- Linear vs non-linear
- Array vs linked list
- Stack vs queue
- Linear vs Circular Queue
- Linear Search vs Binary Search
- Singly Linked List vs Doubly Linked List
- Binary vs Binary Search Tree
- Tree vs Graph
- Binary Search tree vs AVL tree
- Red Black Tree vs AVL tree
- B tree vs B+ tree
- Quick Sort vs Merge Sort
- BFS vs DFS
- Stack vs Heap
- Bubble sort vs. Selection sort
- Stack vs Array
- Full Binary Tree vs Complete Binary Tree
- Binary Tree vs B Tree
- Primitive vs non-primitive data structure
- Data types vs data structure

- Trie Data Structure
- Heap Data Structure
- Splay Tree
- Fundamental of the DS
- Hash Table
- Preorder Traversal
- Tree Traversal
- Implementation of Queue using Stacks
- Implementation of Stack using Queue
- Binomial Heap
- Postorder Traversal
- Sparse Matrix
- Detect loop in a Linked list
- Inorder Traversal
- Convert Infix to Postfix notation
- Convert infix to prefix notation
- Conversion of Prefix to Postfix expression
- Conversion of Postfix to Prefix expression
- Remove the loop in a Linked List
- Implement two stacks in an array
- Reverse a stack using recursion
- Detect cycle in a directed graph
- Optimal Binary Search Tree
- Priority Queue using Linked list
- Balanced Binary Search Tree
- Boundary Traversal of Binary tree
- Diagonal Traversal of Binary Tree
- Vertical Traversal of a Binary tree
- Graph Algorithms
- Time Complexity of Sorting Algorithms
- Applications of Stack in Data Structure
- Dictionary Data Structure
- Structured Data and Unstructured Data
- List Data Structure
- Types of Tree in Data Structure
- Abstract data type in data structure
- Disjoint set data structure
- Dynamic Data Structure
- Hash Function in Data Structure
- Complete Binary Tree
- Threaded Binary Tree
- Diameter of Binary Tree
- Height of Binary Tree
- Inorder Tree Traversal without Stack
- Enumeration of Binary Trees
- Maximum Width of a Binary Tree
- Types of Graph in Data Structure
- Primitive Data Type
- Semi-Structured Data
- Advance Data Structures
- Sort an Array of 0's, 1's, and 2's
- Stock Span Problem
- Implementation of Deque by Circular Array
- Rotate Operation in Linked List
- Subarray with given sum
- Self-organizing List
- Unrolled Linked List
- Types of Sparse Matrices
- Application of Linked List
- Topological Sorting
- Ternary Search Tree
- Stock Span Problem
- Treap Data Structure
- Quicksort on Doubly Linked List
- Inversion count
- Expression tree in DS
- Garbage Collection in DS
- Merge Sort on Doubly Linked List
- Sort Stack using Recursion
- LIFO Approach in data structure
- Big O Notation in DS
- Binary Tree Traversal in DS
- Queue Operations in DS
- What is a Non-Linear Data Structure
- FIFO Approach in data structure
- What are connected graphs in data structure
- Which Python data structure is immutable
- Which data structure is used by map
- What is iteration in data structure
- What are linear search and binary search in data structure
- Hash Table vs STL Map
- Recaman's Sequence
- Maximum area rectangle created by selecting four sides from an array
- Maximum number of distinct nodes in a root-to-leaf path
- Hashing - Open Addressing for Collision Handling
- Introduction to Hashing
- Separate chaining for Collision Handling
- Check if a given array contains duplicate elements within k distance from each other
- Given an array A[] and a number x, check for pair in A[] with sum as x (aka Two Sum)
- Find number of Employees Under every Manager
- Union and Intersection of two Linked Lists
- Kth Largest element in an array
- Sort an almost-sorted, k-sorted or nearly-sorted array
- Fibonacci Heap
- Find whether an array is subset of another array
- Print a Binary Tree in Vertical Order
- Tournament Tree (Winner Tree)
- Lazy Propagation in Segment Tree
- Segment Tree - Range Minimum Query
