In a stroke of luck almost beyond imagination, Farmer John was sent a ticket to the Irish Sweepstakes (really a lottery) for his birthday. This ticket turned out to have only the winning number for the lottery! Farmer John won a fabulous castle in the Irish countryside.
Bragging rights being what they are in Wisconsin, Farmer John wished to tell his cows all about the castle. He wanted to know how many rooms it has and how big the largest room was. In fact, he wants to take out a single wall to make an even bigger room.
Your task is to help Farmer John know the exact room count and sizes.
The castle floorplan is divided into M (wide) by N (1 <=M,N<=50) square modules. Each such module can have between zero and four walls. Castles always have walls on their “outer edges” to keep out the wind and rain.
Consider this annotated floorplan of a castle:
1 2 3 4 5 6 7
#############################
1 # | # | # | | #
#####---#####---#---#####---#
2 # # | # # # # #
#---#####---#####---#####---#
3 # | | # # # # #
#---#########---#####---#---#
4 # -># | | | | # #
#############################
# = Wall -,| = No wall
-> = Points to the wall to remove to make the largest possible new room
By way of example, this castle sits on a 7 x 4 base. A “room” includes any set of connected “squares” in the floor plan. This floorplan contains five rooms (whose sizes are 9, 7, 3, 1, and 8 in no particular order).
Removing the wall marked by the arrow merges a pair of rooms to make the largest possible room that can be made by removing a single wall.
The castle always has at least two rooms and always has a wall that can be removed.
The map is stored in the form of numbers, one number for each module (“room”), M numbers on each of N lines to describe the floorplan. The input order corresponds to the numbering in the example diagram above.
Each module descriptive-number tells which of the four walls exist and is the sum of up to four integers:
Inner walls are defined twice; a wall to the south in module 1,1 is also indicated as a wall to the north in module 2,1.
| Line 1: | Two space-separated integers: M and N |
|---|---|
| Line 2..: | M x N integers, several per line. |
7 4
11 6 11 6 3 10 6
7 9 6 13 5 15 5
1 10 12 7 13 7 5
13 11 10 8 10 12 13
The output contains several lines:
| Line 1: | The number of rooms the castle has. |
| Line 2: | The size of the largest room |
| Line 3: | The size of the largest room creatable by removing one wall |
| Line 4: | The single wall to remove to make the largest room possible |
Choose the optimal wall to remove from the set of optimal walls by choosing the module farthest to the west (and then, if still tied, farthest to the south). If still tied, choose ‘N’ before ‘E’. Name that wall by naming the module that borders it on either the west or south, along with a direction of N or E giving the location of the wall with respect to the module.
5
9
16
4 1 E
First, the map is partitioned like below. Note that walls not on the outside borders are doubled:
1 2 3 4 5 6 7
####|####|####|####|####|####|#####
1 # | #|# | #|# | | #
####| #|####| #|# |####| #
-----|----|----|----|----|----|-----
####|# |####|# #|# #|####|# #
2 # #|# | #|# #|# #|# #|# #
# #|####| #|####|# #|####|# #
-----|----|----|----|----|----|-----
# |####| #|####|# #|####|# #
3 # | | #|# #|# #|# #|# #
# |####|####|# #|####|# #|# #
-----|----|----|----|----|----|-----
# #|####|####| |####| #|# #
4 # #|# | | | | #|# #
####|####|####|####|####|####|#####
Let’s talk about the squares with a (row, column) notation such that the lower right corner is denoted (4, 7).
The input will have four lines, each with 7 numbers. Each number describes one ‘room’. >Walls further toward the top are ‘north’, towards the bottom are ‘south’, towards the left are ‘west’, and towards the right are ‘east’.
Consider square (1,1) which has three walls: north, south, and west. To encode those three walls, we consult the chart:
and sum the numbers for north (2), south (8), and west (1). 2 + 8 + 1 = 11, so this room is encoded as 11.
The next room to the right (1,2) has walls on the north (2) and east (4) and thus is encoded as 2 + 4 = 6.
The next room to the right (1,3) is the same as (1,1) and thus encodes as 11.
Room (1,4) is the same as (1,2) and thus encodes as 6.
Room (1,5) has rooms on the west (1) and north (2) and thus encodes as 1 + 2 = 3.
Room (1,6) has rooms on the north (2) and south (8) and thus encodes as 2 + 8 = 10.
Room (1,7) is the same as room (1,2) and thus encodes as 6.
