/**
Given a binary tree, prints out all of its root-to-leaf
paths, one per line. Uses a recursive helper to do the work.
*/
public void printPaths(Node root, int n) {
  String[] path = new String[n];
  printPaths(root, path, 0);
}
/**
Recursive printPaths helper -- given a node, and an array containing
the path from the root node up to but not including this node,
prints out all the root-leaf paths.
*/
private void printPaths(Node node, String[] path, int pathLen) {
  if (node == null) return;
  // append this node to the path array
    path[pathLen++] = node.value;
  // it's a leaf, so print the path that led to here
  if (node.leftChild == null && node.rightChild == null) {
    printArray(path, pathLen);
  }
  else {
    // otherwise try both subtrees
    printPaths(node.leftChild, path, pathLen);
    printPaths(node.rightChild, path, pathLen);
  }
}
/**
Utility that prints strings from an array on one line.
*/
private void printArray(String[] ints, int len) {
  for (int i = 0; i < len; i++) {
    System.out.print(ints[i] + " ");
  }
  System.out.println();
}