Chapter 6: Problem 2
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Short Answer
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 6: Problem 2
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These are the key concepts you need to understand to accurately answer the question.
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Get started for freeAny program that can be implemented recursively can be implemented iteratively. although sometimes with more difficulty and less clarity. Try writing an iterative version of the Towers of Hanoi. If you succeed, compare your iterative version with the recursive version developed in Exercise 6.42 . Investigate issues of performance, clarity and your ability to demonstrate the correctness of the programs.
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(Computers in Education) Computers are playing an increasing role in education. Write a program that helps an elementary school student learn multiplication. Use rand to produce two positive one-digit integers. It should then type a question such as How much is 6 times \(7 ?\) The student then types the answer. Your program checks the student's answer. If it is correct, print "very good!", then ask another multiplication question. If the answer is wrong. print "No. Please try again.", then let the student try the same question repeatedly until the student finally gets it right.
Write program segments that accomplish each of the following: a. Calculate the integer part of the quotient when integer a is divided by integer \(b\). b. Calculate the integer remainder when integer a is divided by integer \(b\). c. Use the program pieces developed in (a) and (b) to write a function that inputs an integer between 1 and 32767 and prints it as a series of digits, each pair of which is separated by two spaces. For example, the integer 4562 should print as follows: $$4562$$
(PrimeNumbers) An integer is said to be prime if it is divisible by only 1 and itself. For example, 2,3,5 and 7 are prime, but 4,6,8 and 9 are not. a. Write a function that determines whether a number is prime. b. Use this function in a program that determines and prints all the prime numbers between 2 and 10,000 . How many of these numbers do you really have to test before being sure that you have found all the primes? c. Initially, you might think that \(n / 2\) is the upper limit for which you must test to see whether a number is prime, but you need only go as high as the square root of \(n\) Why? Rewrite the program, and run it both ways. Estimate the performance improvement.
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