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The problem gives us an integer array nums and two integers, m and k. We must examine every contiguous subarray whose length is exactly k. Among those subarrays, we only consider the ones that contain at least m distinct values. These are called almost unique subarrays.

The problem gives us a circular array called colors, where each value represents a tile color. A value of 0 means red, and a value of 1 means blue. We are also given an integer k. We must count how many groups of exactly k contiguous tiles form an alternating sequence.

The problem gives us two strings, start and target, both having the same length. Each position in the strings contains one of three characters: - 'L', representing a piece that can only move left - 'R', representing a piece that can only move right - '', representing an empty…

The problem requires transforming a given string s into a good string, where a good string is defined as one in which every character appears the same number of times.

This problem asks us to analyze email addresses stored in a database table and determine how many people belong to each unique email domain, but only for domains ending in .com.

The problem gives us an integer array nums and an integer k. We need to count how many pairs of indices (i, j) satisfy two conditions: 1. i < j 2.

The problem is asking us to reverse-engineer an array arr from its prefix XOR array pref. Specifically, pref[i] represents the XOR of all elements in arr from index 0 to i. Our goal is to reconstruct arr given only pref.

The problem asks us to calculate the k-beauty of a given integer num. To do this, we treat num as a string and examine every possible contiguous substring of length k. For each substring, we interpret it as an integer and check whether it divides the original number num evenly.

We are given up to five axis-aligned rectangles on a plane. Each rectangle is defined by its bottom-left and top-right coordinates. No two rectangles overlap, although they may touch at edges or corners.

The problem gives us an Orders table where each row represents a purchase made by a customer. Every order has an orderid, a customerid, an orderdate, and a price.

We are given two arrays, nums1 and nums2, both of length n. Each index j represents a point: and has an associated value: For every query [xi, yi], we must find an index j such that: and Among all indices satisfying both constraints, we want the maximum possible value: If no…

The problem asks us to determine how many valid placements of Alice and Bob exist on a 2D grid of points such that Alice can build a rectangular fence with her position as the upper left corner and Bob’s position as the lower right corner.

The problem gives us two database tables, Candidates and Rounds, that together describe interview performance for job candidates. The Candidates table contains one row per candidate.

We are given two integer arrays, one belonging to Devu and the other to his brother. We are allowed to repeatedly increase or decrease any single element of either array by 1 in one operation.

The problem gives a tree with n nodes labeled 0 to n-1, rooted at node 0. The tree is represented using a parent array, where parent[i] indicates the parent of node i. Node 0 has no parent, so parent[0] == -1.

We are given a sequence of movie genres scheduled over n days, with exactly one movie per day. There are k genres, and each genre appears at least once. Valentine, a critic, experiences stress whenever the genre of consecutive movies he watches changes.

The problem gives us a string word containing uppercase and lowercase English letters. We must count how many letters are considered "special". A character c is special if two conditions are true: 1. The lowercase version of the letter appears somewhere in the string. 2.

This problem asks us to implement a custom version of JavaScript’s Function.prototype.call method, called callPolyfill. The purpose is to execute a function with an explicit this context. Normally, in JavaScript, this depends on how a function is called.

The problem asks us to compute the total digit difference across every pair of numbers in the array. All numbers have the same number of digits. For any two numbers, their digit difference is defined as the number of positions where the digits are different.

The problem defines an infinite string-building process that starts with the string "a". At every operation, we take the current string and create a transformed version where every character is replaced by the next character in the alphabet.

The problem presents a scenario in which Alice has an original array arr of length n consisting of positive integers. She chooses a positive integer k and generates two new arrays: lower and higher.

The problem asks us to pair elements in an array of even length such that the largest sum among all pairs is minimized. In simpler terms, imagine we have a collection of numbers and we want to form pairs of two numbers each. Each number can only belong to one pair.

The problem gives us an undirected graph with n nodes labeled from 0 to n - 1. We must place every node into a 2D grid so that adjacency in the grid matches adjacency in the graph exactly.

We are given an array nums consisting of distinct integers. For every position i, we need to determine the maximum possible length of a contiguous subarray in which nums[i] is the largest element. More formally, for each index i, we want to find the longest subarray nums[l..

This problem asks us to compute the maximum value of strings in an array according to a specific definition of value. Each string can either be entirely numeric or alphanumeric. If a string consists only of digits, its value is the integer it represents.

This problem asks us to design a data structure that dynamically maintains a collection of integer intervals and efficiently reports how many distinct integers are covered by at least one interval. Initially, the interval set is empty.

