Question

Create a NOTEPAD or PDF file that restates the problem in your own words, specifies what input is needed, what output is expected, the step by step process (algorithm) to get the output from the input, and test data (input for which you know the expected output) for each of the 3 problems given below. You should not write any actual C++ code. Make sure the problem statement is in your own words and is descriptive enough so someone not reading the problem given to you will understand what needs to be done. (See the document containing example algorithms posted on Canvas for Algorithms 1). Attach your file to the Algorithms 3 submission on Canvas Problem 1: Create a process that will generate a random whole number between 1 and 10000. Ask the user to enter a guess and state if the guess is correct, lower than the generated number, or higher than the generated number. Repeat the guessing process until the user has guessed the generated number. Count the number of guesses the user entered. Problem 2: Create a process to complete Programming Challenge 13 of Chapter 5 (The Greatest and Least of These). Problem 3: A specific form of bacteria has been measured to triple each day. Create a process that will ask the user to enter the initial number of cells (day 0). Then create a table that will output the day and the number of cells for days 1 through 10. Do not use exponentiation for this problem. Problem 4: (for this problem your algorithm should be C++ specific and you should describe how the C++ rand function will be employed). Write a process that will use the Monte Carlo method to estimate PI as described below. The Monte Carlo method to estimate probability generates a large number of points then determines how many points meet a specific condition. Consider the figure below containing a square with a circle inside of it, both of which are centered on zero. -1 The area of the circle would be nr where r is 1. The area of the square is s where s is 2 (-1 to 1). Therefore the ratio of the suppose we generate random points to fall uniformly in the area of the square (x varies from -1 to 1 and y varies from-1 to 1). We can state ratio of the number of points falling inside the circle to the total number of the points is equal to the ratio of the area of the circle to the area of the of the circle to the area of the square would be r/4. Now area nbs /4-(number of points in the circle)/(total number of points) Therefore r can be defined by the equation (number of points in the circle)/(total number of points) 4 Generate a process that would generate random numbers between-1 and 1 for x and y positions of 10000 points and count how many points fall with the circle, then determine an estimated version of z. (See below to generate floating point random numbers. This generation is not needed to describe the process, but to implement the process) Generating uniformly distributed random floating point numbers. From Chapter 3, you know that the rand function in C++ generates whole numbers between 0 and a maximum number. If we want to generate random floating point numbers with in a given span we can use the formula FPRN span * GRWN/MRN + offset where FPRN is a floating point random number, span is the maximum floating point number that should be generated- the minimum floating point number that should be generated, GRWN is the generated random whole number that the C++ rand() function will produce, MRN is the maximum number that the rand() function will produce, and offset is the minimum number that should be generated. For example, suppose we want to generate random floating point numbers between 0 and 5. The span would be 5, and the offset would be 0 so the formula would be FPRN-5.0 GWRN/MRN +0 However, if we wanted to generate floating point numbers between -2 and 3, the span would still be 5 but the offset would now be -2. Therefore the formula would be FPRN 5.0 GWRN/MRN + (-2) or FPRN-5.0 GWRN/MRN-2 Similarly if we wanted to generate random floating point numbers between -1.5 and 10, the formula would be FPRN-(10.0-(-1.5)) GWRN/MRN +(-1.5) or FPRN-(11.5) GWRN/MRN-1.5 The Greatest and Least of These Write a program with a loop that lets the user enter a series of integers, followed by -99 to signal the end of the series. After all the numbers have been entered, the program should display the largest and smallest numbers entered.

Answer 1

1. Problem Statement : We need will generate a random number between 1 to 10000. The user tries to guess the number and keep on guessing until he is correct. For each guess made by the user, we tell him whether his guess was higher than, lower than or equal to the generated number. In the end we also print the number of guesses the user took to find the correct number.

Input : A number between 1 to 10000 (user's guess)

Output : Whether the guess is "higher", "Lower" or "correct".

Test Data :

Number guessed : 10

Input : 100

Output : Higher

Input : 50

Output : Higher

Input : 20

Output Higher

Input : 1

Output : Lower

Input : 10

Output: Correct

Number of guesses = 5

Algorithm :

1. num = rand()%10000 + 1
2. count = 0
3. do{
   1. guess = Input()
   2. count = count + 1
   3. if (num == guess) {
      1. print "Correct"
      2. print "Number of guesses is" + count
      3. break}
   4. else if (num<guess)
      1. print "Higher"
   5. else
      1. print "Lower"
4. }while(true)