Computer programming - Lab 12: Structures

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.Continued fractions A real number 0 < x < 1 can be successively approximated in a continued fraction with 1/a1, 1/(a1+1/a2), 1/(a1+1/(a2+1/a3)), ... where a1, a2, a3, ... are natural numbers. In the initial approximation, a1 is ⌊1/x⌋, and one continues using the same rule for the fractional part of the denominator approximated with a1, etc. One obtains a sequence of rational numbers p1/q1, p2/q2, ... that approximate x increasingly well, alternating from above and below.
Define a structure that represents a rational number and compute (recursively) the n^th rational approximation of a fractional number x using a continued fraction.

3.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.

4. 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.

5. 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.

6. 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.

7. Predicate formulas. A formula in predicate logic is

• a predicate over terms (see exercise in class)
• an operator (and, or, not, =>, =) applied to several formulas (one for negation, two for implication and equality, arbitrary number for conjunction/disjunction)
• a universal or existential quantifier applied to a variable in a formula

8.Processor simulation A simple processor has registers labeled by lowercase letters and uses the following instructions:

• assignment: LD reg val . Equivalent to reg = val. val can be either a register or an integer constant.
• arithmetic: ADD reg val, SUB reg val, MUL reg val, DIV reg val . These are equivalent to reg += val, etc.
• unconditional jumps: JMP offset . Jumps as many statements forward or backward as indicated by the integer constant offset, counted from the next instruction after the jump. Thus, JMP 0 does nothing. JMP -1 does an infinite loop.
• comparison: CMP reg val . Computes reg - val but the result is not stored; it remembers only how the result was with respect to zero (less, equal, etc.)
• conditional jumps: JE offset, JNE offset, JG offset, JGE offset, JL offset, JLE offset: jump to the specified offset if the result of the previous CMP or SUB instruction was equal/not equal/greater/greater or equal/less than/less than or equal to zero, else continue with next statement
• stop computation: HLT