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# Patterns for Problem Solving
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## Pattern: Two Pointers
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**Description:** This method uses two pointers to traverse an array or a list from different ends or directions.
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**Usage:** It's particularly useful for ordered data structures, where we can make intelligent decisions based on the position of the pointers.
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**Problems:** 'Pair with Target Sum', 'Remove Duplicates', 'Squaring a Sorted Array'.
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**Description:** This method uses two pointers to traverse an array or a list from different ends or directions.
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**Usage:** It's particularly useful for ordered data structures, where we can make intelligent decisions based on the position of the pointers.
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**Problems:** 'Pair with Target Sum', 'Remove Duplicates', 'Squaring a Sorted Array'.
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## Pattern: Island (Matrix Traversal)
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**Description:** It involves traversing a matrix to find 'islands' or contiguous groups of elements.
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**Usage:** It's generally used in grid-based problems, especially when we need to group connected elements together.
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**Problems:** 'Number of Islands', 'Max Area of Island', 'Flood Fill'.
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**Description:** It involves traversing a matrix to find 'islands' or contiguous groups of elements.
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**Usage:** It's generally used in grid-based problems, especially when we need to group connected elements together.
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**Problems:** 'Number of Islands', 'Max Area of Island', 'Flood Fill'.
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## Pattern: Fast & Slow Pointers
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**Description:** In this method, two pointers move at different speeds in a data structure.
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**Usage:** It is commonly used to detect cycles in a structure, find middle elements, or to solve other specific problems related to linked lists.
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**Problems:** 'LinkedList Cycle', 'Middle of the LinkedList', 'Palindrome LinkedList'.
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**Description:** In this method, two pointers move at different speeds in a data structure.
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**Usage:** It is commonly used to detect cycles in a structure, find middle elements, or to solve other specific problems related to linked lists.
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**Problems:** 'LinkedList Cycle', 'Middle of the LinkedList', 'Palindrome LinkedList'.
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## Pattern: Sliding Window
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**Description:** This pattern involves creating a 'window' into the data structure and then moving that window around to gather specific information.
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**Usage:** Mostly used in array or list-based problems where you need to find a contiguous subset that fulfills certain conditions.
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**Problems:** 'Maximum Sum Subarray of Size K', 'Smallest Subarray with a given sum', 'Longest Substring with K Distinct Characters'.
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**Description:** This pattern involves creating a 'window' into the data structure and then moving that window around to gather specific information.
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**Usage:** Mostly used in array or list-based problems where you need to find a contiguous subset that fulfills certain conditions.
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**Problems:** 'Maximum Sum Subarray of Size K', 'Smallest Subarray with a given sum', 'Longest Substring with K Distinct Characters'.
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## Pattern: Merge Intervals
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**Description:** This pattern involves merging overlapping intervals.
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**Usage:** Often used in problems involving time intervals, ranges, or sequences.
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**Problems:** 'Merge Intervals', 'Insert Interval', 'Intervals Intersection'.
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**Description:** This pattern involves merging overlapping intervals.
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**Usage:** Often used in problems involving time intervals, ranges, or sequences.
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**Problems:** 'Merge Intervals', 'Insert Interval', 'Intervals Intersection'.
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## Pattern: Cyclic Sort
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**Description:** This pattern involves sorting an array containing numbers in a given range.
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**Usage:** It's useful in situations where the data involves a finite range of natural numbers.
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**Problems:** 'Cyclic Sort', 'Find the Missing Number', 'Find all Duplicates'.
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**Description:** This pattern involves sorting an array containing numbers in a given range.
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**Usage:** It's useful in situations where the data involves a finite range of natural numbers.
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**Problems:** 'Cyclic Sort', 'Find the Missing Number', 'Find all Duplicates'.
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## Pattern: In-place Reversal of a Linked List
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**Description:** This pattern involves reversing elements of a linked list in-place.
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**Usage:** It's generally used when reversing a sequence without using extra space.
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**Problems:** 'Reverse a LinkedList', 'Reverse a Sub-list', 'Reverse Every K-element Sub-list'.
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**Description:** This pattern involves reversing elements of a linked list in-place.
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**Usage:** It's generally used when reversing a sequence without using extra space.
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**Problems:** 'Reverse a LinkedList', 'Reverse a Sub-list', 'Reverse Every K-element Sub-list'.
