Description
Problem 1: squareroot.c
In this program you will approximate the square root of a number n using the Babylonian method. This method starts with an initial guess x0 close to √√n, and at the nth step calculates . As n gets larger an larger, xn ≈ n. Your program must take the number n, initial guess x0, and number of steps m and print xm with exactly 5 decimal places.
[rsgysel@pc17 ˜]$ ./squareroot
Enter the integer you wish to find the square root of: 2
Enter your first guess and number of steps: 1 1000
The square root of 2 is approximately 1.41421
[rsgysel@pc17 ˜]$ ./squareroot
Enter the integer you wish to find the square root of: 2
Enter your first guess and number of steps: 1 1
The square root of 2 is approximately 1.50000
[rsgysel@pc17 ˜]$ ./squareroot
Enter the integer you wish to find the square root of: 5
Enter your first guess and number of steps: 2 100
The square root of 2 is approximately 2.23607
Problem 2: guessyournumber.c (70 points, 7 per test case)
Write a program that will guess an integer that the user has picked. Imagine that the user will write down a positive integer x on a piece of paper and your program will repeatedly ask questions in order to guess what x is, and the user replies honestly. Your program will start by asking for an intn, and you must have 1 ≤x≤n. After that, the program will successively guess what x is, and the user must tell the computer if x is equal to the guess (entering ’e’), larger than the guess (entering ’l’), or smaller than the guess (entering ’s’).
Your program will guess by maintaining a lower bound (initially 1) and upper bound (initially n) and pick the largest integer equal to or smaller than[1] the midpoint of the lower bound and upper bound. If the user responds with ’l’ indicating that x is larger, the guess becomes the new lower bound plus one. If the user responds with ’s’ indicating that x is smaller, the guess becomes the new upper bound minus one. If the user responds with ’e’ indicating that x is the guess, your program will report the number of guesses made and terminate execution:
[rsgysel@pc17 ˜]$ ./guessyournumber
Enter n: 50
Is your number 25? l
Is your number 38? l
Is your number 44? s
Is your number 41? e
Your number must be 41. I used 4 guesses.
If the user responds in a way that is not feasible (no such x can exist), print an error and quit:
[rsgysel@pc17 ˜]$ ./guessyournumber
Enter n: 9
Is your number 5? s
Is your number 3? s
Is your number 2? l
Error: that’s not possible.
If only one number is still possible, your program should conclude what it is and report the number of guesses:
[rsgysel@pc17 ˜]$ ./guessyournumber
Enter n: 50
Is your number 25? l
Is your number 38? l
Is your number 44? s
Is your number 41? s
Is your number 39? l
Your number must be 40. I used 4 guesses.
Report invalid input as follows:
[rsgysel@pc17 ˜]$ ./guessyournumber
Enter n: -2
Error: n must be positive.
Enter n: a
Error: invalid input.
Enter n: 9
Is your number 5? m Error: invalid input.
[1] This is called the floor of a number.
