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Practice › LeetCode › LeetCode 38xx ›

LeetCode 3828 - Final Element After Subarray Deletions

LeetCode Problem 3828 Difficulty: 🟡 Medium Topics: Array, Math, Brainteaser, Game Theory Solution Problem Understanding We are given an integer array nums . Two players, Alice and Bob, repeatedly remove a contiguous subarray from the current array. The only restriction is that the removed subarray cannot be the entire current array, so after every move at least one element remains. After a subarray is removed, the remaining elements are concatenated...

Practice › LeetCode › LeetCode 19xx ›

LeetCode 1908 - Game of Nim

LeetCode Problem 1908 Difficulty: 🟡 Medium Topics: Array, Math, Dynamic Programming, Bit Manipulation, Brainteaser, Game Theory Solution Problem Understanding 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. On each turn, a player may choose any non-empty pile and remove any positive...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1872 - Stone Game VIII

LeetCode Problem 1872 Difficulty: 🔴 Hard Topics: Array, Math, Dynamic Programming, Prefix Sum, Game Theory Solution Problem Understanding The problem describes a two-player turn-based game between Alice and Bob with a row of stones, each having an integer value. The key rules are that on a turn, a player removes more than one stone from the left , sums their values to their score, and then places a new stone...

Practice › LeetCode › LeetCode 32xx ›

LeetCode 3227 - Vowels Game in a String

LeetCode Problem 3227 Difficulty: 🟡 Medium Topics: Math, String, Brainteaser, Game Theory Solution Problem Understanding The problem describes a two-player game between Alice and Bob played on a string s . Alice always moves first. The rules for each player are based on vowel counts in substrings: Alice can remove any non-empty substring containing an odd number of vowels , while Bob can remove any non-empty substring containing an even...

Practice › LeetCode › LeetCode 19xx ›

LeetCode 1927 - Sum Game

LeetCode Problem 1927 Difficulty: 🟡 Medium Topics: Math, String, Greedy, Game Theory Solution Problem Understanding The problem describes a two player game played on a numeric string of even length. The string contains digits and possibly some '?' characters. Alice and Bob alternate turns replacing one '?' with a digit from '0' to '9' . Alice moves first. At the end of the game, every '?' has been replaced. The...

Practice › LeetCode › LeetCode 32xx ›

LeetCode 3222 - Find the Winning Player in Coin Game

LeetCode Problem 3222 Difficulty: 🟢 Easy Topics: Math, Simulation, Game Theory Solution Problem Understanding 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 . If a player cannot make such a move, that player loses immediately. We...

Practice › LeetCode › LeetCode 20xx ›

LeetCode 2038 - Remove Colored Pieces if Both Neighbors are the Same Color

LeetCode Problem 2038 Difficulty: 🟡 Medium Topics: Math, String, Greedy, Game Theory Solution Problem Understanding This problem describes a two-player game played on a line of colored pieces. The input colors is a string representing these pieces, where each character is either 'A' or 'B' . Alice always moves first and can only remove 'A' pieces that are surrounded on both sides by 'A' . Bob moves second and can...

Practice › LeetCode › LeetCode 28xx ›

LeetCode 2868 - The Wording Game

LeetCode Problem 2868 Difficulty: 🔴 Hard Topics: Array, Math, Two Pointers, String, Greedy, Game Theory Solution Problem Understanding The problem describes a turn-based game between Alice and Bob, where both players have a lexicographically sorted list of words. Alice always starts by playing her lexicographically smallest word , and the players then alternate turns. On each turn, the current player must select a word from their list that is closely...

Practice › LeetCode › LeetCode 32xx ›

LeetCode 3283 - Maximum Number of Moves to Kill All Pawns

LeetCode Problem 3283 Difficulty: 🔴 Hard Topics: Array, Math, Bit Manipulation, Breadth-First Search, Game Theory, Bitmask Solution Problem Understanding The problem gives us a 50 x 50 chessboard containing exactly one knight and up to 15 pawns. The knight starts at position (kx, ky) , and every pawn is placed at one of the coordinates in positions . Two players, Alice and Bob, alternate turns. Alice moves first. During a...