- Segment Tree - Sum of given Range
- 2-3 Trees (Search, Insertion, and Deletion)
- Print kth least significant bit of a number
- Add two numbers represented by linked lists
- Adding one to the number represented as array of digits
- Find precedence characters form a given sorted dictionary
- Check if any anagram of a string is palindrome or not
- Minimum Insertions to form a Palindrome
- Allocate Minimum Number of Pages
- Assembly Line Scheduling
- Breadth First Search or BFS for a Graph
- Find an element in array such that sum of the left array is equal to the sum of the right array
- Bridges in a Graph
- Bubble Sort in JavaScript
- Burn the Binary tree from the Target node
- Lowest Common Ancestor in a Binary Search Tree
- Types of Hash Functions in C
- Implement Dynamic Deque using Templates Class and a Circular Array
- Iterative Depth First Traversal of Graph
- Linked List Data Structure in C++ With Illustration
- Reverse a Linked List in Groups of Given Size
- Reverse Alternate K nodes in a Singly Linked List
- When should I use a List vs a LinkedList
- Why is deleting in a Singly Linked List O(1)
- Construct Full Binary Tree using its Preorder Traversal and Preorder Traversal of its Mirror Tree
- Find Relative Complement of two Sorted Arrays
- Handshaking Lemma and Interesting Tree Properties -DSA
- How to Efficiently Implement kStacks in a Single Array
- Write C Functions that Modify Head Pointer of a Linked List
- Introduction to Ant Colony Optimization
- What is Array
- The practical Byzantine Fault Tolerance (pBFT)
- Applications of Queue Data Structure
- Line Graph
- Symmetric Binary Tree
- AVL Tree Advantages
- AVL Tree Time Complexity
- Merge Two Binary Trees
- Stack Operations in Data Structure
- Self-Balancing Binary Search Trees
- Sliding Window Maximum (Maximum of all Subarrays of size K)
- AVL Trees Operations
- Limitations of Stack in Data Structures
- Representation of stack in data structure
- Advantages of Threaded Binary Tree
- Serialize and Deserialize a Binary Tree
- Application of Binary Tree
- AVL Tree Applications
- B Tree Visualization
- Properties of AVL Trees
- Push and Pop Operation in Stack in Data Structure
- Binary Search Tree Implementation
- Find Maximum Sum by Replacing the Subarray in Given Range
- Find The Number N, Where (N+X) Divisible By Y And (N-Y) Divisible By X
- Find Values of P and Q Satisfying the Equation N = P^2.Q
- What is the Balance Factor of AVL Tree
- AVL Tree Implementation in Golang
- Concatenation of two Linked Lists in O(1) time
- Find Minimum Area of Rectangle Formed from Given Shuffled Coordinates
- Find the Length of Maximum Path in Given Matrix for Each Index
- How to Parse an Array of Objects in C++ Using RapidJson
- Largest BST in Binary Tree
- How to Print String Literal and Qstring With Qdebug in C++
- Properties of Binary Tree
- Right View of Binary Tree
- Strict Binary Tree
- Difference between Comb Sort and Shell Sort
- Full Binary Tree
- Left View of a Binary Tree
- Level order Traversal in a Binary Tree
- Lowest Common Ancestor of a Binary Tree
- Top View of a Binary Tree
- Types of Binary Trees
- B Tree Insertion
- Evaluation of a Postfix notation
- B+ Tree Insertion
- Bottom View of a Binary Tree
- AVL Tree Program in C
- B Tree Applications
- B Tree Properties
- How to Search, Insert, and Delete in an Unsorted Array
- Count Non-Leaf Nodes in a Binary Tree
- Get the Level of a Given Key in a Binary Tree
- Double Ended Priority Queue
- B+ Tree Deletion
- B+ Tree Insertion
- Checking for the Mirror Images in the Binary Trees
- Count Non-Leaf Nodes in a Binary Tree
- Get a Parent Binary Tree
- Get All Descendants of the Binary Tree Element
- Get the Level of a Given Key in a Binary Tree
- Flatten Binary Tree to Linked List
- Formula to Find a Level of the Node in a Binary Tree
