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Daveed V's Maximal Rectangle algorithm in Java
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.Stack;
final class Cell {
final int col;
final int row;
Cell(final int col, final int row) {
this.col = col;
this.row = row;
}
@Override
public String toString() {
return String.format("[col=%d, row=%d]", col + 1, row + 1);
}
}
final class Cache {
private final LinkedList<Integer> aggregateHeights;
Cache(final int size) {
aggregateHeights = new LinkedList<>();
for(int i = 0; i <= size; i++) {
aggregateHeights.add(0);
}
}
public int get(final int col) {
return aggregateHeights.get(col);
}
public void aggregate(final String row) {
final String[] elements = row.split("\\s+");
for(int col = 0; col < elements.length; col++) {
final String element = elements[col];
System.err.printf("%s ", element);
if("0".equals(element)) {
aggregateHeights.set(col, 0);
} else {
aggregateHeights.set(col, aggregateHeights.get(col) + 1);
}
}
System.err.printf("\n");
}
}
/**
* @see http://stackoverflow.com/a/20039017/1028367
* @see http://www.drdobbs.com/database/the-maximal-rectangle-problem/184410529
*/
public class MaximalRectangle {
public static void main(final String ... args) throws Exception {
int bestArea = 0;
Cell bestLowerLeftCorner = new Cell(0, 0);
Cell bestUpperRightCorner = new Cell(-1, -1);
try(final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in))) {
final Scanner scanner = new Scanner(reader.readLine());
final int numColumns = scanner.nextInt();
final int numRows = scanner.nextInt();
System.err.printf("Reading %dx%d array (1 row == %d elements)\n", numColumns, numRows, numColumns);
final Stack<Cell> stack = new Stack<>();
final Cache rectangleHeightCache = new Cache(numColumns);
for(int row = 0; row < numRows; row++) {
rectangleHeightCache.aggregate(reader.readLine());
for(int col = 0, currentRectHeight = 0; col <= numColumns; col++) {
final int aggregateRectHeight = rectangleHeightCache.get(col);
if(aggregateRectHeight > currentRectHeight) {
stack.push(new Cell(col, currentRectHeight));
currentRectHeight = aggregateRectHeight;
} else if(aggregateRectHeight < currentRectHeight) {
Cell rectStartCell;
do {
rectStartCell = stack.pop();
final int rectWidth = col - rectStartCell.col;
final int area = currentRectHeight * rectWidth;
if(area > bestArea) {
bestArea = area;
bestLowerLeftCorner = new Cell(rectStartCell.col, row);
bestUpperRightCorner = new Cell(col - 1, row - currentRectHeight + 1);
}
currentRectHeight = rectStartCell.row;
} while(aggregateRectHeight < currentRectHeight);
currentRectHeight = aggregateRectHeight;
if(currentRectHeight != 0) {
stack.push(rectStartCell);
}
}
}
}
System.err.printf("The maximal rectangle has area %d.\n", bestArea);
System.err.printf("Location: %s to %s\n", bestLowerLeftCorner, bestUpperRightCorner);
}
}
}
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