Practice › LeetCode › LeetCode 11xx ›

LeetCode 1140 - Stone Game II

LeetCode Problem 1140 Difficulty: 🟡 Medium Topics: Array, Math, Dynamic Programming, Prefix Sum, Game Theory Solution Problem Understanding The problem is a two-player turn-based game played on a row of stone piles. Each pile has a positive number of stones, and players take turns taking stones from the start of the remaining piles. On each turn, a player can take up to 2 * M piles, where M starts at...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 292 - Nim Game

LeetCode Problem 292 Difficulty: 🟢 Easy Topics: Math, Brainteaser, Game Theory Solution Problem Understanding The problem describes a two-player game involving a single heap of stones. There are n stones initially on the table, and players alternate turns removing stones. On each turn, a player may remove either 1, 2, or 3 stones. The player who removes the final stone wins the game. You always move first, and both players...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 877 - Stone Game

LeetCode Problem 877 Difficulty: 🟡 Medium Topics: Array, Math, Dynamic Programming, Game Theory Solution Problem Understanding The problem describes a two-player game played on an array of stone piles. Each pile contains a positive number of stones, and the piles are arranged in a row. Alice and Bob alternate turns, with Alice always moving first. On each turn, the current player may only take the pile from the left end...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1561 - Maximum Number of Coins You Can Get

LeetCode Problem 1561 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting, Game Theory Solution LeetCode 1561 - Maximum Number of Coins You Can Get Problem Understanding The problem gives us an array called piles , where each element represents the number of coins in a pile. The length of the array is always divisible by 3 , meaning there are exactly 3n piles for some integer n . In every...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 810 - Chalkboard XOR Game

LeetCode Problem 810 Difficulty: 🔴 Hard Topics: Array, Math, Bit Manipulation, Brainteaser, Game Theory Solution LeetCode 810, Chalkboard XOR Game Problem Understanding This problem describes a two player game played on an array of integers. The numbers are written on a chalkboard, and players take turns erasing exactly one number. Alice moves first, then Bob, and both players play optimally. The key rule is unusual. A player loses immediately if...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 464 - Can I Win

LeetCode Problem 464 Difficulty: 🟡 Medium Topics: Math, Dynamic Programming, Bit Manipulation, Memoization, Game Theory, Bitmask Solution LeetCode 464 - Can I Win Problem Understanding This problem describes a two-player turn-based game. Players take turns choosing a number from a shared pool of integers ranging from 1 to maxChoosableInteger . Once a number is chosen, it cannot be used again for the rest of the game. Each chosen number is...

Practice › LeetCode › LeetCode 17xx ›

LeetCode 1728 - Cat and Mouse II

LeetCode Problem 1728 Difficulty: 🔴 Hard Topics: Array, Math, Dynamic Programming, Graph Theory, Topological Sort, Memoization, Matrix, Game Theory Solution Problem Understanding This problem describes a two-player perfect-information game played on a small grid. One player controls the mouse and the other controls the cat. Both players move optimally and alternate turns, with the mouse always moving first. The grid contains several kinds of cells: 'M' represents the mouse's starting...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 913 - Cat and Mouse

LeetCode Problem 913 Difficulty: 🔴 Hard Topics: Math, Dynamic Programming, Graph Theory, Topological Sort, Memoization, Game Theory Solution Problem Understanding In this problem, we are given an undirected graph where two players, Mouse and Cat, move alternately across the graph according to specific rules. The graph is represented as an adjacency list, where graph[a] contains all nodes directly connected to node a . The Mouse always starts at node 1...

Practice › LeetCode › LeetCode 20xx ›

LeetCode 2005 - Subtree Removal Game with Fibonacci Tree

LeetCode Problem 2005 Difficulty: 🔴 Hard Topics: Math, Dynamic Programming, Tree, Binary Tree, Game Theory Solution LeetCode 2005 - Subtree Removal Game with Fibonacci Tree Problem Understanding The problem defines a special kind of binary tree called a Fibonacci tree. The structure is recursive: order(0) is an empty tree. order(1) is a single node. order(n) has: a root node, a left subtree equal to order(n - 2) , a right...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 843 - Guess the Word

LeetCode Problem 843 Difficulty: 🔴 Hard Topics: Array, Math, String, Interactive, Game Theory Solution LeetCode 843 - Guess the Word Problem Understanding This is an interactive problem where we must identify a hidden six-letter word from a given list of candidate words. We are not allowed to directly inspect the secret word. Instead, we can interact with the provided Master API by calling master.guess(word) . Each call returns the number...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 294 - Flip Game II

LeetCode Problem 294 Difficulty: 🟡 Medium Topics: Math, Dynamic Programming, Backtracking, Memoization, Game Theory Solution Problem Understanding This problem describes a two-player impartial game played on a string consisting only of '+' and '-' characters. A valid move consists of selecting any pair of consecutive "++" characters and flipping them into "--" . The players alternate turns. If a player cannot make a valid move on their turn, they lose...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 486 - Predict the Winner

LeetCode Problem 486 Difficulty: 🟡 Medium Topics: Array, Math, Dynamic Programming, Recursion, Game Theory Solution Problem Understanding The problem describes a two-player game played on an integer array. Players alternate turns, and during each turn a player may only take a number from one of the two ends of the array. The chosen value is added to that player's score, and the element is removed from the array. The game...

