Michał R. Przybyłek

Solution to the first assignment

A solution to the first assigment. The solution does not use exception handling.

The second big assignment

Write a simulator of the Game of Life ! Please, send your programs to:

mrp 'apud' pjwstk 'dot' edu 'dot' pl

before 12.06.2016. Here you may find more information about the Game of Life .

The first big assignment

Help the monkey escape labyrinth ! Please, send your programs to:

mrp 'apud' pjwstk 'dot' edu 'dot' pl

before 15.05.2016. Here you may find a sample labyrinth .

Lesson 6: elements of dynamic programming

Exercise - write a function that solves the coin problem. A coin problem consists of a value v and n types of coin denominations of values:

1 = c₁ < c₁ < ... < c_n

(coin 1 is always included, so it is always possible to make change for any amount of money). A solution to the coin problem is the minimum number of coins needed to make the change for the amount v.

Lesson 5: playing with arrays 2

Exercise - write implementations of the following functions:

REAL trace(MATRIX matrix, int n);
REAL determinant(MATRIX matrix, int n);
MATRIX coffactors(MATRIX matrix, int n);
MATRIX inverse(MATRIX matrix, int n);

Lesson 4: playing with arrays

Try to understand the code and complete missing definitions.

Lesson 3: the heap

During the lesson we shall learn how the memory management system works (in C/C++).

Warmup: write a declaration of a function that takes a pointer to "a function that takes double and returns a pointer to double" and returns a pointer to a pointer to "a function that takes int and returns a pointer to a pointer to int".

Exercise: write a function that takes an array of integers and returns the array of the same integers sorted (do not use any external functions); the function should not modify the initial array.

Exercise (*): write a function that takes a system of affine equations and returns a solution of the system (do not use any external functions).

Lesson 2: the runtime

During the lesson we shall learn basic concepts of C++ runtime: organization of a memory, names, variables, values, bindings, environment, references, pointers, etc.

Exercise 1: write a function:

double newtonMethod(double (*f)(double),
                    double (*df)(double),
                    double x,
                    int n);

that takes:

a function f
the derivative function df of f
an initial point x
a number of iterations n

and performs n interations of Newton method to find the root of f near x.

Exercise 2: write a function:

double secondOrderMethod(double (*f)(double),
                         double (*df)(double),
                         double (*ddf)(double),
                         double x,
                         int n);

that takes:

a function f
the derivative function df of f
the second derivative function ddf of f
an initial point x
a number of iterations n

and performs n interations of the following method:

approximate f by the second order expansion of f at x, call this approximation g
find roots y, z of g
if |f(y)| < |f(z)| then x = y, otherwise x = z; if g does not have any root then perform one step of Newton method

Sources from Lesson 1

First program and bisection method .

Lesson 1: introduction

During the lesson we shall do some simple number crunching in C++ and recall basic properties of floating-point arithmetic. Exercise - find a root of a given function by:

bisection method
false-point method
secant method
Newton method
second-order expansion (you can use functions from cmath)