CCC '18 S1 - Voronoi Villages - Olympiads Online Judge

CCC '18 S1 - Voronoi Villages

Points: 3 (partial)

Time limit: 1.0s

Memory limit: 256M

Problem type

Canadian Computing Competition: 2018 Stage 1, Senior #1

In the country of Voronoi, there are $N$ ~N~ villages, located at distinct points on a straight road. Each of these villages will be represented by an integer position along this road.

Each village defines its neighbourhood as all points along the road which are closer to it than to any other village. A point which is equally close to two distinct villages $A$ ~A~ and $B$ ~B~ is in the neighbourhood of $A$ ~A~ and also in the neighbourhood of $B$ ~B~.

Each neighbourhood has a size which is the difference between the minimum (leftmost) point in its neighbourhood and the maximum (rightmost) point in its neighbourhood.

The neighbourhoods of the leftmost and rightmost villages are defined to be of infinite size, while all other neighbourhoods are finite in size.

Determine the smallest size of any of the neighbourhoods (with exactly 1 digit after the decimal point).

Input Specification

The first line will contain the number $N$ ~N~ $(3 \le N \le 100)$ ~(3 \le N \le 100)~, the number of villages. On the next $N$ ~N~ lines there will be one integer per line, where the $i^\text{th}$ ~i^\text{th}~ line will contain the integer $V_i$ ~V_i~, the position of the $i^\text{th}$ ~i^\text{th}~ village $(-1\,000\,000\,000 \le V_i \le 1\,000\,000\,000)$ . All villages are at distinct positions.

Output Specification

Output the smallest neighbourhood size with exactly one digit after the decimal point.

Sample Input

Sample Output

3.0

Explanation for Sample Output

The neighbourhoods around $0$ ~0~ and $16$ ~16~ are infinite. The neighbourhood around $4$ ~4~ is $5$ ~5~ units ( $2$ ~2~ to the left, and $3$ ~3~ to the right). The neighbourhood around $10$ ~10~ is $5.5$ ~5.5~ units ( $3$ ~3~ to the left and $2.5$ ~2.5~ to the right). The neighbourhood around $15$ ~15~ is $3.0$ ~3.0~ units ( $2.5$ ~2.5~ to the left and $0.5$ ~0.5~ to the right).

Comments

64

SananR commented on Feb. 18, 2018, 11:53 p.m.

For those who are constantly getting 6/15, make sure that your output isn't in scientific notation, took me a bit to figure that out on the CCC.

28

AlanL commented on Feb. 19, 2018, 5:34 p.m.

It says that in the editorial as well, but it probably only occurs in some languages. Thanks anyways for that useful info!