Q11: in Java

Modify the code below to count the number of recursive calls. Then, modify to include stored values and see how that reduces the number of calls made.

public class ManhattanWithCallCount { public static void main (String[] argv) { // Test case 1: go from (2,2) to (0,0) int r = 2; int c = 2; int n = countPaths (r, c); System.out.println ("r=" + r + " c=" + c + " => n=" + n); // Test case 2: go from (5,7) to (0,0) r = 5; c = 7; n = countPaths (r, c); System.out.println ("r=" + r + " c=" + c + " => n=" + n); } static int countPaths (int numRows, int numCols) { // Bottom-out case: if ( (numRows == 0) || (numCols == 0) ) { return 1; } // Otherwise, reduce to two sub-problems and add. int downCount = countPaths (numRows-1, numCols); int rightCount = countPaths (numRows, numCols-1); return (downCount + rightCount); } }