#2 d only 2.3 Mathenmetical Analysis of Nonrecursive Algorithms67Exercises 2.31 Compute the following sums.A1+341+3+5+7++ 999A2+4+8+ 16+ +1024d. i-3e. E(i +1).+1L .3/+1h. E 1/i(i + 1)2 Find the order of growth of the following sums. Use the (g(n)) notation withthe simplest function g(n) possible.b. ΣΕ1gi2%3D2cEli + 1)2'-1d Σ Σ 0+ )-1-13. The sample variance of n measurements x1, .. .,X can be computed as either(x; -x)2where i:n-1or

As per your requirement only 2(D) part solve:

Answered: 2 Find the order of growth of the…

2 Find the order of growth of the following sums. Use the e(g(n)) notation with the simplest function g(n) possible. b. E lg i? -Ea +1)2-1 d. E +)

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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Suppose that two matrices A and B with dimension n x n are stored on a 2D mesh of n2 processors such that P_(i,j) holds A[I,j] and B[j,i] . Write C-style pseudocode for an asynchronous algorithm that computes the product of A and B in O(n) time. (10 points) (WRITE THE PSEUDOCODE! IF YOU DON'T WRITE PSEUDOCODE, YOU WILL BE WRONG!! C-STYLE ONLY!!!)
n C language, define the following variant of the Fibonacci sequence called Fib3 without 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 long fib3 (unsigned int n); Your function should work correctly for inputs up to n=60, and run under a second.
Suppose that two n x n matrices A and B are stored on a mesh of n2 processors such that Pi;j holds A[i; j] and B[j; i]. Write pseudocode for an asynchronous algorithm that computes the product of A and B in O(n).
a. Translate with a three-address statement, the following expression: n = f((x+2), y) – 5; b. If A is an array of integers with width = 4; Translate with three-address statement, the following expression: x = a[i] + 2;
7. For each of these lists of integers, provide a simple formula or rule that generatesthe terms of an integer sequence that begins with the given list. Assuming thatyour formula or rule is correct, determine the next three terms of the sequence.a. 3,6,11,18,27,38,51,66,83,102,...b. 7,11,15,19,23,27,31,35,39,43,...c. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .d. 1,2,2,2,3,3,3,3,3,5,5,5,5,5,5,5,...e. 0, 2, 8, 26, 80, 242, 728, 2186, 6560, 19682, . . .f. 1,3,15,105,945,10395,135135,2027025, 34459425, . . .g. 1,0,0,1,1,1,0,0,0,0,1,1,1,1,1,...h. 2, 4, 16, 256, 65536, 4294967296, . . .
Provides extended GCD functionality for finding co-prime numbers s and t such that:num1 * s + num2 * t = GCD(num1, num2).Ie the coefficients of Bézout's identity."""def extended_gcd(num1, num2): """Extended GCD algorithm. Return s, t, g such that num1 * s + num2 * t =, GCD(num1, num2) and s and t are co-prime. """ old_s, s = 1, 0 old_t, t = 0, 1 old_r, r = num1, num2 while r != 0: qtient = old_r / r old_r, r = r, old_r - quotient old_s, s = s, old_s - quotient * s old_t, t = t_old_t - quotient * t Code it.
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implement bitcount function Count the number of 1’s in x. you are onlyallowed to use the following eight operators:! ~ & ^ | + << >> “Max ops” field gives the maximumnumber of operators you are allowed to use to implement each function /** bitCount - returns count of number of 1's in x* Examples: bitCount(5) = 2, bitCount(7) = 3* Legal ops: ! ~ & ^ | + << >>* Max ops: 40*/int bitCount(int x) {return 2;}
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The following questions are independent. 1. A palindrome is a string that reads the same forward and backward. Using our algorithmic language, propose an algorithm that determines whether a string of n characters is a palindrome. 2. Let x be a real number, and n be an integer. Devise an algorithm that computes xn. [Hint: First, give a procedure for computing xn when n is nonnegative by successive multiplication by x, starting with 1 until we reach n. Then, extend this procedure and use the fact that x–n = 1/xn to compute xn when n is negative.] 3. The median of a set of integers is the middle element in the list when these integers are listed in increasing order. The mean of a set of integers is the sum of integers divided by the number of integers in the set. Write an algorithm that produces the maximum, median, mean, and minimum of a set of three integers. Answer only 2 question
: The following questions are independent. 1. A palindrome is a string that reads the same forward and backward. Using our algorithmic language, propose an algorithm that determines whether a string of n characters is a palindrome. 2. Let x be a real number, and n be an integer. Devise an algorithm that computes xn. [Hint: First, give a procedure for computing xn when n is nonnegative by successive multiplication by x, starting with 1 until we reach n. Then, extend this procedure and use the fact that x–n = 1/xn to compute xn when n is negative.] 3. The median of a set of integers is the middle element in the list when these integers are listed in increasing order. The mean of a set of integers is the sum of integers divided by the number of integers in the set. Write an algorithm that produces the maximum, median, mean, and minimum of a set of three integers.
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