I use the following method to traverse* a binary tree of 300 000 levels:
Node* find(int v){
if(value==v)
return this;
else if(right && value<v)
return right->find(v);
else if(left && value>v)
return left->find(v);
}
However I get a segmentation fault due to stack overflow. Any ideas on how to traverse the deep tree without the overhead of recursive function calls?
* By "traverse" I mean "search for a node with given value", not full tree traversal.
Yes! For a 300 000 level tree avoid recursion. Traverse your tree and find the value iteratively using a loop.
Binary Search Tree representation
25 // Level 1
20 36 // Level 2
10 22 30 40 // Level 3
.. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. // Level n
Just to clarify the problem further. Your tree has a depth of n = 300.000 levels. Thus, in the worst case scenario a Binary Search Tree (BST) will have to visit ALL of the tree's nodes. This is bad news because that worst case has an algorithmic O(n) time complexity. Such a tree can have:
2ˆ300.000 nodes = 9.9701e+90308 nodes (approximately).
9.9701e+90308 nodes is an exponentially massive number of nodes to visit. With these numbers it becomes so clear why the call stack overflows.
Solution (iterative way):
I'm assuming your Node class/struct declaration is a classic standard integer BST one. Then you could adapt it and it will work:
struct Node {
int data;
Node* right;
Node* left;
};
Node* find(int v) {
Node* temp = root; // temp Node* value copy to not mess up tree structure by changing the root
while (temp != nullptr) {
if (temp->data == v) {
return temp;
}
if (v > temp->data) {
temp = temp->right;
}
else {
temp = temp->left;
}
}
return nullptr;
}
Taking this iterative approach avoids recursion, hence saving you the hassle of having to recursively find the value in a tree so large with your program call stack.
Node* temp = this; not Node* temp = root; and temp = left; instead of temp = temp->left; etc. – see the original code, it looks like an inline method in the Node class.
A simple loop where you have a variable of type Node* which you set to the next node, then loop again ...
Don't forget the case that the value you are searching for does not exist!
You could implement the recursion by not using the call stack but a user-defined stack or something similar; this could be done via the existing stack template. The approach would be to have a while loop which iterates until the stack is empty; as the existing implementaion uses depth-first search, elimination of the recursive calls can be found here.
When the tree that you have is a Binary Search Tree, and all you want to do is search for a node in it that has a specific value, then things are simple: no recursion is necessary, you can do it using a simple loop as others have pointed out.
In the more general case of having a tree which is not necessarily a Binary Search Tree, and wanting to perform a full traversal of it, the simplest way is using recursion, but as you already understand, if the tree is very deep, then recursion will not work.
So, in order to avoid recursion, you have to implement a stack on the C++ heap. You need to declare a new StackElement class that will contain one member for each local variable that your original recursive function had, and one member for each parameter that your original recursive function accepted. (You might be able to get away with fewer member variables, you can worry about that after you have gotten your code to work.)
You can store instances of StackElement in a stack collection, or you can simply have each one of them contain a pointer to its parent, thus fully implementing the stack by yourself.
So, instead of your function recursively calling itself, it will simply consist of a loop. Your function enters the loop with the current StackElement being initialized with information about the root node of your tree. Its parent pointer will be null, which is another way of saying that the stack will be empty.
In every place where the recursive version of your function was calling itself, your new function will be allocating a new instance of StackElement, initializing it, and repeating the loop using this new instance as the current element.
In every place where the recursive version of your function was returning, your new function will be releasing the current StackElement, popping the one that was sitting on the top of the stack, making it the new current element, and repeating the loop.
When you find the node you were looking for, you simply break from the loop.
Alternatively, if the node of your existing tree supports a) a link to its "parent" node and b) user data (where you can store a "visited" flag) then you don't need to implement your own stack, you can just traverse the tree in-place: in each iteration of your loop you first check if the current node is the node you were looking for; if not, then you enumerate through children until you find one which has not been visited yet, and then you visit it; when you reach a leaf, or a node whose children have all been visited, then you back-track by following the link to the parent. Also, if you have the freedom to destroy the tree as you are traversing it, then you do not even need the concept of "user data": once you are done with a child node, you free it and make it null.
Well, it can be made tail recursive at the cost of a single additional local variable and a few comparisons:
Node* find(int v){
if(value==v)
return this;
else if(!right && value<v)
return NULL;
else if(!left && value>v)
return NULL;
else {
Node *tmp = NULL;
if(value<v)
tmp = right;
else if(value>v)
tmp = left;
return tmp->find(v);
}
}
else branch can be made much more readable and less error-prone (and, lastly, much shorter) by directly initialising the variable tmp: Node* tmp = value < v ? right : left;.Walking through a binary tree is a recursive process, where you'll keep walking until you find that the node you're at currently points nowhere.
It is that you need an appropriate base condition. Something which looks like:
if (treeNode == NULL)
return NULL;
In general, traversing a tree is accomplished this way (in C):
void traverse(treeNode *pTree){
if (pTree==0)
return;
printf("%d\n",pTree->nodeData);
traverse(pTree->leftChild);
traverse(pTree->rightChild);
}
traverse (or find) can be made into a tail call, but the first one cannot. This has nothing to do with optimisation, in fact: it’s simply not possible. I should have made that clear in my previous comment.