Stanford introduction

    This [the following section until marked as end of Stanford University items] is article #110 in the Stanford CS Education Library. This and other free CS materials are available at the library (http://cslibrary.stanford.edu/). That people seeking education should have the opportunity to find it. This article may be used, reproduced, excerpted, or sold so long as this paragraph is clearly reproduced. Copyright 2000-2001, Nick Parlante, nick.parlante@cs.stanford.edu. [Stanford items are marked by a very light Stanford cardinal background.]

Pointer Changing Code

    There is a common problem with pointer intensive code: what if a function needs to change one of the pointer parameters passed to it? For example, the insert() function below may want to change the root pointer. In C and C++, one solution uses pointers-to-pointers (aka “reference parameters”). That’s a fine technique, but here we will use the simpler technique that a function that wishes to change a pointer passed to it will return the new value of the pointer to the caller. The caller is responsible for using the new value. Suppose we have a change() function that may change the the root, then a call to change() will look like this…

// suppose the variable "root" points to the tree
root = change(root);

    We take the value returned by change(), and use it as the new value for root. This construct is a little awkward, but it avoids using reference parameters which confuse some C and C++ programmers, and Java does not have reference parameters at all. This allows us to focus on the recursion instead of the pointer mechanics. (For lots of problems that use reference parameters, see CSLibrary #105, Linked List Problems, http://cslibrary.stanford.edu/105/).

Insert()

    Insert() -- given a binary search tree and a number, insert a new node with the given number into the tree in the correct place. The insert() code is similar to lookup() [see tree lookup], but with the complication that it modifies the tree structure. As described above, insert() returns the new tree pointer to use to its caller. Calling insert() with the number 5 on this tree…

  2
 / \
1   10

    returns the tree…

  2
 / \
1   10
   /
  5

    The solution shown here introduces a newNode() helper function that builds a single node. The base-case/recursion structure is similar to the structure in lookup() -- each call checks for the NULL case, looks at the node at hand, and then recurs down the left or right subtree if needed.

/*
 Helper function that allocates a new node
 with the given data and NULL left and right
 pointers.
*/
struct node* NewNode(int data) {
  struct node* node = new(struct node);    // "new" is like "malloc"
  node->data = data;
  node->left = NULL;
  node->right = NULL;

  return(node);
}

/*
 Give a binary search tree and a number, inserts a new node
 with the given number in the correct place in the tree.
 Returns the new root pointer which the caller should
 then use (the standard trick to avoid using reference
 parameters).
*/
struct node* insert(struct node* node, int data) {
  // 1. If the tree is empty, return a new, single node
  if (node == NULL) {
    return(newNode(data));
  }
  else {
    // 2. Otherwise, recur down the tree
    if (data <= node->data) node->left = insert(node->left, data);
    else node->right = insert(node->right, data);

    return(node); // return the (unchanged) node pointer
  }
}

    The shape of a binary tree depends very much on the order that the nodes are inserted. In particular, if the nodes are inserted in increasing order (1, 2, 3, 4), the tree nodes just grow to the right leading to a linked list shape where all the left pointers are NULL. A similar thing happens if the nodes are inserted in decreasing order (4, 3, 2, 1). The linked list shape defeats the lg(N) performance. We will not address that issue here, instead focusing on pointers and recursion.

copyright notice

    This [the quoted passages above] is article #110 in the Stanford CS Education Library. This and other free CS materials are available at the library (http://cslibrary.stanford.edu/). That people seeking education should have the opportunity to find it. This article may be used, reproduced, excerpted, or sold so long as this paragraph is clearly reproduced. Copyright 2000-2001, Nick Parlante, nick.parlante@cs.stanford.edu. [Stanford items are marked by a very light Stanford cardinal background.]

    {NOTE; the original Stanford document separated the C/C++ and the Java discusssions. The material is interwoven here because this book uses the approach of teaching abasic concept and then showing it in multiple languages.]

end of Stanford introduction