Graded Practice

• Program 1

  In the file sumSqr.c write a function int sumSqr ( int n ) that accepts one integer parameter and returns the sum of the squares of the numbers from 1 to n: 1*1 + 2*2 + 3*3 + ... +n*n. For example, if n = 1, the function returns 1, if n = 2, the function returns 5, if n = 3, the function returns 14.

  Write a C program that reads a sequence of positive numbers, the first non-positive integer terminates the input. The program prints for each input number the corresponded sum of squares, using function sumSqr.

• Program 2 - Challenge
  • Write a function int gcd(int a, int b) that determins and returns the gcd of the a and b.

    The greatest common divisor (GCD)of two integers is the largest number that divides each of the two numbers. For example, GCD (12, 8) = 4, GCD (12, 13) = 1. GCD could be found using the following Euclidean Algorithm:
    gcd (a, b) = b,                               if a % b is 0
    gcd ( a, b )= gcd( b, a % b),       if a % b is not 0

  • Write a C program to test your function: the program reads two positive integers (you can assume that the input is valid). The program calculates and prints the gcd of the input numbers.
  • Compile and run your program a few time to make sure that function works correctly.
  • Modify the C program to do the following: the program reads two pairs of integers. Each pair represents the fraction: first number in the pair is the numerator of the fraction and the second number in the pair is the denominator of the fraction. The program finds the sum of two fractions, using the following rule: a/b + c/d = (a*d+b*c)/(b*d). You would need to simplify the fraction after you found a sum, using function gcd. The program outputs the sum of the fractions after simplification. If the resulting sum is improper fraction (improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number)) you also would need to find an integer part and fractional part for the improper fraction.

    For example, if the input is 2 3 4 6 your program first, will find the sum which is: 24/18. After that, the program will find gcd of 24 and 18 which is 6 and simlify the fraction by dividing numerator and denominator by gcd. The result will be 4/3. Since this is improper fraction (4 >3) the program will print the result in the following way 1 1/3 (finding the integer part and fractional part).