4n2 + 4n + 1 belongs to a) O(1) b) O(n) c) O(n2) d) O(log n) function f(n) = n2 + 100 log n belongs to a) O(1) b) O(n) c) O(n2) d) O(log n)
A 2 × n checkerboard is to be tiled using three types of tiles. The first tile is a white 1 × 1 square tile. The second tile is a red 2 × 2 tile and the third one is a black 2 × 2 tile. Let t(n) denote the number of tilings of the 2 × n checkerboard using white, red and black tiles. (a) Find a recursive formula for t(n) and use it to determine t(7). (b) Let...
Q-6e: Determine the big-O expression for the following T(N) function: T(1) = 1 T(N) = 2T(N – 1)+1 O 0(1) O O(log N) OO(N2) O O(N log N) O 0(2) OO(N)
Using the definition of the Big-Oh asymptotic notation, show that 10? = ?( n2 )
In Java code provide the desired Big O notation methods and then call those methods in the main. Problem: Let n be the length of an integer array a, for each of the following classes ?(log(log(log(?)))) ?([log(?)] 3 ) ?(? 5 ) ?(4 ? ) ?(?!) ?(? ? ) write a method that takes as sole input an array a of length n, non-recursive, whose running time belongs to only one of the above classes.