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 cas

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 cas

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 10PE

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Problem Description: In the Whimsical Library, each book is enchanted with a magical code to ensure the protection of knowledge. The validation process for these magical codes involves a combination of mathematical spells. The validation process is described as follows: Take the sum of the digits at odd positions from left to right. Take the sum of the squared digits at even positions from left to right. If the absolute difference between the results from step 1 and step 2 is a prime number, the book code is considered valid; otherwise, it is invalid. Example 1: Consider the magical book code 86420137. Step 1. Take the sum of the digits at odd positions from left to right. 8+4+0+3=15 Step 2. Take the sum of the squared digits at even positions from left to right. 6^2+2^2+1^2+7^2=36+4+1+49 = 90 Step 3. If the absolute difference between the results from step 1 and step 2 is a prime number. 115-901 75 (not a prime number) Book code 86420137 is invalid. Example 2: Now, let's examine the…
Exercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…
* Question Completion Status: A Moving to another question will save this response. Question 9 Given the function F(X,Y,Z) =XZ + Z(X'+ XY), the equivalent, most simplified Boolean representation for F is O a. Z+XYZ O b.XZ O c. Z O d.Z+YZ A Moving to another question will save this response. مشمس 36°C
Brute force equation solver this is python program. Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 38 3 -5 -1 Then the output is: 3 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: No solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy. ''' Read in first equation, ax + by = c '''a = int(input())b = int(input())c = int(input()) ''' Read in…
Extreme Fizz BuzzFizz Buzz is a classic Computer Science problem about Selection. For an integer x, print:• “Fizz” if x is only divisible by 3,• “Buzz” if x is only divisible by 5,• “FizzBuzz” if x is divisible by both 3 and 5,• the number x if it is not divisible by both 3 and 5.This problem is the extreme version of Fizz Buzz. You are given a list of K distinct integers A and a list of K characters S. Both lists are numbered from 1 to K. The integer Ai corresponds to the character Si. Denote B as the subset of A. There will be a rule for each possible subset: if an integerx is only divisible by all elements in B, print a string which is the concatenation of the corresponding character of each element in B, sorted by the index in ascending order. However, if B is an empty subset, print the first digit of x instead. Does it look complicated? Do not worry, as it is just a generalization of the regular Fizz Buzz. For example, if A = [3, 5] and S = [F, B], you will get the normal Fizz…
Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. Draw a flow chart of perfect number.
Problem Descriptions: In this problem, your task is to write a program to find whether a user-entered 2-D point (P) lies (i) (ii) (iii) The circles are specified using their center coordinates and radii. See the illustrations below showing all three cases you need to consider: within both of the two given circles, within only one of those circles, or outside both circles (treat a point ON a circle as being inside the circle). Pis outside both circles Pis inside ONLY one circle Sample Outputs: Sample output #1 POINT MEMBERSHIP WITHIN TWO CIRCLES Circle 1: center at ( 6, -5 ) and radius: 3 Circle 2: center at ( 12, -7 ) and radius: 5 Please enter the x-coordinate of the test point: 8 -5 Please enter the y-coordinate of the test point: Point lies within both circles. Sample output #2 POINT MEMBERSHIP WITHIN TWO CIRCLES Circle 1: center at ( 6 , -5 ) and radius: 3 Circle 2: center at ( 12 , -7 ) and radius: 5 Please enter the x-coordinate of the test point: 12 Please enter the y-coordinate…
QUICK-BASIC64 In a 50-person class, students with grades below 70 are considered unsuccessful. Write an algorithm that calculates students who fail the exam. (Please explain everything the program in details and please check whether the program runs or not by using q- basic64. Thank you so much)
Celebrity problem A celebrity among a group of n people is a person who knows nobody but is known by everybody else. The task is to identify a celebrity by only asking questions to people of the form: ”Do you know him/her?” Solution Select two people from the group given, say, A and B, and ask A whether A knows B. If A knows B, remove A from the remaining people who can be a celebrity; if A doesn’t know B, remove B from this group. Solve the problem recursively for the remaining group of people who can be a celebrity Which design strategy does the following solution use? A-)Decrease-by-a-constant factor algorithm B-)Variable-size-decrease algorithm C-)Decrease-by-a-constant algorithm D-)Divide-and-Conquer
Compare Numbers - Python Language please! Programming challenge description: Little Tommy is in kindergarten on the first day of class. His teacher has taught him about inequalities today, and he is learning how to draw crocodiles to represent them. When there are two numbers, A and B, there are three options:1. If A is greater than B, then draw '>'. The crocodile's mouth is pointed toward the bigger number, A.2. If A is less than B, then draw '<'. The crocodile faces B.3. If A is equal to B, draw '='. The crocodile is confused and keeps its mouth shut.Unfortunately, Tommy does not like to do his homework, and has bribed you to write a program to do it for him. Input: The input consists of two integers A and B on a line, separated by a space. |A,B| < 2^63. Output: Print a line containing the appropriate symbol that describes the relationship between the numbers. Test 1 Test InputDownload Test 1 Input 35 40 Expected OutputDownload Test 1 Output <
Question: 1A perfect number is an integer that is the sum of its positive proper divisors (all divisors except itself). For example, 6 is a perfect number. The divisors of 6 except itself are 1,2 and 3. The sum of the proper divisors of 6 is 6. Thus 6 is a perfect number. You have to take integers as input and continue taking input until the word “STOP” is given as input. After taking the inputs you have to classify the integers as Perfect and Imperfect and store it in a dictionary(Please see the output for better understanding).[Note: You CANNOT use any built in functions EXCEPT input(),range(),print()]Sample Input :61082528100496530STOPSample Output:(No need to follow the output format. Just print the resultant dictionary.){Perfect: [6,28,496],Imperfect: [10,8,25,100,530]}
The data type bool: Group of answer choices Can only be used in a selection statement. Can take on any expression as a value. Can take on values -1, 0 or 1. Can take on values true and false.