QuestionB.java

package Q17_21_Volume_of_Histogram;

public class QuestionB {
	public static int borderedVolume(HistogramData[] data, int start, int end) {
		if (start >= end) return 0;
		
		int min = Math.min(data[start].getHeight(), data[end].getHeight());
		int sum = 0;
		for (int i = start + 1; i < end; i++) {
			sum += min - data[i].getHeight();
		}
		return sum;
	}
	
	public static int subgraphVolume(HistogramData[] histogram, int start, int end, boolean isLeft) {
		if (start >= end) return 0;	
		int sum = 0;
		if (isLeft) {
			int max = histogram[end - 1].getLeftMaxIndex();	
			sum += borderedVolume(histogram, max, end);
			sum += subgraphVolume(histogram, start, max, isLeft);	
		} else {
			int max = histogram[start + 1].getRightMaxIndex();	
			sum += borderedVolume(histogram, start, max);
			sum += subgraphVolume(histogram, max, end, isLeft);		
		}
		
		return sum;
	}
	
	public static HistogramData[] createHistogramData(int[] histo) {
		HistogramData[] histogram = new HistogramData[histo.length];
		for (int i = 0; i < histo.length; i++) {
			histogram[i] = new HistogramData(histo[i]);
		}
		
		/* Set left max index. */
		int maxIndex = 0;
		for (int i = 0; i < histo.length; i++) {
			if (histo[maxIndex] < histo[i]) {
				maxIndex = i;
			}
			histogram[i].setLeftMaxIndex(maxIndex);
		}
		
		/* Set right max index. */
		maxIndex = histogram.length - 1;
		for (int i = histogram.length - 1; i >= 0; i--) {
			if (histo[maxIndex] < histo[i]) {
				maxIndex = i;
			}
			histogram[i].setRightMaxIndex(maxIndex);			
		}		
		
		return histogram;
	}
	
	public static int computeHistogramVolume(int[] histogram) {
		int start = 0;
		int end = histogram.length - 1;
		
		HistogramData[] data = createHistogramData(histogram);
		
		int max = data[0].getRightMaxIndex();
		
		int leftVolume =  subgraphVolume(data, start, max, true);
		int rightVolume = subgraphVolume(data, max, end, false);
		
		return leftVolume + rightVolume;		
	}
	
	public static void main(String[] args) {
		int[] histogram = {0, 0, 4, 0, 0, 6, 0, 0, 3, 0, 8, 0, 2, 0, 5, 2, 0, 3, 0, 0};
		int result = computeHistogramVolume(histogram);
		System.out.println(result);
	}

}