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## Pattern: Tree Breadth First Search
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**Description:** This pattern involves level-by-level traversal of a tree.
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**Usage:** It's used when we need to traverse a tree or graph in a level-by-level (breadth-first) manner.
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**Problems:** 'Level Order Traversal', 'Reverse Level Order Traversal', 'Zigzag Traversal'.
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**Description:** This pattern involves level-by-level traversal of a tree.
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**Usage:** It's used when we need to traverse a tree or graph in a level-by-level (breadth-first) manner.
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**Problems:** 'Level Order Traversal', 'Reverse Level Order Traversal', 'Zigzag Traversal'.
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## Pattern: Tree Depth First Search
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**Description:** This pattern involves traversing a tree or graph depth-wise before visiting siblings or neighbors.
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**Usage:** It's used when you need to search deeper into a tree/graph first before going across.
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**Problems:** 'Binary Tree Path Sum', 'All Paths for a Sum', 'Count Paths for a Sum'.
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**Description:** This pattern involves traversing a tree or graph depth-wise before visiting siblings or neighbors.
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**Usage:** It's used when you need to search deeper into a tree/graph first before going across.
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**Problems:** 'Binary Tree Path Sum', 'All Paths for a Sum', 'Count Paths for a Sum'.
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## Pattern: Two Heaps
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**Description:** This pattern involves using two heaps to divide a set of numbers into two parts.
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**Usage:** It's useful when you need to find median numbers in a sequence, or other similar problems.
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**Problems:** 'Find the Median of a Number Stream', 'Sliding Window Median', 'Maximize Capital'.
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**Description:** This pattern involves using two heaps to divide a set of numbers into two parts.
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**Usage:** It's useful when you need to find median numbers in a sequence, or other similar problems.
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**Problems:** 'Find the Median of a Number Stream', 'Sliding Window Median', 'Maximize Capital'.
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## Pattern: Subsets
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**Description:** This pattern involves generating all subsets of a set.
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**Usage:** It's helpful for solving problems that require exploring all subsets of a given set.
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**Problems:** 'Subsets', 'Subsets With Duplicates', 'Permutations'.
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**Description:** This pattern involves generating all subsets of a set.
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**Usage:** It's helpful for solving problems that require exploring all subsets of a given set.
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**Problems:** 'Subsets', 'Subsets With Duplicates', 'Permutations'.
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## Pattern: Modified Binary Search
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**Description:** This is a tweaked version of the binary search algorithm.
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**Usage:** It's used when a simple binary search isn't sufficient, like finding a number in a bitonic array.
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**Problems:** 'Order-agnostic Binary Search', 'Ceiling of a Number', 'Next Letter'.
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**Description:** This is a tweaked version of the binary search algorithm.
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**Usage:** It's used when a simple binary search isn't sufficient, like finding a number in a bitonic array.
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**Problems:** 'Order-agnostic Binary Search', 'Ceiling of a Number', 'Next Letter'.
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## Pattern: Top 'K' Elements
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**Description:** This pattern is used to find the top 'k' elements among a certain category.
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**Usage:** It's commonly used in problems involving sorting, searching, and in heap data structures.
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**Problems:** 'Top K Frequent Numbers', 'Kth Largest Number in a Stream', 'Top K Frequent Elements'.
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**Description:** This pattern is used to find the top 'k' elements among a certain category.
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**Usage:** It's commonly used in problems involving sorting, searching, and in heap data structures.
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**Problems:** 'Top K Frequent Numbers', 'Kth Largest Number in a Stream', 'Top K Frequent Elements'.
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## Pattern: Bitwise XOR
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**Description:** This pattern involves the use of Bitwise XOR to solve various array-based problems.
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**Usage:** It's used when we need to manipulate and compare bits directly.
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**Problems:** 'Single Number', 'Two Single Numbers', 'Complement of Base 10 Number'.
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**Description:** This pattern involves the use of Bitwise XOR to solve various array-based problems.
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**Usage:** It's used when we need to manipulate and compare bits directly.
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**Problems:** 'Single Number', 'Two Single Numbers', 'Complement of Base 10 Number'.
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## Pattern: Backtracking
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**Description:** This pattern involves exploring all possible solutions and then backtracking to correct the course whenever you're on the wrong path.
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**Usage:** It's typically used for solving complex combinatorial problems, puzzles, and games.
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**Problems:** 'Sudoku Solver', 'N-Queens', 'Generate Parentheses'.
