# Third Bulgarian National Olympiad in Informatics

**February, 1987**

### First round (for high school students, 8-11 grades)

### Problem 1.

Work out a program, that performs subsequently the following tasks:

a) Writing into the computer memory coordinates of n points, A_1, A_2,
..., A_n, (n >= 1) given in the plane.

b) Rendering on the computer screen the visible part of a piecewise
line *F* composed of straight line segments subsequently connecting
A_1, A_2, ..., A_n. If some point A_i is not within the domain of the computer
screen, then line segments A_(i-1)A_i
and A_iA_(i+1) should not be
dispayed.

c) Execution of the subroutines described in items a) and
b).

### Problem 2.

Let us consider a rectangle *P* with sides parallel to the coordinate
axes. The rectangle *P* is specifyed by coordinates of its vertices.

a) Find out whether the figure *F* (from the problem
1) can be completely placed within the rectangle* P* after applying
appropriate moves described in problem 3.

b) Find out whether there exists at least one set of 4 subsequent points,
A_i, A_(i+1), A_(i+2),
A_(i+3), (i=1, 2, 3, ..., n) from among the above
given points, which are vertices of a right trapezoid (i.e. four-sided
figure having two sides parallel and a right angle).

### Problem 3.

Realize by a subroutine the moves of the figure *F,* which transfer
it toward any one of the four main directions: upwards, downwards, leftwards
and rightwards. Each move must be started by pressing a designated key
on the computer keyboard. Have in mind, that during the process of movement,
some parts of *F* may become invisible, whereas some other parts may
come into the field of vision.

Source: Obuchenieto po matematika, journal published by Bulgarian Ministry
of Education, n. 3, 1987, p. 61.

© The text is translated from Bulgarian by Emil
Kelevedzhiev (keleved@math.bas.bg)

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