How to find the kth leaf in an avl tree

Question

i want to solve this by adding a leaf field to my avl tree node to represent leafs below node the leaf field would tell how many leaves are below each node (n->leaves =n->left->leaves + n->right->leaves ) and modify during inserting and deletion. With this, I can move through faster ex if I am looking for 100th leaf and the left subtree has 90 leaves I can directly move to right subtree changing time complexity to O(logn) rather than O(n)

typedef struct tr_n_t { 
//int leaf
    key_t key;
    struct tr_n_t *left;
    struct tr_n_t *right;
    int height; 
} tree_node_t;

You don't need a "is a leaf" field for your nodes. A leaf is a node with no children, i.e. where the `left` and `right` pointers are both `NULL`. — Some programmer dude, Mar 23 '20 at 12:49
With that said, what is your real question? You seem to have three questions or problems in this question ("[h]ow to find the kth leaf in an avl tree", "[I] want to add a leaf field", "assign 1 to leafs"). Which one is you really asking about? Please ask one question per post. Also please take some time to read [the help pages](http://stackoverflow.com/help), take the SO [tour], read [ask], as well as [this question checklist](https://codeblog.jonskeet.uk/2012/11/24/stack-overflow-question-checklist/). — Some programmer dude, Mar 23 '20 at 12:51

Ian Abbott · Answer 1 · 2020-03-23T15:28:30.500

A node is a leaf if it has no child nodes. In OP's case, if (and only if) both the left and right members of a node are NULL, then the node is a leaf node.

Since OP's tree_node_t type has no pointer to the parent node, a recursive function can be used to perform an in-order traversal. The in-order traversal is being used to find the kth leaf node. A counter can be used to keep track of how many leaf nodes have been encountered so far. When this counter reaches the desired value k, the desired leaf node has been found so the function can return a pointer to the desired node, otherwise it should return 0.

// recursive helper function
static tree_node_t *find_leaf_k_internal(tree_node_t *node, unsigned int *count, unsigned int k)
{
    tree_node_t *kth;

    if (!node)
        return NULL; // not a node

    if (!node->left && !node->right) {
        // node is a leaf
        if (*count == k)
            return node; // node is the kth leaf

        (*count)++; // increment leaf counter
        return NULL; // not the kth leaf
    }

    // node is not a leaf
    // perform in-order traversal down the left sub-tree
    kth = find_leaf_k_internal(node->left, count, k);
    if (kth)
        return kth; // return found kth leaf node
    // kth leaf node not found yet
    // perform in-order traversal down the right sub-tree
    return find_leaf_k_internal(node->right, count, k);
}

// find kth in-order leaf node of tree counting from 0.
// returns pointer to kth leaf node, or NULL if tree contains fewer than k+1 leaf nodes.
tree_node_t *find_leaf_k(tree_node_t *root, unsigned int k)
{
    unsigned int count = 0; // in-order running count of leaf nodes

    return find_leaf_k_internal(root, &count, k);
}

How to find the kth leaf in an avl tree

1 Answers1