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.

A list of directed connections forms a tree structure, but one extra connection has been added. This results in an error, like a node with two parents or a cycle. Find the single connection that can be removed to restore the tree.

Determine whether an integer is a palindrome. That is, it reads the same forwards and backward.

You are given two linked lists, each representing a non-negative integer. Add the two numbers and return the sum as a linked list.

Divide an array into subarrays and maximize the sum of the GCDs of each subarray. Find the maximum achievable score by optimally splitting the array.

Given an unsorted array of integers, find the length of the longest consecutive elements sequence. These consecutive numbers do not need to be adjacent in the original array.

You're given daily stock prices. Find the maximum profit you can make by buying and selling the stock once. You must buy before you sell.

Distribute candies to children standing in a line such that each child with a higher rating gets more candies than their neighbors. Find the minimum number of candies needed.

Find the median of two sorted arrays. The arrays can be of different sizes, and you should aim for an efficient solution.

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

Find the longest string that is a prefix of all strings in a given array. If no common prefix exists, return an empty string.

Convert a Roman numeral string into its corresponding integer value. The input string will represent a valid Roman numeral.

Find the k-th smallest integer in lexicographical order among all integers from 1 to n. Consider "lexicographical order" as the order you'd find the numbers in a dictionary.

Find all unique triplets in an array that sum to zero. You'll need to consider the potential for duplicate numbers and avoid duplicate triplets in your solution.

Find the length of the longest substring within a given string that contains no repeating characters. The substring must be contiguous.

Convert a given string into a zigzag pattern with a specified number of rows. Then read the characters row by row to return the converted string.

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.

Given an array representing the height of bars, calculate how much water can be trapped between them after rain. Think about finding the maximum height to the left and right of each bar.

You are given an array representing the heights of vertical lines. Find two lines that, together with the x-axis, form a container that holds the most water.

Determine if a string containing parentheses is valid. A valid string has matching and properly nested opening and closing parentheses.