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**Description:** This pattern involves exploring all possible solutions and then backtracking to correct the course whenever you're on the wrong path.
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**Usage:** It's typically used for solving complex combinatorial problems, puzzles, and games.
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**Problems:** 'Sudoku Solver', 'N-Queens', 'Generate Parentheses'.
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## Pattern: 0/1 Knapsack (Dynamic Programming)
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**Description:** This pattern deals with problems where items have different values and weights, and we need to determine the maximum value we can carry.
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**Usage:** It's typically used in optimization problems, especially those involving physical constraints.
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**Problems:** '0/1 Knapsack', 'Equal Subset Sum Partition', 'Subset Sum'.
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**Description:** This pattern deals with problems where items have different values and weights, and we need to determine the maximum value we can carry.
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**Usage:** It's typically used in optimization problems, especially those involving physical constraints.
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**Problems:** '0/1 Knapsack', 'Equal Subset Sum Partition', 'Subset Sum'.
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## Pattern: Topological Sort (Graph)
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**Description:** This pattern involves sorting nodes in a directed graph in a specific order where the preceding node comes before the following node.
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**Usage:** It's used for scheduling problems and in scenarios where order needs to be imposed on how you process nodes.
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**Problems:** 'Task Scheduling Order', 'All Tasks Scheduling Orders', 'Alien Dictionary'.
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**Description:** This pattern involves sorting nodes in a directed graph in a specific order where the preceding node comes before the following node.
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**Usage:** It's used for scheduling problems and in scenarios where order needs to be imposed on how you process nodes.
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**Problems:** 'Task Scheduling Order', 'All Tasks Scheduling Orders', 'Alien Dictionary'.
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## Pattern: K-way Merge
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**Description:** This pattern involves merging 'k' sorted lists.
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**Usage:** It's typically used in problems involving lists, where merging is required.
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**Problems:** 'Merge K Sorted Lists', 'Kth Smallest Number in M Sorted Lists', 'Smallest Number Range'.
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**Description:** This pattern involves merging 'k' sorted lists.
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**Usage:** It's typically used in problems involving lists, where merging is required.
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**Problems:** 'Merge K Sorted Lists', 'Kth Smallest Number in M Sorted Lists', 'Smallest Number Range'.
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## Pattern: Monotonic Stack
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**Description:** This pattern involves using a stack to maintain a monotonic (either entirely non-increasing or non-decreasing) order of elements.
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**Usage:** It's often used for solving problems where you need to find the next greater or smaller elements.
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**Problems:** 'Next Greater Element', 'Next Smaller Element', 'Largest Rectangle in Histogram'.
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**Description:** This pattern involves using a stack to maintain a monotonic (either entirely non-increasing or non-decreasing) order of elements.
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**Usage:** It's often used for solving problems where you need to find the next greater or smaller elements.
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**Problems:** 'Next Greater Element', 'Next Smaller Element', 'Largest Rectangle in Histogram'.
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## Pattern: Multi-threaded
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**Description:** This pattern involves designing algorithms that can execute multiple threads in parallel.
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**Usage:** It's used in situations where a task can be divided into independent sub-tasks that can execute concurrently.
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**Problems:** 'Invert Binary Tree', 'Binary Search Tree Iterator', 'Same Tree'.
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**Description:** This pattern involves designing algorithms that can execute multiple threads in parallel.
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**Usage:** It's used in situations where a task can be divided into independent sub-tasks that can execute concurrently.
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**Problems:** 'Invert Binary Tree', 'Binary Search Tree Iterator', 'Same Tree'.
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## Pattern: Union Find
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**Description:** Union Find, also known as Disjoint Set Union (DSU), is a data structure that keeps track of a partition of a set into disjoint subsets.
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**Usage:** This pattern is particularly useful for problems where we need to find whether 2 elements belong to the same group or need to solve connectivity-related problems in a graph or tree.
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**Problems:** 'Graph Redundant Connection', 'Number of Provinces', 'Is Graph Bipart
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**Description:** Union Find, also known as Disjoint Set Union (DSU), is a data structure that keeps track of a partition of a set into disjoint subsets.
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**Usage:** This pattern is particularly useful for problems where we need to find whether 2 elements belong to the same group or need to solve connectivity-related problems in a graph or tree.
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**Problems:** 'Graph Redundant Connection', 'Number of Provinces', 'Is Graph Bipart'.

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