Paradigms

Procedural (C++)

1. Plateau program (max sequence length)

This program finds the longest sequence of identical numbers in a sorted array.

2. Parabolic Approximation

This program reads 3 points on a curve: (x1, y1), (x2, y2), (x3, y3) and computes y values for n=40 equidistant x values such that x1 <= x <= x3 using Cramer's rule and Lagrange interpolation.

3. Array Processing (array reduction)

This program reduces an array by eliminating from it all values that are equal to the three highest unique integers.

4. Integer Plot Function

This program displays an arbitrary positive integer n using big characters of size 7x7.

5. Iteration vs Recursion

This program searches through an array and finds a number using a binary search algorithm both iteratively and recursively.

6. Polynomials

This program performs addition, multiplication, derivatives, and integrals of polynomials.

Logic (Prolog)

1. Family tree

This program showcases the use of facts and inference rules in Prolog using a family tree.

2. CS class schedule

Same as previous program, but with the schedule of CS classes for the SFSU Fall 2015 semester.

3. Family tree 2

This program investigates family relationships using lists in Prolog.

4. List operations

This program showcases the use of list processing in Prolog.

5. 8 queens problem

This program solves the 8 queens problem (location of 8 queens on a chess board such that no queens have each other in check, i.e., are not located in the same row/column/diagonal).

6. List min & max sum

This program finds the sum of the min and max of a list in Prolog.

7. Findall

This program uses the findall predicate in Prolog to find the youngest grandchildren of a person P.

Functional (Racket/Scheme)

1. Sigma

This program computes the standard deviation of any number of arguments.

2. Histogram

This program recursively prints a histogram of stars for a list of integers.

3. Max of function

This program computes the maximum max(f x1 x2) of a function f within the interval [x1, x2]. It uses the trisection method and finds the coordinates of maximum xmax with an accuracy of 6 significant decimal digits.

4. Scalar product of two vectors

This program computes the scalar product of two vectors both iteratively (using the DO loop) and recursively.

5. Matrix row & col

The files "matrix1.dat" and "matrix2.dat" contain two rectangular matrices. In both cases the first row contains the number of rows and columns in the matrix. The remaining rows contain the elements within the matrix.

This program reads from a file containing a matrix and outputs any one its rows or columns. The matrices are stored in memory as vectors whose components are vectors.

Object-Oriented (Ruby)

1. Mean & sigma

This program calculates and returns the mean value and standard deviation of numbers stored in an array.

2. Sort array

This program sorts an array v without changing it and returns the sorted array.

3. Triangle

This program computes the perimeter and the area of arbitrary triangles and classifies them as being either equilateral, isosceles, scalene, right, or not a triangle.

4. Recognizer methods

This program implements the recognizer methods limited? and sorted? that expand the Ruby class Array.

• The expression array.limited?(amin,amax) returns true if amin <= a[i] <= amax for all values of i.

• The expression array.sorted? returns

  • 0 if the array is not sorted
  • +1 if a[0] <= a[1] <= a[2] <= ... (increasing sequence)
  • -1 if a[0] >= a[1] >= a[2] >= ... (decreasing sequence)

Extra: BNF (Backus-Naur form)

1. numbers.txt

BNF syntax definitions of the following objects:

1. Natural number (1, 2, 3, ...)
2. Unsigned integer (0, 1, 2, 3, ...)
3. Integer (..., -2, -1, 0, 1, 2, ...)
4. Odd number (..., -3, -1, 1, 3, ...)
5. Even number (..., -4, -2, 0, 2, 4, ...)
6. Integer divisible by five (..., -10, -5, 0, 5, 10, ...)

2. input_output.txt

BNF definition of the syntax of (all possible) input and output statements in C++.

Example input statement:

cin >> sclr >> vec[2*i-1] >> mat[f(i)][j+k] >> t[i/3][j][k];

Example output statement:

cout    << 12.34*a/rate << " " << 43.21 << " "
        << alpha + x[2*i-1] << " " << (p && q) << " "
        << pow(t[i][j], 1.2) << " string " << 's'
        << " " << myfun(x, sin(x+y), third_argument);

Note:

• Variables may have any number of indices and indices can be arbitrary arithmetic expressions.
• Theoretically, I/O statements can reach rather high levels of complexity; therefore, options beyond those presented in the above examples are not included.