- Substring with Maximum Number of Vowels of Given Length (k)
- Flatten Binary Tree to Sorted Linked List
- Floor and Ceiling in Binary Search Tree
- Find Level in a Binary Tree with Max Sum
- Find kth Smallest Element in a Binary Search Tree
- Find Next Greater Element in Binary Tree
- Hashing in Data Structure
- Primitive Data Structure
- Find if Binary Tree Satisfies Balanced Height Property
- Find the Largest Perfect Binary Tree in a Given Tree
- Find Immediate Parents of Two Nodes in a Binary Tree
- Applications, Advantages and Disadvantages of Circular Doubly linked List
- Sorting Techniques in Data Structures
- Find Clockwise Array in Binary Search Tree
- Find Duplicate Subtrees in Binary Tree
- Find the Index of the Number Using a Binary Tree
- Find the In-Order Successor of a Node in a Binary Tree
- Reversing a Queue
- Different Types of Stack Operations
- Time Complexity in Data Structure
- Arrays are best Data Structure
- Dynamic memory allocation in Data Structure
- Application of Data Structure
- Applications of Tree in Data Structure
- How to Check if a Binary Number is Divisible by 3
- Stock Buy and Sell Problem
- Find Minimum in Rotated Sorted Array
- Interpolation Search vs. Binary Search
- Boggle (find all possible words in a board of characters)
- Difference Between Prim's and Kruskal's algorithm
- Interpolation Search
- Quick Sort Using Hoare's Partition
- Longest common substring
- Longest Repeated Substring
- Substring Check
- Clone a Binary Tree with Random Pointers
- How to efficiently implement k stacks in a single array
- Kasai's algorithm for construction of LCP array from Suffix array
- Strassen's Matrix Multiplication
- suffix array introduction
- Suffix Array nLogn Algorithm
- Suffix tree introduction
- Binary indexed tree
- Given a n x n square matrix, find the sum of all sub-squares of size k x k
- Inplace MxN size matrix transpose
- longest palindrome substring
- Maximum Size Square Sub-matrix with all 1s
- Maximum Sum Rectangle in a 2D Matrix
- Printing All Elements in Sorted Order from Row and Column Wise Sorted Matrix
- Arraylist vs linked list
- Diameter of an N-ary Tree
- Generic Trees (N-ary Trees)
- Level Order Traversal of N-ary Tree
- Mirror of n-ary Tree
- Serialize and Deserialize an N-ary Tree
- Sum of all elements of N-ary Tree
- The Great Tree-List Recursion Problem
- Two dimensional Binary Indexed Tree or Fenwick Tree
- Binary Indexed Tree Range Updates and Point Queries
- Binary Indexed Tree Range Updates and Range Queries
- Closest greater or same value on left side for every element in array
- Construct an array from its pair-sum array
- Equilibrium index of an array
- Fermat's Factorization Method in Java
- Find a triplet that sum to a given value in an array
- Find k numbers with most occurrences in the given array
- Find maximum value of Sum(i*arr[i]) with only rotations on given array allowed
- Handshaking Lemma and Interesting Tree Properties
- Implementation of Dynamic Segment Trees with Poly Hash Tables
- Majority Element
- Maximum equilibrium sum in an array
- Maximum profit by buying and selling a share at most twice
- Median in a stream of integers (running integers)
- Merge Sort Tree for Range Order Statistics
- Merge two sorted arrays with O(1) extra space
- Minimum increment by k operations to make all elements equal
- Minimum number of jumps to reach end
- MO's Algorithm
- Search in a row-wise and column-wise sorted matrix
- Smallest subarray with sum greater than a given value
- Sparse Table
- Square Root (Sqrt) Decomposition Algorithm
- Two Pointers Technique
- Compressed segment trees and merging sets in O(N*logN)
- Intersection of Linked List
- Intersection Point in Y shaped linked list
- Make Array Zero By Subtracting Equal Amounts In Java
- Maximum Sum Pair with Equal Highest Digits
