QuestionC.java

package Q17_21_Volume_of_Histogram;

public class QuestionC {

	/* Go through each bar and compute the volume of water above it. 
	 * Volume of water at a bar =
	 *   height - min(tallest bar on left, tallest bar on right)
	 *   [where above equation is positive]
	 * Compute the left max in the first sweep, then sweep again to 
	 * compute the right max, minimum of the bar heights, and the 
	 * delta. */
	public static int computeHistogramVolume(int[] histo) {
		/* Get left max */
		int[] leftMaxes = new int[histo.length];
		int leftMax = histo[0];
		for (int i = 0; i < histo.length; i++) {
			leftMax = Math.max(leftMax, histo[i]);
			leftMaxes[i] = leftMax;
		}
		
		int sum = 0;
		
		/* Get right max */
		int rightMax = histo[histo.length - 1];
		for (int i = histo.length - 1; i >= 0; i--) {
			rightMax = Math.max(rightMax, histo[i]);
			int secondTallest = Math.min(rightMax, leftMaxes[i]);
			
			/* If there are taller things on the left and right side, then there is 
			 * water above this bar. Compute the volume and add to the sum. */
			if (secondTallest > histo[i]) { 
				sum += secondTallest - histo[i];
			}
		}
		
		return sum;
	}
	
	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);
	}

}