(Mathematical Analysis of Recursive Algorithms) 9. Consider the following recursive algorithm for computing the sum of the first n cube: S(n)=1³ +2³ +3³ +...+n³. Algorithm S(n) //Input: A positive integer n //Output: The sum of the first n cubes if n = 1 return 1 else return S(n-1)+n*n*n a) Set up and solve a recurrence relation for the number of times the algorithm's basic operation is executed. b) How does this algorithm compare with the straightforward non-recursive algorithm for computing this function?

(Mathematical Analysis of Recursive Algorithms) 9. Consider the following recursive algorithm for computing the sum of the first n cube: S(n)=1³ +2³ +3³ +...+n³. Algorithm S(n) //Input: A positive integer n //Output: The sum of the first n cubes if n = 1 return 1 else return S(n-1)+nnn a) Set up and solve a recurrence relation for the number of times the algorithm's basic operation is executed. b) How does this algorithm compare with the straightforward non-recursive algorithm for computing this function?

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

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Determine the output of the following recursive function when n = 64. (show your working/steps) int func (int n) { if (n ==1) return 0 else return 2 + func ( ) }
Using recursion, write a function sum that takes a single argument n and computes the sum of all integers between 0 and n inclusive. Do not write this function using a while or for loop. Assume n is non-negative. def sum(n): """Using recursion, computes the sum of all integers between 1 and n, inclusive. Assume n is positive. >>> sum(1) 1 >>> sum(5) # 1 + 2 + 3+ 4+ 5 15 "*** YOUR CODE HERE ***"
2. Consider the following function: def func1(n): output = 1 for i in range (1, n) : output = i return output Rewrite the function as a recursive function.
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.
Write a recursive function that adds all the elements in an array. The function will take two arguments, 1) An integer value that is greater than 0 and indicates the size of the array, and 2) An integer array of that size. The function should return an integer value that is the sum of the elements in the array. The function should add elements of the input array using recursion and should not use a loop.ii) Read both a string and the key (integer) is entered through the keyboard. Define a function to encrypt each and every character in a string with the given key. As a programmer, implement the same by writing the C code using pointers. If the given Key is positive, then traverse towards left of the character in the Alphabet sequence. Otherwise, move traverse towards the right of the character in the Alphabet sequence. Example : if the given string is "PRADEEP" and Key = 3 then the encrypted string is "SUDGHHS" iii) An ISBN (International Standard Book Number) is a 10 digit number…
Chapter 8 Irvine book, When I compiled this code I get the following errors ;Greatest Common Divisor Comment !Write a recursive implementation of Euclid’s algorithm for finding the greatest common divisor (GCD) of two integers. Descriptions of this algorithm are available in algebra books and on the Web. Write a test program that calls your GCD procedure five times, using the following pairs of integers: (5,20), (24,18), (11,7), (432,226), (26,13). After each procedure call, display the GCD.! INCLUDE Irvine32.incCalcGcd PROTO,int1:DWORD, int2:DWORD .dataarray SDWORD 5,20,24,18,11,7,438,226,26,13str1 BYTE "Greatest common divisor is: ",0 .codemain PROC mov ecx,LENGTHOF array / 2 mov esi,OFFSET array L1: INVOKE CalcGcd,[esi],[esi+4] mov edx,OFFSET str1 call WriteString call WriteDec call Crlf add esi,TYPE array * 2 loop L1 exitmain ENDP ;---------------------------------------------CalcGcd PROC, int1:DWORD, int2:DWORD;; Calculate the greatest common…
What does the following recursive function do? int f(int n){ if (n==1) return 1; else returm n*f(n-1); } O sum of numbers from 1 to n Factorial of numbern Square of numbers from 1 to n Print the numbers from 1 to n
Write a recursive function to sort an array of integers into ascending order using the following idea: the function must place the smallest element in the first position, then sort the rest of the array by a recursive call. This is a recursive version of the selection sort. (Note: You will probably want to call an auxiliary function that finds the index of the smallest item in the array. Make sure that the sorting function itself is recursive. Any auxiliary function that you use may be either recursive or iterative.) Embed your sort function in a driver program to test it. Turn in the entire program and the output.
use java
1.)I have to recursive with python language and was asked to do a buy 2 get 1 free where you have some amount of money(x) each item costs a given amount(y), for each 2 item you get 1 free, builda recursive solution to find out how many items you can buy for x amount of money. 2.) Buy M, get N free Then alter your first answer to allow for the user to enter any M and N for how many you need to buy to get free items
What will be the output if the main method is called? Method func(x) { IF x == 1 OR x == 3 PRINT "reach to the base!" RETURN PRINT x func(x-1) } Method main0 { func(7) } 7654321 reach to the base! 765432reach to the base! 7654321! 7654reach to the base! 76543reach to the base! 7654321!reach to the base!