- Minimum Possible value of |ai + aj - k| for given array and k
- Tango Tree Data Structure
- Check if two arrays are equal or not
- Construct BST from its given level order traversal
- Elements to be added so that all elements of a range are present in the array
- Find Missing Elements in Range
- K-th Largest Sum Contiguous Subarray
- Minimum number of subsets with distinct elements
- Minimum product of k integers in an array of positive integers
- The non-overlapping sum of two sets
- Palindrome substring queries
- Recaman's Sequence
- The sum of Elements Between k1th and k2th smallest elements
- Print Matrix in a Snake Pattern
- An Interesting Method to Generate Binary Numbers from 1 to n
- Bottom View of a Binary Tree
- Circular List Application
- Deleting a Node in a Linked List
- Diameter of a Binary Tree
- Find distance between two nodes of a Binary Search Tree
- Inorder Tree Traversal without Recursion
- Inorder Tree Traversal without recursion and stack!
- Maximum product of indexes of next greater on left and right
- Print Left View of a Binary Tree
- Remove all leaf nodes from the binary search tree
- Sort a stack using a temporary stack
- Split a Circular List into 2 Halves
- Check given array of size n can represent BST of n levels or not
- Construct a linked list from 2D matrix
- In place, convert BST into a Min-Heap
- Polish and Reverse Polish Notation
- Suffix Trees in data structure
- Weight Balanced Binary Tree
- Transform a BST to greater sum tree
- Vertical order traversal of Binary Tree using Map
- Application of heap tree
- Construct a linked list from 2D matrix
- Define Abstract Data Type in Data Structure
- Detect and Remove Loop in a Linked List
- Difference Between a Tree and a Forest in Data Structures
- Difference between bubble sort and merge sort
- Difference between merge sort and quick sort
- Explain double ended queue in detail
- Find the median from running data stream
- Flattening a Linked List
- Generate All Subarrays
- Heap memory vs. stack memory
- Huffman encoding
- Huffman Tree in Data Structure
- Implementation of Graph in JavaScript
- K-D Tree in Data Structures
- Knapsack Problem in Data Structure
- Largest Sum Contiguous Subarray (Kadane's Algorithm)
- Multiway Trees in Data Structures
- Optimal binary search tree in data structure
- polynomial addition in data structure
- Postfix deferred queue
- Properties of tree in data structure
- Recurrence Relation of Merge Sort
- Recursive Bubble Sort
- RSS linked list
- Search in a Rotated Sorted Array
- Sort an array of 0s, 1s and 2s | Dutch National Flag problem
- Assign directions to edges so that the directed graph remains acyclic
- Dependency Graph
- Diameter of an N-ary tree
- Height of n-ary tree if parent array is given
- Introduction to Heavy Light Decomposition
- LCA in a binary tree using RMQ
- Number of Siblings of a given node in n-arr tree
- Number of ways to traverse an N-arr
- XOR Linked List - A Memory Efficient Doubly Linked List
- Callback Queue
- Inorder Predecessor and Successor in a Binary Search Tree
- What is Internal Sorting
- Block Swap Algorithm for Array Rotation in Python
- CHECK FOR BALANCED BRACKETS IN AN EXPRESSION (WELL FORMEDNESS)
- Count pairs from two BSTs whose sum is equal to given value x
- Counting Inversions Problem in Data Structure
- Differences between Insertion Sort and Selection Sort
- LEFTIST TREE / LEFTIST HEAP
- Find if there is a triplet in a balanced bst that adds to zero
- Find the Maximum English Letter Present in Both Lowercase and Uppercase
- K-way Merge Sort
- Perfect Binary Trees
- Reverse Sort
- Scapegoat Trees
- Stack Organisation
- Time Complexity of using heap
- Two-way merge sort
- Validity of a given Tic-Tac-Toe board configuration
- Weighted Prefix Search
- Binary Tree to CDLL
- Check if a Binary Tree is a Subtree of Another Binary Tree
