Given a string with parentheses, determine the minimum number of parentheses you must remove to make the string valid. A valid string has balanced and properly nested parentheses.

Determine if a given abbreviation is valid for a given word. An abbreviation can contain digits representing the number of skipped characters.

Traverse a binary tree and return a list of node values for each vertical line, ordered from left to right. Nodes on the same vertical line should be ordered from top to bottom.

Determine if a string is a palindrome after removing at most one character. Consider both left and right removals when checking for palindrome validity.

Find the lowest common ancestor of two nodes in a binary tree where each node has a parent pointer. You're given the two nodes directly, not the root of the tree.

Find the kth largest element in an unsorted array. Note that it is the kth largest element in sorted order, not the kth distinct element.

Find the lowest common ancestor of two nodes in a given binary tree. The lowest common ancestor is defined as the farthest node from the root that is an ancestor of both nodes.

Given a binary tree, imagine you are standing on the right side of it. Return the values of the nodes you can see, ordered from top to bottom.

Implement a basic calculator to evaluate a simple expression string. The expression can contain non-negative integers, '+', '-', '*', '/' operators, and spaces; integer division should truncate toward zero.

You're given an array representing weights. Implement a function to randomly pick an index from the array, where the probability of picking each index is proportional to its weight.

You are given a nested list of integers where each integer has a depth. Calculate the weighted sum of all integers in the list, where the weight of an integer is its depth within the nested structure.

Find a peak element in an array, where a peak is greater than its neighbors. You only need to return the index of any one peak element if multiple exist.

Imagine a binary tree where each path from the root to a leaf represents a number. Calculate the sum of all these root-to-leaf numbers.

Find the longest path between any two nodes in a binary tree. The path may or may not pass through the root.

You are given a collection of intervals. Merge all overlapping intervals into a single interval and return the result.

Find the k most frequent elements in a given array of numbers. Return the top k elements based on their frequency.

Rearrange the characters of a given string according to a custom order defined by another string. If a character isn't in the custom order, place it at the end in any order.

Find two numbers in a given array that add up to a specific target value, and return their indices. Essentially, you need to efficiently locate the pair that satisfies the sum requirement.

Calculate x raised to the power of n. Be mindful of potential edge cases and optimize for efficiency, as a naive approach might not be sufficient.

You are given k sorted lists. Combine all of their elements into a single sorted list and return it.