Question

Assuming the tree is balanced, how much stack space will the routine use for a tree of 1,000,000 elements?

void printTree(const Node *node) {
  char buffer[1000];
  if(node) {
    printTree(node->left);
    getNodeAsString(node, buffer);
    puts(buffer);
    printTree(node->right);
  }
}

This was one of the algo questions in “The Pragmatic Programmer” where the answer was 21 buffers needed (lg(1m) ~= 20 and with the additional 1 at very top)

But I am thinking that it requires more than 1 buffer at levels lower than top level, due to the 2 calls to itself for left and right node. Is there something I missed?

*Sorry, but this is really not a homework. Don’t see this on the booksite’s errata.

Answer 1

First the left node call is made, then that call returns (and so its stack is available for re-use), then there’s a bit of work, then the right node call is made.

So it’s true that there are two buffers at the next level down, but those two buffers are required consecutively, not concurrently. So you only need to count one buffer in the high-water-mark stack usage. What matters is how deep the function recurses, not how many times in total the function is called.

This assuming of course that the code is written in a language similar to C, and that the C implementation uses a stack for automatic variables (I’ve yet to see one that doesn’t), blah blah.