- Check if the Given String of Words can be Formed from Words Present in the Dictionary
- Count sort vs bucket sort
- FIFO vs LIFO approach in Programming
- If you are given two traversal sequences, can you construct the binary tree
- Linked List Deletion (Deleting a key at a given position)
- Mastering Bracket Problems for Competitive Programming
- Merge Overlapping Intervals
- MIRROR OF MATRIX ACROSS DIAGONAL
- Pair of strings having longest common prefix of maximum length in given array
- Print all Possible Combinations of Words from the Dictionary using Trie
- Segment Tree (Range Maximum Query with Node Update)
- Tree Vertex Splitting in data structure
- Why is Binary Heap Preferred over BST for Priority Queue
- Arrange Consonants and Vowels in a linked list
- Copy a linked list with next and arbit pointer
- Kahn's Algorithm vs DFS Approach: A Comparative Analysis
- Minimum flip required to make Binary Matrix symmetric
- Sorted insert for circular linked list
- C++ Program for Arranging Single Linked List in Alternate Odd and Even Nodes Order
- Reservoir sampling in C++
- 0/1 Knapsack using Least Cost Branch and Bound
- Merge K Sorted Linked Lists using Min Heap
- Number of elements greater than K in the range L to R using Fenwick Tree (Offline queries)
- Detect Cycle in Graph using DSU
- Merkle Tree and Hash Chain Data Structures with a difference
- Create a matrix with alternating rectangles of O and X
- Find the first non-repeating character from a stream of characters
- Find the first circular tour that visits all petrol pumps
- Find the tasks completed by soldiers based on their ranks
- K-th Largest Sum Contiguous Subarray
- Numbsubarrayer of elements less than or equal to a given number in a given
- Queries to add, remove and return the difference of maximum and minimum
- Time Complexity of building a heap
- Build linear type suffix
- Count of Valid Splits in a String
- Delete all occurrences of a given key in a linked list
- Design a data structure that supports insert, delete, search and getRandom in constant time
- Find the largest subarray with 0 sum
- Free Tree in Data Structures
- How to insert Strings into an AVL Tree
- Longest Consecutive Subsequence
- Merge two binary Max Heaps
- Secure Message Encoding
- Sort an almost sorted array
- Tree of Space - Locking and Unlocking N-Ary Tree
- Triply Linked list
- COUNT OF ZEROES
- Design a Chess Game
- Design a data structure that supports insert, delete, search and getRandom in constant time
- Design and Implement Special Stack Data Structure
- Enhancing Password Strength
- Enumeration of Binary Tree
- Eulerian and Hamiltonian path
- Fair Array Removal Indices
- Find the Absolute Difference between the Right View Sum of two Binary Trees
- Find the number of colored nodes according to given queries in a full Binary Tree
- Finding Minimum Steps in Special Binary Tree
- Finding the Largest Multiple of Three
- Flatten a binary tree into linked list
- General Tree (Each node can have arbitrary number of children) Level Order Traversal
- Generating the Maximum Number from Two Arrays
- Hashing and its Applications
- Islands in a graph using BFS
- Iterative Letter Combinations of a Phone Number
- K-way Merge Sort
- Maximize Total Score
- PERMUTED ROWS IN A MATRIX
- Remove extra edge from a BST
- Van Emde Boas Tree
- Which Minimum Spanning Tree Algorithm is better
- Ackermann Function
- BINARY TO SYMMETRIX
- INPLACE MATRIX TRANSPOSE
- Print all words matching a pattern in CamelCase Notation Dictionary
- Reduce the string by removing K consecutive identical characters
- Subtraction in Linked List
- TRANSITIONS OF MATRIX
- Blending vs Stacking
- Bloom Filters
- Count Array Pairs Divisible by k
- Counting Beautiful Numbers in a Specified Range
- Find the Closest Palindrome
- Minimizing water collection distance in javaT village
