ACM International Collegiate
Programming Contest, Asia-Amritapuri Site, 2011
Problem J: Goblin Wars
The wizards and witches of Hogwarts School of Witchcraft found Prof. Binn's History of Magic
lesson to be no less boring than you found your own history classes.
Recently Binns has been droning on about Goblin wars, and which
goblin civilization fought which group of centaurs where etc etc.
The students of Hogwarts decided to use the new-fangled computer
to figure out the outcome of all these wars instead of memorizing the
results for their upcoming exams. Can you help them?
The
magical world looks like a 2-D R*C grid. Initially there are many
civilizations, each civilization occupying exactly one cell. A
civilization is denoted by a lowercase letter in the grid. There are
also certain cells that are uninhabitable (swamps, mountains, sinkholes
etc.) - these cells are denoted by a '#' in the grid. All the other
cells - to which the civilizations can move - are represented by
a '.' in the grid.
A cell is said to be adjacent to another cell
if they share the same edge - in other words, for a cell (x,y), cells
(x-1, y), (x, y-1), (x+1, y), (x, y+1) are adjacent, provided they are
within the boundaries of the grid.
Every year each civilization will expand to all unoccupied adjacent
cells.
If it is already inhabited by some other civilization, it just leaves
the cell alone. It is possible that two or more civilizations may move
into an unoccupied cell at the same time - this will lead to a battle
between the civilizations and the cell will be marked with a '*'. Note
that the civilizations fighting in a particular cell do not try to
expand from that cell, but will continue to expand from other cells, if
possible.
Given the initial grid, output the final state of the grid after no further expansion by any civilization is possible.
Input (STDIN):
The first line contains T, the number of cases. This is followed by T test case blocks.
Each test case contains two integers, R, C.
This
is followed by R lines containing a string of length C. The j-th letter
in the i-th row describes the state of the cell in year 0.
Each cell is either a
1. '.' which represents an unoccupied cell
2. '#' which represents a cell that cannot be occupied
3. A civilization represented by a lowercase letter ('a' - 'z')
Output (STDOUT):
For each test case, print the final grid after
no expansion is possible. Apart from the notations used in the input,
use '*' to denote that a battle is being waged in that particular cell.
Print a blank line at the end of each case.
Constraints:
1 <= R, C <= 500
1 <= T <= 5
Time Limit: 3 s
Memory Limit: 64 MB
Sample Input:
5
3 5
#####
a...b
#####
3 4
####
a..b
####
3 3
#c#
a.b
#d#
3 3
#c#
...
a.b
3 5
.....
.#.#.
a...b
Sample Output:
#####
aa*bb
#####
####
aabb
####
#c#
a*b
#d#
#c#
acb
a*b
aa*bb
a#.#b
aa*bb