Which XXX completes the C++ AVLTree class's Insert() function? void Insert(Node* node) { if (!root) { root = node; } else { Node* currentNode = root; while (currentNode) { if (node-key key) { if (currentNode-left == nullptr) { currentNode-left = node; node-parent = currentNode; currentNode = nullptr; } else { currentNode = currentNode-left; } } else { if (currentNode-right == nullptr) { currentNode-right = node; node-parent = currentNode; currentNode = nullptr; } else { currentNode = currentNode-right; } } } XXX while (node) { Rebalance(node); node = node-parent; } } }

Question

Which XXX completes the C++ AVLTree class's Insert() function?

void Insert(Node* node) {
   if (!root) {
      root = node;
   }
   else {
      Node* currentNode = root;
      while (currentNode) {
         if (node->key < currentNode->key) {
            if (currentNode->left == nullptr) {
               currentNode->left = node;
               node->parent = currentNode;
               currentNode = nullptr;
            }
            else {
               currentNode = currentNode->left;
            }
         }
         else {
            if (currentNode->right == nullptr) {
               currentNode->right = node;
               node->parent = currentNode;
               currentNode = nullptr;
            }
            else {
               currentNode = currentNode->right;
            }
         }
      }
      XXX
      while (node) {
         Rebalance(node);
         node = node->parent;
      }
   }
}

BlackTom AI · Accepted Answer

The question asks what should fill the XXX in the AVLTree Insert function after linking the new node into the tree.
First, note what the code does: it inserts the new node as a leaf, setting its parent appropriately, and then reaches the XXX placeholder. After insertion, rebalancing must propagate from the newly inserted node up toward the root, since AVL trees require balancing based on the ancestors of the inserted node.
Option assessment (only one option is provided):
- node = node->parent; This choice moves the current focus from the newly inserted node to its parent. Since the subsequent loop is while (node) { Rebalance(node); node = node->parent; }, setting node to its parent ensures that Rebalance is called for the parent, then its grandparent, and so on up to the root. This is exactly the intended behavior for updating balance factors and performing rotations as needed for AVL properties.
Why this is correct conceptually: after inserting a new node, the primary balance violations (if any) can only occur on the path from the new node up to the root. Starting the rebalance sequence at the parent avoids rebalancing the newly inserted leaf (which has no imbalance), and aligns with the standard approach of updating ancestors.
Why other possibilities (if any) would be incorrect: since only one option is presented, we can reason about what would happen if a different action were taken (e.g., continuing with node unchanged). Keeping node as the newly inserted node would attempt to rebalance from the leaf itself, which is unnecessary and could disrupt the intended parent-to-root rebalancing flow. It would also fail to correctly traverse up to higher ancestors unless additional logic were added elsewhere. In general, after insertion, the balancing logic should ascend from the parent of the inserted node, not from the inserted node itself.
In summary, setting node to its parent before entering the rebalance loop correctly initiates upward rebalancing along the path from the insertion point to the root, aligning with AVL-tree balancing mechanics.

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