- Minimum Array Length After Pair Removals
- Nth even Fibonacci Sequence
- Persistent Data Structure
- Queue for Competitive Programming
- Recursively remove all adjacent duplicates
- Remove the letter to equalize the frequency
- Chocolate Distribution Problem
- Find out the person who got the ticket last problem in queue
- Product Array Puzzle
- MCQs on backtracking
- Design a data structure that supports insert, delete, search, and getRandom in constant time
- Assign directions to edges so that the directed graph remains acyclic
- Print the frequency of each character in Alphabetical order
- Check if a queue can be sorted into another queue using a stack
- Auto-complete feature using Trie
- Connect nodes at same level
- Construct Tree from Given Inorder and Preorder Traversals
- Decimal Equivalent of Binary Linked List
- How do you implement Stack using Priority Queue or Heap
- Introduction to Monotonic Stacks
- Minimum Initial Points to Reach Destination
- Print Ancestors of a given node in Binary Tree
- Priority Queue using Doubly Linked List
- Shortest distance between two cells in a matrix or grid
- Sort an Array in Wave Form
- Burn the binary tree starting from the target node
- Check for possible paths in the 2D Matrix
- Find Triplets with zero-sum
- Print a Given Matrix in Spiral form
- Alien Dictionary problem in dsa
- Array Pair Sum Divisibility Problem
- DIFFERENCE BETWEEN GREEDY AND DIVIDE AND CONQUER
- How do you check if a given array represents a heap
- LINKED LIST REVERSE
- MAXIMUM SIZE RECTANGLE
- Priority queue of pairs in C++ with ordering by first and second element
- Reversing Individual Words and Unveiling the Secrets of Histograms
- Sliding SubArray Beauty
- Two Pointer Technique
- UGLY NUMBERS IN DSA
- Check for Balanced Brackets in an expression
- Largest Number After Digit Swaps By Parity
- Minimize Deviation In Array
- Print a given matrix in spiral form
- Print unique rows in a given Boolean matrix
- Restrictive Candy Crush
- Search in a row wise and column wise sorted matrix
- SIP Stack
- Stacked Bar Chart
- Search Query Auto Complete
- Applications of the greedy algorithm
- Applications, Advantages and Disadvantages of Arrays
- Applications, Advantages and Disadvantages of Queue
- Applications, Advantages and Disadvantages of Stacks
- Floor and Ceil from a BST
- India Stack
- Next Higher Palindromic Numbers using the Same Set of Digits
- QuickSort on Singly Linked List
- Reverse a Number using Stacks
- Serialize and Deserialize an N-ary Tree
- Stack Pointer
- What is a K-connected Graph
- Append K Integers with Minimal Sum Problem
- Circular Linked Lists Introduction and Application
- Detect cycle in an undirected graph in C++
- Detect Cycle in Graph using DSU
- Find the maximum number of marked indices problem
- Generalized Suffix Tree
- Interval Tree
- Maximum Number of Tasks Assignment Problem
- Merge K Sorted Lists
- Triplet sum closest to given number
- Apply Operations To Maximize Frequency Score
- Difference between malloc and realloc
- Merge Sort on Singly Linked Lists
- Minimum Number Of Frogs Croaking
- Total Distance Travelled
- X Of A Kind In A Deck Of Cards
- Applications, Advantages and Disadvantages of Linked List
- Balls rolling in the maze
- Destroy Sequential Targets
- Difference Between Push and Pop in Stack
- Dynamic Programming (DP) on Grids
- Find all good strings problem in Data Structure
- Find Itinerary from a given list of tickets
- Height of n-ary tree if parent array is given
- Maximum Deletions on a String
- Reversal algorithm for Array rotation
- Reverse Pairs Problem in Data Structure
- String Hashing using the Polynomial Rolling Hash Function
- The Great Tree-List Recursion Problem
- Trapping of rainwater problem in Data Structure
- What Does Big O(N^2) Complexity Mean
