Program | SULTAN.PAS, SULTAN.C, SULTAN.CPP |
The Sultan of Nubia has no children, so she has decided that the country will
be split into up to k separate parts on her death and each part will be inherited
by whoever performs best at some test. It is possible for any individual to
inherit more than one or indeed all of the portions. To ensure that only highly
intelligent people eventually become her successors, the Sultan has devised
an ingenious test. In a large hall filled with the splash of fountains and the
delicate scent of incense have been placed k chessboards. Each chessboard has
numbers in the range 0 to 99 written on each square and is supplied with 8 jewelled
chess queens. The task facing each potential successor is to place the 8 queens
on the chess board in such a way that no queen threatens another one, and so
that the numbers on the squares thus selected sum to a number at least as high
as one already chosen by the Sultan. (For those unfamiliar with the rules of
chess, this implies that each row and column of the board contains exactly one
queen, and each diagonal contains no more than one.)
Write a program that will read in the number and details of the chessboards and determine the highest scores possible for each board under these conditions. (You know that the Sultan is both a good chess player and a good mathematician and you suspect that her score is the best attainable.)
Input will consist of k (the number of boards), on a line by itself, followed by k sets of 64 numbers, each set consisting of eight lines of eight numbers. Each number will be in the range 0 to 99. There will never be more than 20 boards.
Output will consist of k numbers consisting of your k scores, each score on a line by itself and right justified in a field 5 characters wide.
Sample input
1
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
48 50 51 52 53 54 55 56
57 58 59 60 61 62 63 64
Sample output
260