This problem asks us to sort an array using a custom sorting rule. Instead of sorting elements directly by their own value, we are given a function fn that transforms each element into a numeric value, and that numeric value determines the order.

This problem models a tournament as a directed acyclic graph (DAG). Each node represents a team, and each directed edge u - v means team u is stronger than team v. A team is considered the champion if no other team is stronger than it.

The problem asks us to analyze shift overlaps for employees. We are given a table EmployeeShifts with columns employeeid, starttime, and endtime. Each row represents one work shift for an employee.

The problem asks us to count how many integers in the inclusive range [l, r] are not special. A number is considered special if it has exactly two proper divisors. A proper divisor of a number x is any positive divisor of x other than x itself.

The problem gives us an array nums of positive integers and asks us to count how many contiguous non-empty subarrays can be removed so that the remaining elements form a strictly increasing array.

We are given the root of a binary tree and an integer k. Our goal is to find the size of the k-th largest perfect binary subtree contained anywhere within the tree. A perfect binary tree has two defining properties: 1. Every internal node has exactly two children. 2.

This problem gives us a collection of equations of the form: Each variable is represented as a string, and each equation defines a multiplicative relationship between two variables. The task is to determine whether all equations can simultaneously be true.

The problem presents a 0-indexed array nums of non-negative powers of 2 and an integer target. Each element in nums is guaranteed to be a power of two, which is important because it allows us to reason about sums and splits in terms of binary representation.

We must construct a small string rewriting program. The program consists of ordered commands. Each command searches for a substring and replaces its first occurrence with another string. Some commands continue execution after replacement, while others terminate immediately.

This problem provides a pandas DataFrame named students with three columns: | Column | Type | | --- | --- | | studentid | int | | name | object | | age | int | Some rows contain missing values in the name column.

We are asked to count substrings of a binary string that contain exactly k ones. A substring is any contiguous sequence of characters within the string, and different occurrences at different positions count separately.

This problem asks us to maximize the total value of coins collected from multiple piles while following a strict removal rule. Each pile is ordered from top to bottom, meaning we cannot arbitrarily pick any coin in a pile. We may only remove coins from the top, one at a time.

The problem asks us to determine the number of distinct ways to spend a given amount of money, total, on pens and pencils, each with fixed costs, cost1 for pens and cost2 for pencils.

The problem is asking us to purchase exactly two chocolates from a store given their individual prices, while ensuring that after buying them we do not end up in debt.

We are given a directed structure on n objects representing a ski resort. Each object is either a mountain or a hotel. Every object has at most one outgoing ski track leading to another object, and a hotel never has outgoing tracks at all.

We are asked to arrange a sequence consisting of two kinds of objects, boys and girls, into a single line. The only freedom we have is the order.

The game consists of two flower lanes containing x and y flowers respectively. Alice moves first, and on every turn a player removes exactly one flower from either lane. A very important observation is that the players do not have any meaningful strategic choice.

The problem asks us to find all pairs of prime numbers (x, y) such that both numbers are between 1 and n inclusive, their sum equals n, and x <= y.

We are given several independent sequences of integers, one sequence per scientist. Each sequence must be kept in its original internal order, but we are allowed to interleave these sequences arbitrarily when forming one global list.

The reviewer identified a sign error in the swap argument, so the first task is to determine the correct monotonicity direction before rebuilding the proof. For , there is only one permutation, so the statement is trivial.

The problem asks us to determine the minimum number of keypresses required to type a given string s using a keypad with 9 buttons. Each button can map to at most 3 letters, and each letter must be mapped to exactly one button.

The problem gives us a string s that contains only two possible characters, 'a' and 'b'. We must determine whether every 'a' appears before every 'b'. Another way to think about the requirement is this: once we encounter a 'b', we should never see another 'a' later in the string.

The problem gives us the head of a singly linked list whose length is always even. The nodes are grouped into pairs based on their indices: - Nodes at indices (0, 1) form the first pair - Nodes at indices (2, 3) form the second pair - Nodes at indices (4, 5) form the third…

We have a two-dimensional gym represented as a grid of size n × m. Each cell contains a positive integer representing the calories burned by doing the workout at that location.

The game gives us two types of coins: - x coins worth 75 - y coins worth 10 Two players, Alice and Bob, take turns. Alice always moves first. On every turn, the current player must select coins whose total value is exactly 115.