This same method continues for rooms (2,1) through (4,7).
Since we are going to use the westernmost and then the southernmost squares, we only need to consider removing the walls on the north and east.
This problem can be solved using recursion.
First use recursion to assign a room number to each square. Then loop through each square to compute the size of each room number. Once computed, use recursion to remove walls (north and east) one at a time to see if a larger room is created, and keep track of which removal resulted in the creation of the largest room.
public class castle {
static final int WEST = 0x1;
static final int NORTH = 0x2;
static final int EAST = 0x4;
static final int SOUTH = 0x8;
public static void main(String[] args) throws IOException {
try (final BufferedReader f = new BufferedReader(new FileReader("castle.in"));
final PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("castle.out")))) {
// read castle dimensions
final String[] dimensions = f.readLine().split(" ");
final int maxColumns = Integer.parseInt(dimensions[0]);
final int maxRows = Integer.parseInt(dimensions[1]);
// read castle squares into array
final int[][] squares = new int[maxRows][maxColumns];
for (int row = 0; row < maxRows; row++) {
final String[] tokens = f.readLine().split(" ");
for (int col = 0; col < maxColumns; col++) {
squares[row][col] = Integer.parseInt(tokens[col]);
}
}
// assign room numbers to each square
final int[][] roomNumbers = new int[maxRows][maxColumns];
final int numberOfRooms = assignAllRoomNumbers(roomNumbers, maxRows, maxColumns, squares);
// output the number of rooms the castle has
out.println(numberOfRooms);
// compute room sizes and find the largest room size
final int[] roomSizes = computeRoomSizes(roomNumbers, numberOfRooms, maxRows, maxColumns);
final int maxRoomSize = getLargestRoomSize(roomSizes);
// output the size of the largest room
out.println(maxRoomSize);
// remove walls (from westernmost and southernmost squares)
int afterRemoveMaxRoomSize = maxRoomSize;
int afterRemoveRow = maxRows;
int afterRemoveCol = maxColumns;
int afterRemoveWall = 0;
for (int col = 0; col < maxColumns; col++) {
for (int row = 0; row < maxRows; row++) {
final int[] result = removeWall(row, col, maxColumns, squares, roomNumbers, roomSizes);
final int lastSize = result[0];
final int lastRow = result[1] + 1;
final int lastCol = result[2] + 1;
if (lastSize > afterRemoveMaxRoomSize) {
afterRemoveMaxRoomSize = lastSize;
afterRemoveRow = lastRow;
afterRemoveCol = lastCol;
afterRemoveWall = result[3];
} else if ((lastSize == afterRemoveMaxRoomSize) && (lastCol <= afterRemoveCol)) {
afterRemoveRow = lastRow;
afterRemoveCol = lastCol;
afterRemoveWall = result[3];
}
}
}
// output size of the largest room created by removing one wall
out.println(afterRemoveMaxRoomSize);
// output the single wall to remove to make the largest room possible
out.println(afterRemoveRow + " " + afterRemoveCol + " " + (afterRemoveWall == NORTH ? "N" : "E"));
}
}
private static boolean hasWestWall(int number) {
return (number & WEST) == WEST;
}
private static boolean hasNorthWall(int number) {
return (number & NORTH) == NORTH;
}
private static boolean hasEastWall(int number) {
return (number & EAST) == EAST;
}
private static boolean hasSouthWall(int number) {
return (number & SOUTH) == SOUTH;
}
private static int assignAllRoomNumbers(int[][] roomNumbers, int maxRows, int maxColumns, int[][] squares) {
// first mark all rooms with room number = -1
for (int row = 0; row < maxRows; row++) {
for (int col = 0; col < maxColumns; col++) {
roomNumbers[row][col] = -1;
}
}
// then assign room numbers to each square
int nextRoomNumber = 1;
for (int row = 0; row < maxRows; row++) {
for (int col = 0; col < maxColumns; col++) {
nextRoomNumber = assignRoomNumber(roomNumbers, row, col, nextRoomNumber, maxRows, maxColumns, squares);
}
}
// return the number of rooms
return nextRoomNumber - 1;
}
private static int assignRoomNumber(int[][] roomNumbers, int row, int col, int nextRoomNumber,
