Solve the recurrence relations below. Fill in the blanks for the closed form expression and rate of growth. T(n) = { 17 (n − 1) + n² + 2₂ Express final answers in simplest form. Closed form expression of T(n)= Rate of Growth: ( n=0 n>0 )
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- How would I find the recurrence relation(or so called recursion equation) for the following code, and how would that help me get "average time analysis" for big Theta notation? double func3(int[] A) {int count = 0;int sum = 0;Random prng = new Random();for (int i=0; count < 25 && i < A.length; i++) {if (prng.nextDouble() < 0.5){count++;sum+=A[i];}}return sum / 25.0;} what I had got so far is that this function would iterate for the half of the length of the data array that is passed(int[] A) until input array A reaches length of 50, where it will start to get stuck to the 25 iteration for average which is limited by count<25 condition so the recurrence relation would be something like 1. f(x) = 0, when the x reaches the recursion stack that the anymore recursion would not affect sum anymore(reaches 25 count) 2.f(x) = f(x+1) +1/2 , x>0 something like this, that it would make progress toward base case. I am not sure this would be the right form, but I am…Question 1) . Apply Master Theorem to bound each one of the following recurrence relations using Big-O notation. Show all your work. In all cases T(n)=1. a) T(n)= 4T(n/4) + 12 n4 b) T(n)= T(n/2) + log n c) T(n)= 2 T(n/2) + 57 n3 d) T(n)= 3 T(n/2) + O(n)Solve the recurrence relation: T (n) = T (n/2) + T (n/4) + T (n/8) + n. Use the substitution method, guess that the solution is T (n) = O (n log n)
- (b) Prove, by using mathematical induction, that the iteration rule you haveobserved in 4(a) is correct and you have solved the recurrence relation correctly.[Hint: You can write out the general form of T(n) at the iteration step t, and provethat this form is correct for any iteration step t by using mathematical induction.Then by finding out the eventual number of t and substituting it into your generalform of T(n), you get the O(·) notation of T(n). See image for reference to part a, the answer to part a came out to be O(n^2). Need help with b?Solve this and show how you solved it Construct a truth table for the following, remembering to observe the order of operations discussed in class: q Λ ~p → rFind a bound for each recurrence below using Master Theorem:(a) T(n) = 3T(n=2) + n2(b) T(n) = 2T(n=4) + n0:49(c) T(n) = 3T(n=3) + n=2
- Use the Master Theorem to find the complexity class ( Θ notation ) of the following recurrences a) T(n) = 4T(n/2) + n3 b) T(n) = 4T(n/3) + n c) T(n) = 4T(n/3) + n2Need help with in-depth step-by-step solving of the recurrence relations below Fill in the blanks for closed-form expression, and the Big Theta. T(n) = {1, if n = 1 { T(n/5)+5, if n > 1 Assume n is a power of 5.Express final answers in simplest form. Closed-form expression: Rate of growth : For reference the answers are :Closed-form expression: Answer -> 1+5log5nRate of growth: Answer -> Θ (log n)Consider the following recurrence relation, give the Big-Theta behaviour of T(n) using induction: T(1) = 1 T(n) = 5 T(n/5) + 2
- Question 3 Please solve the recurrence and show its proof by induction of: T(1) = 3 T(n) = T(n/3) + 2n, n > 1Consider the following recurrence relation: T(0) = 1, T(1) = 5, T(n) = 4T(n − 1) + 5T(n − 2) for n ≥ 2 Use the guess and check method to guess a closed form for T(n) and then prove that it is a closed form for T(n) using induction.recurrence relation obtain L(1) = 0; L(N) = n+4 * L(n/4) T(1) = 1; T(n)= n+2*T(n/2)