Practice › LeetCode › LeetCode 20xx ›

LeetCode 2029 - Stone Game IX

LeetCode Problem 2029 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Counting, Game Theory Solution Problem Understanding The problem describes a turn-based game between Alice and Bob with a row of stones, each having a numeric value. On each turn, a player removes any stone of their choice. The game has a losing condition based on the sum of removed stones: if the cumulative sum of all removed stones becomes divisible...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1510 - Stone Game IV

LeetCode Problem 1510 Difficulty: 🔴 Hard Topics: Math, Dynamic Programming, Game Theory Solution Problem Understanding This problem is a two-player combinatorial game problem where Alice and Bob alternately remove stones from a single pile. On each turn, a player may remove any positive number of stones that is a perfect square (1, 4, 9, 16, etc.) as long as that number does not exceed the current pile size. The game...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1563 - Stone Game V

LeetCode Problem 1563 Difficulty: 🔴 Hard Topics: Array, Math, Dynamic Programming, Game Theory Solution Problem Understanding In this game, we are given an array stoneValue where each element represents the value of a stone. The stones are arranged in a row, and Alice repeatedly splits the current row into two non-empty contiguous parts. After Alice chooses a split point, Bob compares the sums of the left and right parts: If...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1406 - Stone Game III

LeetCode Problem 1406 Difficulty: 🔴 Hard Topics: Array, Math, Dynamic Programming, Game Theory Solution Problem Understanding In this game, two players, Alice and Bob, take turns removing stones from the beginning of a row. Each stone has an integer value, which may be positive, zero, or negative. On each turn, a player may take exactly 1, 2, or 3 stones from the front of the remaining row. The score of...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1686 - Stone Game VI

LeetCode Problem 1686 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting, Heap (Priority Queue), Game Theory Solution This is a long, structured technical guide with multiple substantial sections, worked examples, code, tables, and test coverage. To make sure it is complete and properly formatted according to your rules, I should generate it as a document/canvas rather than risk truncation in chat. I can produce the full guide for LeetCode 1686...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 375 - Guess Number Higher or Lower II

LeetCode Problem 375 Difficulty: 🟡 Medium Topics: Math, Dynamic Programming, Game Theory Solution Problem Understanding This problem is a variant of the classic number guessing game with a twist: incorrect guesses cost money equal to the value guessed, and the goal is to minimize the maximum cost required to guarantee a win . In other words, we want a strategy that ensures we will always find the correct number while...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1690 - Stone Game VII

LeetCode Problem 1690 Difficulty: 🟡 Medium Topics: Array, Math, Dynamic Programming, Game Theory Solution Problem Understanding This problem describes a two player game played on an array of stones. Each stone has a positive integer value, and the stones are arranged in a row. Alice moves first, and on every turn the current player removes either the leftmost stone or the rightmost stone. The scoring rule is the key detail...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1025 - Divisor Game

LeetCode Problem 1025 Difficulty: 🟢 Easy Topics: Math, Dynamic Programming, Brainteaser, Game Theory Solution Problem Understanding The problem describes a two-player turn-based game between Alice and Bob. The game starts with a single integer n written on a chalkboard. Alice always takes the first turn. On each turn, the current player must choose a positive integer x such that: 0 < x < n x divides n evenly, meaning n...

Practice › LeetCode › LeetCode (archived) › LeetCode 08xx ›

LeetCode 843: Guess the Word

Problem Restatement We are given a list of unique strings words . Each word has length 6 . One word from the list is chosen as the secret word. We can call: master.guess(word) This returns: Return value Meaning -1 The guessed word is not in the word list 0 to 6 Number of positions where the guessed word matches the secret word We must find the secret word within at...

Practice › LeetCode › LeetCode (archived) › LeetCode 09xx ›

LeetCode 913: Cat and Mouse

Problem Restatement We are given an undirected graph. Mouse starts at node 1 . Cat starts at node 2 . The hole is node 0 . Mouse moves first. Then Cat moves. They alternate turns. On each turn, the current player must move along one graph edge. Cat is not allowed to move into node 0 . The game ends in one of three ways: Result Condition Mouse wins Mouse...

Practice › LeetCode › LeetCode (archived) › LeetCode 08xx ›

LeetCode 810: Chalkboard XOR Game

Problem Restatement We are given an array nums of non-negative integers written on a chalkboard. Alice and Bob take turns erasing exactly one number. Alice moves first. After a player erases a number, if the XOR of all remaining numbers becomes 0 , that player loses. There is one special rule: if a player starts their turn and the XOR of all numbers is already 0 , that player wins...

Practice › LeetCode › LeetCode (archived) › LeetCode 08xx ›

LeetCode 877: Stone Game

Problem Restatement Alice and Bob play a game with an even number of stone piles arranged in a row. Each pile has a positive number of stones. Alice moves first. On each turn, a player must take one entire pile from either the left end or the right end of the row. The game ends when all piles are taken. The player with more stones wins. The total number of...

