Consider the following code, assuming that i, x, and n are integers, with n ≥ 0. • State a non-trivial loop invariant (which must include conditions for i and x). • Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended. • Note: a correct proof of an incorrect invariant will still receive partial credit. Give the final value of x in terms of n. • Note: (for the sake of readability) the value 2² in the code below is 2 to the power of i. • Note: I or symbol (with ranges) meaning product or sum of terms can be used as part of loop invariant.

Consider the following code, assuming that i, x, and n are integers, with n ≥ 0. • State a non-trivial loop invariant (which must include conditions for i and x). • Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended. • Note: a correct proof of an incorrect invariant will still receive partial credit. Give the final value of x in terms of n. • Note: (for the sake of readability) the value 2² in the code below is 2 to the power of i. • Note: I or symbol (with ranges) meaning product or sum of terms can be used as part of loop invariant.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 8SA

See similar textbooks

Similar questions

Course:Artificial Intelligence Topic:Sample Neural Network to calculate total error using Forward pass backpropagation. Problem:Implement forward pass backpropagation for 100(for two input 200)random numbers.(Set range for random numbers 0.01-1.00) using C++/Python with short explanation with key points.
Modified coin-row problem:If we modified the coin-row problem, so that you cannot take the adjacent coin, and youcannot take the coin next to the adjacent coin also (see example below), what would thedynamic programming formula F(n) be?Example: A, B, C, D, E, F, G, H, I, JIf A is taken, then B & C cannot be taken, but D (or above D, like E and so on) can be taken.If B is taken, then A, C, D cannot be taken.And so on.
2, Towers of Hanoi Problem. (10 points) The Towers of Hanoi is a famous problem for studying recursion in computer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. Answer the following questions. (1) Determine a state representation for this problem. (4points) (2) What is the size of the state space? (3 points) (3) Supposing K=3, N=4, what is the start state by using your proposed state representation method and what is the goal state? (3 points)
Describe what the following code is doing (the outcome), by annotating each line of code and giving an overall description of the function of the code. Also, perform a desk check (trace) of the program. Must show multiple iterations of the program loops in the desk check (trace). MOV RO, #100 MOV R1, #2O Loop: CMP RO, R1 BEQ Stop BLT Less SUB RO, RO, R1 BAL Loop Less: SUB R1, R1, RO BAL Loop Stop: MOV R7, #1 SWI O
▼ Part A - The effect of an arithmetic shift on signed numbers Let's look at see what happens to signed numbers during a shift operation. As with most problems with number representations, errors can be intermittent. Sometimes the code will work as expected, and other times it will behave in a manner that seems to be totally arbitrary. Consider the following code fragment that makes use of the fact that shifting a value left by one place multiplies the number by 2. By passing in the number to be multiplied and the power of 2 to multiply it by (for example 4 = 22) the correct answer should be passed back from the function after the results are printed for the user to examine. signed int mult_2_to_n (signed int num, int n) { signed int result; result = num << n; printf("%d multiplied by 2^%d %d\n", num, n, result); return result; } Using a signed number as the manipulated integer may cause an error in some cases. Several approaches may be used to fix the problem. Which solutions below…
Heat capacity of a solid: Debye's theory of solids gives the heat capacity of a solid at temperature T to be 3 T rOp/T Cy = 9VpkB (e* – 1)2 dx, - where V is the volume of the solid, p is the number density of atoms, kg is Boltzmann's constant, and 0D is the so-called Debye temperature, a property of solids that depends on their density and speed of sound. Develop a computer code to evaluate Cy (T) for a given value of the temperature, for a sample consisting of 1000 cubic centimeters of solid aluminum, which has a number density of p = 6.022 x 1028m-3 and a Debye temperature of 0p = 428K. The Boltzmann's constant kg = 1.380649 x 10-23 J · K-1. Please evaluate the integral with the following methods: (a) MATLAB adaptive Simpson quadrature, [Q.FCNT] = QUAD(FUN,A,B,TOL) with TOL =le-10.
[Unbalanced Rod] Given a set of n weights {w₁,..., wn} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown in the figure below. -1". /10 2 3 12 2 4 We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights to hooks, we can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks). where 0 ≤ Pi≤n-1 is the position of weight along the rod. For example, in the figure shown above, the center of mass is computed as C= C = i Wi Pi Σi Wi 10 0+2 1+3·2+4·3+12.4 +2.5 10+2+3+4+12+2 78 33 The problem is to find an assignment of weights to hooks that makes the center of mass as far as possible to the left, i.e., minimize the value of c. Answer the following questions. 1. Describe a greedy algorithm that finds the assignments that…
Write recursive functions for the following equations:a. Harmonic number is defined by the equationb. Fibonacci numbers are defined by the formula:FN = FN-2 + FN-1, for N ≥ 2 with F0 = 0 and F1 = 1
Problem Statement: Consider a permutation of numbers from 1 to N written on a paper. Let's denote the product of its element as 'prod' and the sum of its elements as 'sum'. Given a positive integer N, your task is to determine whether 'prod' is divisible by 'sum' or not. Input Format: First input will be an integer T. It depicts a number of test cases. Followed by the value for each test case. Each test case will contain an integer N (1<= N <=10^9). It is nothing but the length of the permutation. Output Format: For each test case, print "YEAH" if 'prod' is divisible by 'sum', otherwise print "NAH".
(Data Structures and Algo C++ Weiss 4th ed - ch7.40): The following divide-and-conquer algorithm is proposed for finding the simultaneous maximum and minimum: If there is one item, it is the maximum and minimum, and if there are two items, then compare them, and in one comparison you can find the maximum and minimum. Otherwise, split the input into two halves, divided as evenly as possibly (if N is odd, one of the two halves will have one more element than the other). Recursively find the maximum and minimum of each half, and then in two additional comparisons produce the maximum and minimum for the entire problem. In C++, find a function which will take in a vector and solve the problem, producing a vector of two elements, the min and max.
Correct answer will be upvoted else downvoted. Computer science. You are given three integers a, b, k. Find two parallel integers x and y (x≥y) to such an extent that both x and y comprise of a zeroes and b ones; x−y (additionally written in double structure) has precisely k ones. You are not permitted to utilize driving zeros for x and y. Input The main line contains three integers a, b, and k (0≤a; 1≤b; 0≤k≤a+b≤2⋅105) — the number of zeroes, ones, and the number of ones in the outcome. Output In case it's feasible to find two reasonable integers, print "Yes" trailed by x and y in base-2. In any case print "No". In case there are various potential replies, print any of them.
Implement programs involving the use of while, do..while and for loop statement.