1. Rational numbers Define a structure type for rational numbers, holding numerator and denominator. Implement functions to add and multiply rationals. Return results that are in canonical form (denominator is positive and gcd with numerator is 1).2. 2D vectors Define a structure type for vectors in 2-dimensional space. Define functions for addition, subtraction and magnitude, and to read a vector (space-separated real coordinates of endpoint, assuming zero origin). Use this function to compute the total length of the segments drawn in the path d="..." element read from a SVG file. The path keeps a current point, and the commands are of the form letter x y, with L/l for "line to" and M/m for "move", uppercase for absolute coordinates, and lowecase for relative.
3. Polynomials Define a structure type for polynomials, containing the degree and an array of real coefficients. Write a function that prints a polynomial (in X) and one that adds two polynomials, returning a dynamically allocated result.
4. Big numbers Define a structure type for big numbers, represented in binary, using an arbitrary number of bytes (stored as a structure field). Write a function that takes two big numbers and returns their sum, as a dynamically allocated structure.
5.Continued fractions A real number x can be successively
approximated in a
fraction as a0, a0 + 1/a1, a0 + 1/(a1+1/a2), a0 + 1/(a1+1/(a2+1/a3)), ...
where a0 is an integer, and a1, a2, a3, ... are positive naturals. In the initial
approximation, a0 is ⌊x⌋. The remaining fractional part is either 0 (we stop), or a number 0 < x1 < 1, so 1/x1 > 1 and we continue applying the same process, taking the integer part, etc.
One obtains a sequence of rational numbers p0/q0 (= a0), p1/q1 (= a0 + 1/a1),
p2/q2, ... that approximate x increasingly well, alternating from above
Define a structure that represents a rational number and compute (recursively) the nth rational approximation of a real number x using a continued fraction.
6.Prime factors. Define a data structure to represent an unsigned number as a product of powers of primes. Write a function that computes the product of two numbers, in the same representation.
7. CSV files A .csv file contains the grade situation for a class of
students. Each line contains fields separated by commas. The first
field is the student name, followed by up to 10 fields with real-numbered
grades or other characters; any remainder of the line is ignored.
Read the file using an appropriate data structure; you may assume there are at most 200 students. Compute averages for the students that have 10 passing grades. Sort students in decreasing order of their grade averages; break ties in alphabetical order. Print the sorted list with grade averages.
8. Sorting text Design a data structure that stores a line of text, together with its length (in characters) and number of words. Read all lines of a file named on the command line into an array of such structures. Sort and print the file with lines in increasing order of length, breaking ties first in decreasing order of words and then in alphabetical order.
9. List ZIP file contents
Write a program that lists the names of the files from a .zip archive (whose name is given on the commandline) in decreasing order of their uncompressed size.
Here is a zip archive of sample programs written this semester.
The .zip file format is defined here. We will handle a simplified case; additional checks should be added for a robust program.
All integer values are stored in binary, in little-endian byte order. Since the x86 architecture is little-endian, they will be placed in memory in the correct byte order when read with fread.
Offset Byte count Meaning ------------------------------- 10 2 number of entries in central directory (list of files) 12 4 size of central directory 16 4 offset of central directory within zipfile
Offset Byte count Meaning ------------------------------- 12 2 file modification time 14 2 file modification date 24 4 uncompressed file size 28 2 file name length: fnlen 30 2 extra field length: xlen 32 2 comment length: clen 46 fnlen file name (not null-terminated) xlen extra field clen comment