The factory has a row of lights indexed from left to right. Every light starts in the “on” state. Mashmokh performs a sequence of button presses, and each button has an index that determines how far to the right its effect extends.

The problem asks us to determine the minimum number of adjacent swaps required to rearrange a string of black and white balls such that all white balls (0s) are grouped on the left and all black balls (1s) are grouped on the right.

We are given two polynomials, $P(x)$ and $Q(x)$, written in descending powers of $x$. The task is to compute: $$lim{x to infty} frac{P(x)}{Q(x)}$$ The input gives the degrees of the two polynomials and all coefficients from the highest-degree term down to the constant term.

The problem asks us to count how many digit strings of length n satisfy a specific positional rule. A digit string is considered "good" when: - Every digit placed at an even index, meaning indices 0, 2, 4, ..., must itself be an even digit.

The problem presents a simple two-player game between Alice and Bob using an array of positive integers. Each number in the array is either a single-digit number (1 to 9) or a double-digit number (10 to 99).

The problem asks us to compute the maximum factor score of an array of integers, where the factor score is defined as the product of the GCD (greatest common divisor) and LCM (least common multiple) of all elements in the array.

The problem asks us to analyze a maze represented as an undirected graph of n rooms connected by corridors. Each corridor allows travel in both directions, and the input corridors lists all such connections.

The problem asks us to process a string representing a sentence containing words and prices, where prices are words that start with a dollar sign 1e5 or 5$) should remain unchanged.

We have a directed graph of debts. An edge a - b means employee a owes money to employee b. We must arrange all employees in a sequence such that for every pair of consecutive employees (x, y) in the sequence, there is no edge x - y.

The problem gives us a single positive integer k. We start with an array containing exactly one element: We are allowed to perform two kinds of operations any number of times: 1. Increase the value of any existing element by 1 2.

We have an array and a fixed window length len. For every subarray of length len, we compute its sum and then take the absolute value. The "optimal sum" of the whole array is the maximum absolute subarray sum among all windows of that fixed length.

This problem asks us to design a custom Bitset data structure that supports several operations efficiently. A bitset is simply a sequence of binary values, where each position stores either 0 or 1.

The problem is asking us to implement a simple counter function with a closure-like behavior. Given an integer n, we need to return a function counter() that, when called the first time, returns n, and then increments the returned value by one for every subsequent call.

A group of friends wants to make identical toasts using three resources: soft drink, lime slices, and salt. Every toast consumes a fixed amount of each resource. The task is to determine how many complete toasts each friend can make before at least one resource runs out.

We are given an array of integers a with n elements. The task is to select two distinct indices i and j and compute a function f(i, j) that combines both the squared distance between the indices and the squared sum of the elements strictly between them.

The problem is asking us to transform a JSON-like array of objects or arrays into a matrix representation. Each row of the resulting matrix corresponds to one object (or array) in the input array, and the first row contains the column names.

The problem asks us to find the integer that appears most frequently immediately after a given key value in the array. More specifically, we are given an integer array nums and an integer key, which is guaranteed to exist in the array.

The problem asks us to design a data structure that manages a 3D binary matrix of size n x n x n. Every cell initially contains 0, and we must support three operations efficiently: 1. setCell(x, y, z) sets a specific cell to 1. 2.

The problem asks us to determine the minimum cost to buy exactly one apple starting from each city in a network of cities connected by bidirectional roads. Each city has a specific cost for buying an apple, and each road has a travel cost.

I can do that, but the guide will be very long for a single chat response because your required format includes detailed prose, brute force and optimal approaches, proof sketch, Python and Go implementations, worked traces for every example, complexity analysis, comprehensive…

The problem asks us to construct a strictly increasing array nums of length n such that the bitwise AND of all elements equals x. Among all valid arrays, we want to minimize the last element, nums[n - 1]. The constraints are important: - Every element must be a positive integer.

We are asked to count rhombi inside a rectangle of width w and height h, where each rhombus has its vertices on integer coordinates and diagonals aligned with the axes. Each rhombus must have positive area and be fully contained in the rectangle.

We are given a tree with n nodes rooted at node 0. Each node contains a certain number of coins. We must collect coins from every node while respecting the tree hierarchy, meaning a node can only be processed after all of its ancestors have already been processed.

In this problem, we are given a positive integer n, and we must find the smallest integer greater than or equal to n that is considered "fair". A number is fair when the count of even digits is exactly equal to the count of odd digits.

