F'ind / (1), S(2), S (3), and f (4) if s(n) is defined recur- sively by f(0) =1 and for n 0, 1, 2, ... a) /(n + 1) -/ (n) + 2. b) S(n + 1) = 3/ (n). c) (n + 1) = 2/(), d) S(n + 1) = s(n)? + s(n) + 1.

Q: O(1) if n = 1 , T(n) = 8T (п/2) + Ө(n?) if n > 1.

A:

Q: Given T1(n)=O(f(n)) and T2(n)=O(g(n)) . Find T1(n).T2(n) and proof the statement is true

A: Proved the given functions

Q: Examples: Find the tight bound of the following recursive functions, T(n). T(n)=9T(n/3)+n T(n)=…

A: the solution is an given below :

Q: Find a regular expression for the set {a"bm:(n + m) is even}.

A: Given: We are given a language L = { a^nb^m : (n+m) is even} Goal: To find the regular expression…

Q: Prove by induction that T(n) = 2T(n/2) + cn is O(n logn).

A: Induction is a mathematical proof technique where a statement is proven true for a base case, often…

Q: : a. [(a mod n) - (b mod n)] mod n = (a - b) mod n

A:

Q: (n) and

A:

Q: Solve following recurrence with iterative substitution: T(n)= 2T(n/2)+c *O(1)

A: Let's solve the following equation using iterative substitution. T(n)= 2T(n/2)+c *O(1)

Q: Give regular expressions for the i (a) {w : w contains at most two 1s} (b) {w : w contains at least…

A: REGULAR EXPRESSION: Regular Expression refers to a sequence of characters that represents any…

Q: f(x)= 5/(2x+4) is continuous at * O R O [0,1/2] O Non

A: Given:   f(x)=5/(2x+4) is continuous at?

Q: T(n) = T(n - 1) + 3n and T(0)=0. Then T(n) is e (n³1 e (n) e (n lg n) e (2")

A: Given question about  Recursive relation Find time complexity

Q: Heuristics Prove or disprove: If h1(n), ..., hk(n) are admissible, so is h(n) = h1(n) + ... + hk(n)

A: It is generally understood that the pointwise maximum of any set of admissible heuristics h1,...,hk…

Q: Given the function T(n) = n3 + 20n + 5, show that T(n) is O(n3)

A: The Big-Oh definition says that, T(n) is O(n3 ) if T(n) ≤ c·n 3 for some n ≥ n0. This condition will…

Q: Let Tk (n) denote the value returned by A(k, n). This gives T0(n) = 2 + n, T1(0) = 0, Tk (0) = 1 for…

A: Solving:

Q: uppose that f(n) = 0(g(n)) and f(n) = 0(h(n)), then it is ( always / sometimes / never) the case…

A: Defined the given statement always, sometimes or never

Q: Show Let f(.) be a computable, strictly monotonic function, that is, f(n+ 1) > f(n) for all n. Show…

A: If f:Σ∗→Σ∗ is a function, and ∃ a Turing machine which on the input w∈Σ∗ writes f(w), ∀w∈Σ∗, then we…

Q: 7. Prove or disprove: f(n) + g(n) = 0 (min(f(n), g(n)))

A: Let ,f(n) = n2g(n) = n

Q: Suppose, T(n) = 12+22+32+…..+n2. Show that, T(n) is in Θ(n3 ).

A: Given  T(n) = 12+22+32+…..+n2

Q: Answer the following short questions: a) Is 2n+1 = O(2n )? b) Is 22n = O(2n )? c) f(n)=O(g(n))…

A: a) Is 2n+1 = O(2n)?   2n+1 = O(2n) because 2n+1 = 21 * 2n = O(2n). Suppose 22n = O(2n) Then there…

Q: For n > 1, in how many out of the n! permutations 7 = (7(1), 7(2),., "(n)) of the numb {1, 2, ...,…

A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…

Q: Function f grows no faster than function g O f (n) = O(g(n)) O f (n) = w(g(n)) O f (n) = O(g(n)) %3D…

A: Solution:

Q: Use two ways to count the number of r-combinations of[n]={1,2,…,n}that contains 1 or 2 or 3. First,…

A: We are aware that there are exactly as many ways to select r things from n diverse objects is equal…

Q: 8. Give a recursive definition of the sequence {an}, n = 1, 2, 3, ... if a) an = 4n − 2. b) an = 1 +…

A: Solution:   a)

Q: If lim n->oo (f(n))/(g(n)) = 0 then f(n) = ω( g(n) ) true false

A: The question is asking whether the statement 'If the limit as n approaches infinity of the ratio of…

Q: Function f grows no slower than function g. O f (n) = O(g(n)) O f (n) = Q(g(n)) O f (n) = o(g(n)) O…

A: This question comes from Data Structure which is a paper of Computer Science. Let's discuss it in…

Q: Question 4: The function T(n) is recursively defined as follows: 1 if n = 1, A + A T(n – 1) if n 2…

A: The answer is given below:-

Q: 11. Show that lower order terms don't matter in the O() notation by showing that if g(n) = O(f(n))…

A: We need to prove that, if g(n)=O(f(n), then, g(n) +f(n)=O(f(n)).

Q: Calculate DFT of x (n) = {1, 0, 1, O). * wfw

A: DFT of x(n)={1,0,1,0}

Q: Show that T(n) = 0(n²) where T(n) = 1+ 2 + 3+. .. +n

A: We have to show that T(n) = O(n2)  Where T(n) = 1+2+3+.......+n