Practice › LeetCode › LeetCode (archived) › LeetCode 03xx ›

LeetCode 375: Guess Number Higher or Lower II

Problem Restatement We are playing a guessing game. A number is picked from: 1 to n Each time we guess a number x : Result Cost Guess is correct Pay 0 Guess is wrong Pay x dollars If the guess is wrong, we are told whether the hidden number is higher or lower, then we continue guessing in the remaining range. We need to return the minimum amount of money...

Practice › LeetCode › LeetCode (archived) › LeetCode 04xx ›

LeetCode 464: Can I Win

Problem Restatement We are given two integers: maxChoosableInteger desiredTotal There are numbers from 1 to maxChoosableInteger . Two players take turns choosing one unused number. Each chosen number is added to a running total. The player who makes the running total reach or exceed desiredTotal wins. Both players play optimally. We need to return whether the first player can force a win. The official problem asks whether the first player...

Practice › LeetCode › LeetCode (archived) › LeetCode 02xx ›

LeetCode 294: Flip Game II

Problem Restatement We are given a string currentState containing only: "+" "-" Two players take turns. On each turn, a player chooses two consecutive plus signs: "++" and flips them into: "--" The player who cannot make a move loses. We start first. We need to return whether the starting player can guarantee a win. The source statement defines the game this way: players take turns flipping two consecutive "++"...

Practice › LeetCode › LeetCode (archived) › LeetCode 02xx ›

LeetCode 292: Nim Game

Problem Restatement We are given a heap with n stones. Two players take turns removing stones from the heap. On each turn, a player must remove: 1, 2, or 3 stones. You go first. The player who removes the last stone wins. We need to return True if we can force a win assuming both players play optimally. Otherwise, return False . The source statement gives the same rules: there...

Practice › LeetCode › LeetCode (archived) › LeetCode 04xx ›

LeetCode 486: Predict the Winner

Problem Restatement We are given an integer array nums . Two players play a game with this array. Player 1 moves first. On each turn, the current player must take one number from either end of the array. That means the player may take either the leftmost number or the rightmost number. The chosen number is added to that player's score, and the number is removed from the array. Both...

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91. Game Theory, Economics, Social and Behavioral Sciences

This volume studies strategic interaction, economic systems, and quantitative models of behavior. It connects optimization, probability, and equilibrium theory. Part I. Foundations of Game Theory Chapter 1. Strategic Games 1.1 Players and strategies 1.2 Payoff functions 1.3 Normal form games 1.4 Examples 1.5 Applications Chapter 2. Nash Equilibrium 2.1 Definition 2.2 Existence results 2.3 Mixed strategies 2.4 Computation 2.5 Examples Chapter 3. Extensive Form Games 3.1 Game trees 3.2 Perfect...

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LeetCode 3828 - Final Element After Subarray Deletions

LeetCode 1908 - Game of Nim

LeetCode 1872 - Stone Game VIII

LeetCode 3227 - Vowels Game in a String

LeetCode 1927 - Sum Game

LeetCode 3222 - Find the Winning Player in Coin Game

LeetCode 2038 - Remove Colored Pieces if Both Neighbors are the Same Color

LeetCode 2868 - The Wording Game

LeetCode 3283 - Maximum Number of Moves to Kill All Pawns

LeetCode 1140 - Stone Game II

LeetCode 292 - Nim Game

LeetCode 877 - Stone Game

LeetCode 1561 - Maximum Number of Coins You Can Get

LeetCode 810 - Chalkboard XOR Game

LeetCode 464 - Can I Win

LeetCode 1728 - Cat and Mouse II

LeetCode 913 - Cat and Mouse

LeetCode 2005 - Subtree Removal Game with Fibonacci Tree

LeetCode 843 - Guess the Word

LeetCode 294 - Flip Game II

LeetCode 486 - Predict the Winner

LeetCode 2029 - Stone Game IX

LeetCode 1510 - Stone Game IV

LeetCode 1563 - Stone Game V

LeetCode 1406 - Stone Game III

LeetCode 1686 - Stone Game VI

LeetCode 375 - Guess Number Higher or Lower II

LeetCode 1690 - Stone Game VII

LeetCode 1025 - Divisor Game

LeetCode 843: Guess the Word

LeetCode 913: Cat and Mouse

LeetCode 810: Chalkboard XOR Game

LeetCode 877: Stone Game

LeetCode 375: Guess Number Higher or Lower II

LeetCode 464: Can I Win

LeetCode 294: Flip Game II

LeetCode 292: Nim Game

LeetCode 486: Predict the Winner

91. Game Theory, Economics, Social and Behavioral Sciences