1. Consider the following program: (a) What is the recurrence relation? T(n)= if n l: Algorithm int recursive(n){ Ifn 1, return 1; Else T(n) = If n>1: a- recursive(n/2); b-recursive (n/2); For i from I ton do something: endFor return a+b; EndIF (b) Solve the recurrence relation you've obtained in terms of n and show the O

1. Consider the following program: (a) What is the recurrence relation? T(n)= if n l: Algorithm int recursive(n){ Ifn 1, return 1; Else T(n) = If n>1: a- recursive(n/2); b-recursive (n/2); For i from I ton do something: endFor return a+b; EndIF (b) Solve the recurrence relation you've obtained in terms of n and show the O

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

4. Write the recurrence relation of the following recursive algorithm. What is the complexity of the algorithm? int Test(int n) int result; begin if (n==1) return (1); result = 1; for i=1 to n do result = result + Test(i-1); return (result); end
Consider the following recursive algorithm Algorithm Q(n)// Input: a positive integer nif n == 1 return 1else return Q(n-1)+2*n-1 1) Set up a recurrence relation for this function’s value and solve it to determine what this algorithm computes. 2) Setup a recurrence relation for the number of multiplication made by this algorithm and solve it to find the total number of multiplications that are executed.
Define the following variant of the Fibonacci sequence called Fib3 using recursion : ● fib3(0) = 0 ● fib3(1) = 1 ● fib3(2) = 2 ● fib3(n) = fib(n-1)+fib(n-2)+fib(n-3) for all n>=3 That is, the sequence is 0,1,2,3,6,11,20,37,68,125... unsigned int fib3(unsigned int n);
The factorial function n! has value 1, when n ≤ 1and value n * (n- 1)!, when n > 1. Write both a recursive and an iterative algorithm to Compute n!.
Give a recursive algorithm which takes as input a sequence of numbers and returns the minimum (i.e., smallest) member in the sequence. Your algorithm should not use an iterative loop. FindMin (al, a2,..., an) If (length (alan) = 1), Return (_A_) m: FindMin (al an-1) // The recursive call If (an S m) Else End-if Return (_B__) Return (_C_)
The n-th harmonic is the sum of the reciprocals of the first n natural numbers given by: 17 1.1 1 1 H₁ =Σ =1+=+=+ - 2 3 4 k=1 k +. + n (i) Write a recursive algorithm of this function returning, H, with nε N. (ii) Give a recurrence relation for the number of divisions the recursive algorithm calculates for an input n & N. iii) Solve the recurrence relation and give the O(n) of the algorithm.
The following recursive procedure computes the n-th Fibonacci number. Fib(n) 1 ifn<= 1 2 return n 3 else return Fib(n - 1) + Fib(n - 2) Use memoization technique to develop an efficient version of Fib(n). Give your solution in pseudocode, similar to what is given above.
Prove that the following recursive algorithmfor computing factorials is correct. function factorial(n) comment Return n!. 1. if n ≤ 1 then return(1) 2. else return(n · factorial(n − 1))
Question 6 What is the time complexity of this recursive function? def foo(x): if x == 0: return 1 else: return foo(x-1) O O O(N) O(N^2) O(log N) 0(1)
2. Write the recurrence relation of the following recursive algorithm. What is the complexity of the algorithm? Test (n) if n =1 then return 1 tmp = test (n/2) + test (n/2) for i = 1 to n do tmp = tmp +i 1 2 3 4 5 end for return tmp 7 end
Apply the recursive GCD algorithm. Show the calls to gcd with the arguments for each recursive call and then all of the return values. 1 - GCD(72, 18)
The n-th harmonic is the sum of the reciprocals of the first n natural numbers given by: 1 1 1 1 1 H₁₁ = Σ k=1 - =1+=+=+ 2 3 4 + + n (ii) Give a recurrence relation for the number of divisions the recursive algorithm calculates for an input n & N.