int maxRows, int maxColumns, int[][] squares) {
// assign room number and increment counter for next room number
if (roomNumbers[row][col] == -1) {
roomNumbers[row][col] = nextRoomNumber++;
}
// check west wall
if ((col != 0) && !hasWestWall(squares[row][col]) && (roomNumbers[row][col - 1] == -1)) {
roomNumbers[row][col - 1] = roomNumbers[row][col];
assignRoomNumber(roomNumbers, row, col - 1, nextRoomNumber, maxRows, maxColumns, squares);
}
// check south wall
if ((row != maxRows - 1) && !hasSouthWall(squares[row][col]) && (roomNumbers[row + 1][col] == -1)) {
roomNumbers[row + 1][col] = roomNumbers[row][col];
assignRoomNumber(roomNumbers, row + 1, col, nextRoomNumber, maxRows, maxColumns, squares);
}
// check north wall
if ((row != 0) && !hasNorthWall(squares[row][col]) && (roomNumbers[row - 1][col] == -1)) {
roomNumbers[row - 1][col] = roomNumbers[row][col];
assignRoomNumber(roomNumbers, row - 1, col, nextRoomNumber, maxRows, maxColumns, squares);
}
// check east wall
if ((col != maxColumns - 1) && !hasEastWall(squares[row][col]) && (roomNumbers[row][col + 1] == -1)) {
roomNumbers[row][col + 1] = roomNumbers[row][col];
assignRoomNumber(roomNumbers, row, col + 1, nextRoomNumber, maxRows, maxColumns, squares);
}
return nextRoomNumber;
}
private static int[] computeRoomSizes(int[][] roomNumbers, int numberOfRooms, int maxRows, int maxColumns) {
final int[] roomSizes = new int[numberOfRooms];
for (int row = 0; row < maxRows; row++) {
for (int col = 0; col < maxColumns; col++) {
final int roomNumber = roomNumbers[row][col];
roomSizes[roomNumber - 1] += 1;
}
}
return roomSizes;
}
private static int getLargestRoomSize(int[] roomSizes) {
int maxRoomSize = 0;
for (int roomSize : roomSizes) {
maxRoomSize = Math.max(maxRoomSize, roomSize);
}
return maxRoomSize;
}
public static int[] removeWall(int row, int col, int maxColumns, int[][] squares,
int[][] roomNumbers, int[] roomSizes) {
final int originalSquare = squares[row][col];
final int currentRoomNumber = roomNumbers[row][col];
int maxRoomSizeFromNorthWall = roomSizes[currentRoomNumber - 1];
if ((row != 0) && hasNorthWall(squares[row][col])) {
// remove north wall from current square
final int modifiedSquare = originalSquare ^ NORTH;
squares[row][col] = modifiedSquare;
// remove south wall from adjoining square
final int originalAdjoiningSquare = squares[row - 1][col];
final int modifiedAdjoiningSquare = originalAdjoiningSquare ^ SOUTH;
squares[row - 1][col] = modifiedAdjoiningSquare;
// compute newly combined room size (if combined distinct rooms)
final int adjoiningRoomNumber = roomNumbers[row - 1][col];
if (currentRoomNumber != adjoiningRoomNumber) {
maxRoomSizeFromNorthWall += roomSizes[adjoiningRoomNumber - 1];
}
// restore original walls
squares[row][col] = originalSquare;
squares[row - 1][col] = originalAdjoiningSquare;
}
int maxRoomSizeFromEastWall = roomSizes[currentRoomNumber - 1];
if ((col != maxColumns - 1) && hasEastWall(squares[row][col])) {
// remove east wall from current square
final int modifiedSquare = originalSquare ^ EAST;
squares[row][col] = modifiedSquare;
// remove west wall for adjoining square
final int originalAdjoiningSquare = squares[row][col + 1];
final int modifiedAdjoiningSquare = originalAdjoiningSquare ^ WEST;
squares[row][col + 1] = modifiedAdjoiningSquare;
// compute newly combined room size (if combined distinct rooms)
final int adjoiningRoomNumber = roomNumbers[row][col + 1];
if (currentRoomNumber != adjoiningRoomNumber) {
maxRoomSizeFromEastWall += roomSizes[adjoiningRoomNumber - 1];
}
// restore original walls
squares[row][col] = originalSquare;
squares[row][col + 1] = originalAdjoiningSquare;
}
// return the removal that resulted in the largest combined rooms
if (maxRoomSizeFromNorthWall >= maxRoomSizeFromEastWall) {
return new int[]{maxRoomSizeFromNorthWall, row, col, NORTH};
} else {
return new int[]{maxRoomSizeFromEastWall, row, col, EAST};
}
}
}
Link To: Java Source Code