Description
Problem 1: squareroot.c (40 points, 4 per test case)
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 n
th step
calculates xn =
1
2
(xn +
n
xn
). 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
∗Last updated January 22, 2017
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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 int n, 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 than1
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
1This is called the floor of a number.
2
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.
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