Code Flow-Chart statementi If expressioni statementl Flow-Graph e1 statement2 expressionl n2 else statement3 statement2 statement3 n3 statement4 e4 e5n4 do statement5 while expression2 statement6 statement4 statements expression2 e6 n6 e7 e10 statement6 n8 The following pseudocode finds all prime numbers less then n. Eratosthenes (n) { e[1] = 0 == for i: = p: = 2 2 to n do e[i]: = 1 while p*2

Code Flow-Chart statementi If expressioni statementl Flow-Graph e1 statement2 expressionl n2 else statement3 statement2 statement3 n3 statement4 e4 e5n4 do statement5 while expression2 statement6 statement4 statements expression2 e6 n6 e7 e10 statement6 n8 The following pseudocode finds all prime numbers less then n. Eratosthenes (n) { e[1] = 0 == for i: = p: = 2 2 to n do e[i]: = 1 while p*2

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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int BinDig (int n){ if (n == 1) return 1;else return (1 + BinDig(n/2)); } Find T(n) = number of arithmetic operations. Calculate the complexity of this algorithm.
function recursion(B[0..n − 1], i) if n == 0 then return False if n == 1 then return (B[0] == i)x ← recursion(B[0........n/2 − 1], i) y ← recursion(B[n/2..........4 × n/2 − 1], i) z ← recursion(B[4 × n/2..........n − 1], i) return (x OR y OR z) input array is of length n = 2^p, p is a positive integer Write the recursive formula for above algorithm as of worst case inputs.
T(n) = 9T(n/3) + O(n2)
Ackermann’s function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a function A(m, n) that solves Ackermann’s function. Use the following logic in your function: If m = 0 then return n + 1 If n = 0 then return A(m-1, 1) Otherwise, return A(m-1, A(m, n-1)) Test your function in a driver program that displays the following values:A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2)
Convolution is associative if O xn)*[y(n)+h(n)]=[x(n)+y[n]*h(n) O x(n)*[yln)*h(n]]=[x(n)*y[n]*h(n) x[n)+[y{n)*h(n)]=[x{n)*y{n)]+h(n) O x(n)+[y[n)+h(n)]=[x(n}+y(n)]+h(n)
The complexity of the following code is void f(int n) { if (n > 0) { DoSomething (n); // O (n) f (n-1); } Select one: a. O(nlgn) b. O(n) c. O(gn) d. O(n)
Finish the splitOdd10 using recursion to determine if the elements of an array can be split into two groups such that the sum of one group is a non-zero multiple of 10 and the sum of the other group is odd
The first examples of recursion are the mathematical functions factorial and fibonacci. These functions are defined for non-negative integers using the following recursive formulas:factorial(0) = 1factorial(N) = N*factorial(N-1) for N > 0fibonacci(0) = 1fibonacci(1) = 1fibonacci(N) = fibonacci(N-1) + fibonacci(N-2) for N > 1Write recursive functions to compute factorial(N) and fibonacci(N) for a given non-negative integer N, and write a main() routine to test your functions.(In fact, factorial and fibonacci are really not very good examples of recursion, since the most natural way to compute them is to use simple for loops. Furthermore, fibonacci is a particularly bad example, since the natural recursive approach to computing this function is extremely inefficient.)
Write a pseudocode to solve the following problem: Odd index element probleminput: a non-empty sequence S of n elementsoutput: a list of all the elements in the odd index, or None if S is empty
Count the divisions double fct (const double A[], int n) { } if (n == 0 ) return 1 else return (A [n-1]/A [n-1])/fct (A, n-1);
You, Alice and Bob are working on recursive search algorithms and have been studying a variant of binary search called trinary search. Alice has created the following pseudocode for this algorithm: TSearch (A[a...b], t) If a b return -1 Let p1= a + Floor ((b-a)/3) If A[p1] t return p1 If A[p1]> t return TSearch (A[a...p1-1], t) Let p2 = a + Ceiling (2(b-a)/3) If A[p2] = t return p2 If A[p2]> t return TSearch (A [p1+1...p2-1],t) Return TSearch (A [p2+1...b],t) EndTSearch a) State a recurrence relation that expresses the number of operations carried out by this recursive algorithm when called on an input array of size n. b) Bob has heard that trinary search is no more efficient than binary search when considering asymptotic growth. Help prove him correct by using induction to show that your recurrence relation is in (log₂ n) as well. i. Split the tight bound into and upper (big-O) and lower (big-1). ii. For each bound select a function from (log₂ n) to use in your proof, like alog₂ n or…
*Find a non-recursive formula for f (n) : f (0) = 7, f (n) = 4f (n − 1)/9 for n ≥ 1 *Define the sequence: an = 1+ (n+3)2 for n = 1,2,3, ... recursively.