The problem asks us to count how many integers in the inclusive range [a, b] contain only unique digits. A number has unique digits if no digit appears more than once within that number. For example, the number 123 has unique digits because 1, 2, and 3 each appear exactly once.

We have a path graph with n platforms and n - 1 bridges between consecutive platforms. Bridge i connects platform i and i + 1, and can be crossed exactly a[i] times before disappearing permanently.

The problem gives us a string representing a time in 12-hour format using the pattern "HH:MM". Some characters may already be fixed digits, while others are replaced with "?". Our task is to replace every "?

The problem asks us to find the largest square that can fit inside the overlapping region of at least two rectangles on a 2D plane. Each rectangle is axis-aligned, meaning its sides are parallel to the x-axis and y-axis.

The problem asks us to determine the minimum time needed for all hens to eat all grains when both hens and grains are located on a one-dimensional line.

We are given a string word consisting of lowercase English letters. Two adjacent characters are considered almost-equal if either: - They are exactly the same, such as 'a' and 'a' - Their positions in the alphabet differ by exactly one, such as 'a' and 'b', 'c' and 'b', 'x'…

The problem gives us a database table named Tweets with two columns: | Column | Description | | --- | --- | | tweetid | Unique identifier for each tweet | | content | The text content of the tweet | We need to identify all tweets that are considered invalid.

Here’s a fully detailed technical solution guide for LeetCode 3080 following your requested format. The problem gives a zero-indexed array nums of size n consisting of positive integers and a 2D array queries of size m where each query is [indexi, ki].

This problem is the classic mathematical game known as Nim. We are given an array piles, where each element represents the number of stones in a pile. Two players, Alice and Bob, take turns removing stones.

We are given an array of integers, and for every element we must find another array element whose bitwise AND with it is zero. Two numbers are compatible exactly when they do not share any bit set to 1.

This problem is asking us to determine the minimum number of levels Alice should play in order to score more points than Bob, given that both play optimally and that some levels may be impossible to clear. The input is a binary array possible of length n.

We are given a binary string s, meaning the string contains only the characters '0' and '1', along with a positive integer k. The goal is to find a substring of s that is considered beautiful, where a beautiful substring contains exactly k occurrences of '1'.

This is a Type A - “Find all X” problem. A valid proof must do two things: 1. Verify that every claimed solution actually satisfies the conditions. 2. Prove that no other solutions exist. The proposed solution does not complete either direction fully.

The problem asks us to calculate the final price for each product in a database, taking into account any category-specific discounts. We are given two tables: Products and Discounts. The Products table contains each product's unique ID, its category, and its original price.

This problem asks us to process a sequence of update queries on an array. After each update, we must compute the maximum possible sum of a subsequence where no two selected elements are adjacent in the array. The key detail is that the subsequence does not need to be contiguous.

The problem gives us n players and a list called pick, where each entry is of the form [xi, yi]. This means player xi picked a ball with color yi. A player wins if they have picked strictly more than their player index number of balls of the same color.

The problem gives us an integer array nums and asks us to count how many contiguous subarrays have an even product. A subarray is a continuous segment of the array. For each possible subarray, we compute the product of all its elements.

The problem requires us to find the number of arithmetic triplets in a strictly increasing array of integers. An arithmetic triplet (i, j, k) satisfies the conditions i < j < k, nums[j] - nums[i] == diff, and nums[k] - nums[j] == diff.

We are asked to count the number of ways an ant can start at vertex D of a tetrahedron and return to D after exactly n steps, moving along edges at every step. The tetrahedron has four vertices labeled A, B, C, D, and each vertex is connected to the other three.

We have a directed graph of cities and roads. City 1 is the capital. Every road is either already usable or broken. A broken road may be repaired, after which it behaves like a normal directed edge. The government wants every city to become reachable from the capital.

This problem asks us to identify users who requested confirmation messages at least twice within a 24 hour time window. We are given two database tables: The Signups table contains one row per user and records when the user signed up. The userid column is unique.

We have a four-team football group where every pair of teams plays exactly once, so the full tournament contains six matches. Five results are already known, and the only remaining match is the one involving BERLAND. Each match contributes points in the usual way.

This problem describes a painting scenario represented as a one-dimensional number line. Each element in the input array paint[i] = [starti, endi] represents the section that needs to be painted on the ith day.

The problem asks whether there is a clear, unobstructed path from the bottom-left corner (0, 0) to the top-right corner (xCorner, yCorner) of a rectangle, such that the path does not touch or go inside any given circles.