## Check children-sum property in a binary tree

Given the root of a binary tree, determine if the binary tree holds children-sum property. For a tree to satisfy the children-sum property, each node’s value should be equal to the sum of values at its left and right subtree.

## Shrink an array by removing triplets that satisfy given constraints

Given an integer array, shrink it by removing adjacent triplets that satisfy the given constraints and return the total number of elements in the resultant array.

Given a BST, count the total number of nodes that lie within a given range.

## Check whether a directed graph is Eulerian

An Eulerian trail (or Eulerian path) is a path in a graph that visits every edge exactly once. Given a directed graph, check whether it has an Eulerian path or not.

## Find the minimum number of merge operations to make an array palindrome

Given a list of non-negative integers, find the minimum number of merge operations to make it a palindrome. A merge operation can only be performed on two adjacent elements and replace them with their sum.

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Given a linked list, construct a complete binary tree from it. Assume that the order of elements present in the linked list is the same as that in the complete tree’s array representation.

## Find read-write conflicts among given database transactions

Given a list of database transactions, find all read-write conflicts among them. Assume that there is no strict two-phase locking (Strict 2PL) protocol to prevent read-write conflicts.

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Given a binary tree, check if removing an edge can split it into two binary trees of equal size.

## In-place merge two height-balanced BSTs

Given two height-balanced binary search trees, in-place merge them into a single balanced binary search tree. For each node of a height-balanced tree, the difference between its left and right subtree height is at most 1.

## Find height of a binary tree represented by the parent array

Given an array representing the parent-child relationship in a binary tree, find the tree’s height without building it. The parent-child relationship is defined by `(A[i], i)` for every index `i` in array `A`.

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Given a binary tree and two tree pointers, `x` and `y`, write an efficient algorithm to check if they lie on the same root-to-leaf path in the binary tree. In other words, determine whether `x` is an ancestor of `y`, or `x` is a descendant of `y`.

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Given an array representing the preorder traversal of a BST, determine whether it represents a skewed BST or not. In a skewed BST, each node’s descendants are either smaller or larger than the node itself.