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Kth Largest Element in Binary Search Tree

The kth largest element problem in a binary search tree (BST) is a classic algorithmic challenge. Given a binary tree, the task is to find the kth largest value among all the nodes. This problem is often approached using a reverse order traversal method, similar to a modified depth-first search (DFS).

The algorithm leverages the reverse order traversal to determine the kth largest element efficiently. The recursive function traverses the tree in reverse order, counting nodes in a way that allows us to pinpoint the kth largest value without incurring the overhead of sorting the entire tree.

Here is an implementation of this approach:

public class offer54 { int num = 0; public int kthLargest(TreeNode root, int k) { if (root == null) return 0; return reverseInOrder(root, k); }

public int reverseInOrder(TreeNode node, int k) {
    if (node == null) return 0;
    int i = reverseInOrder(node.right, k);
    if (i != 0) return i;
    num++;
    if (num == k) return node.val;
    i = reverseInOrder(node.left, k);
    if (i != 0) return i;
    return 0;
}

}

The function reverseInOrder performs a post-order traversal by first checking the right subtree and then the left subtree. Each time the function visits a node, it increments the count (num). When the count reaches k, the current node's value is returned as the kth largest element.

Key points to consider:

To test this implementation, you can use the following use case:

• Input Tree: 3 /
  1 4 / \ / 2 3 5
• k = 2 Output: 3

This approach efficiently finds the kth largest element in a binary tree by utilizing a reverse order traversal strategy.