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ELTE

VersenyVizsga portál

Kísérletek.hu

Matematika oktatási portál

S. 91. Alice, Bob and Cecil are given \(\displaystyle N\) (\(\displaystyle 1\le N\le 60\)) boxes of presents. The value of each box is known: the \(\displaystyle i\)th box is worth \(\displaystyle a_i\) with \(\displaystyle 1\le a_i\le 100\). They would like to distribute these presents in a fair way. A particular distribution of the presents among the three people is said to be fair, if the person getting the set of presents with the highest total value gets a set of presents having the smallest possible total value. For example, if the presents have values 2, 4, 5, 8, 9, 14, 15 and 20, then a fair distribution could be the following: Alice gets the presents with values 2, 9 and 15 (the total sum is 26); Bob gets the presents 4, 8 and 14 (with total sum 26); and Cecil gets the presents 5 and 20 (with total sum 25). Given the list of presents, your task is to determine the maximal sum of presents a person can get during a fair distribution (in other words, that maximal sum is to be minimized). Your program should read \(\displaystyle N\) from the first line of the standard input, then the \(\displaystyle a_i\) integers (separated by a space) from the following \(\displaystyle N\) lines. The first and only line of the standard output should contain the minimal maximum value in a fair distribution. In the example, ``Példa bemenet'' is a sample input, while ``Példa kimenet'' is the corresponding output.

Scoring and bounds. You can obtain 1 point for a brief and proper documentation clearly describing your solution. Nine further points can be obtained provided that your program solves any arbitrary valid input within 1 second of running time. Partial points can be obtained if your program yields a solution

\(\displaystyle \bullet\) for \(\displaystyle a_i\le 40\), or

\(\displaystyle \bullet\) for \(\displaystyle N\le 10\).

The source code (s91.pas, s91.cpp, ...) without the .exe or any other auxiliary files generated by the compiler but with a short documentation (s91.txt, s91.pdf, ...), also describing which developer environment to use for compiling the source, should be submitted in a compressed file s91.zip.

(10 points)

Deadline expired on 10 October 2014.


Statistics on problem S. 91.
22 students sent a solution.
10 points:Erdős Márton, Fuisz Gábor, Molnár-Sáska Zoltán, Németh 123 Balázs, Zalavári Márton.
9 points:Kiss Gergely.
8 points:2 students.
7 points:4 students.
6 points:2 students.
5 points:1 student.
4 points:1 student.
3 points:3 students.
2 points:2 students.
0 point:1 student.


  • Problems in Information Technology of KöMaL, September 2014

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