- How to handle duplicates in Binary Search Tree
- Optimal cell in matrix to collect maximum coins
- Maximizing Chocolates in Grid using 2 robots
- Create a matrix with alternating rectangles of O and X
- Interleave the first half of the queue with the second half
- The sum of all elements between k1'th and k2'th smallest elements
- Binary Indexed Tree Range Updates and Point Queries
- Burn the binary tree starting from the target node
- Check Matrix Transformation by Flipping Sub-Matrices along the Principal or Anti-Diagonal
- DFS for an n-ary Tree(Acyclic Graph) Represented as an Adjacency List
- Difference Between Counting Sort and Bucket Sort
- Internal Data Structures and Time Complexity Table of All the C++ STL Containers
- K Centres Problem (Greedy Approximate Algorithm)
- Left Rotation and Right Rotation of a String
- Merge Two Sorted Linked Lists
- Move all Zeroes to End of Array
- Number of flips to make binary string alternate
- Program to Reveal the Positions in Minesweeper
- Tarjan's Algorithm to Find Strongly Connected Components
- Difference between big o and big theta ? and big omega ? notations

## Segment Tree - Range Minimum QueryIn the previous post, we described segment trees with a straightforward example. Another application of Segment Tree is explained in this post when it comes to the Range Minimum Query problem. The issue at hand is as follows: We have an array called arr[0, 1, n]. Where 0 = qs = qe = n-1, we should be able to efficiently identify the least value from index qs (query start) to qe (query end) 0 <= qs <= qe <= n-1. Finding the least element in the provided range by running a loop from qs to qe is a straightforward solution. In the worst situation, this solution takes O(n) time. Making a 2D array with an entry I j] that saves the smallest value in the range arr[i..j] is another option. Preprocessing takes O(n2) time, however it is now possible to find the minimum of a given range in O(1) time. Additionally, this method requires O(n2) additional space, which could be very expensive for big input arrays. Querying and preprocessing can be done quickly using segment trees. Preprocessing time with a segment tree is O(n), while a range minimum query has an O time complexity (Logn). The additional storage needed for the segment tree is O(n). Segment tree representation - The elements of the input array are called Leaf Nodes.
- Every internal node indicates at least one leaf below it.
Segment Trees are shown as an array representation of a tree. The left child of each node at index I is at index 2*i+1, the right child is at index 2*i+2, and the parent is at index( I - 1) / 2. ## Building a segment tree from an arrayWe begin by examining the segment arr[0,... n-1]. the current segment is split in half each time (assuming it hasn't already become a segment of length 1), the identical operation is then run on both halves, and we store the minimum value for each such segment in a segment tree node. Except for the last level, every level of the created segment tree will be fully filled. Additionally, since we consistently split segments into two halves at every level, the tree will be a full binary tree. There will be n-1 internal nodes because the created tree is always a full binary tree with n leaves. Consequently, there will be 2*n - 1 nodes overall. The segment tree will be log2n in height. Given that the tree is represented using an array and that the relationship between parent and child indexes must be preserved, 2 * 2 log2n - 1 of memory will be allocated for the segment tree. ## Find the least value of the specified range.How to perform a range minimum query utilising the segment tree once it has been built. The algorithm to find the minimum is as follows. ## C++ CodeThe application of the aforementioned strategy is seen below:
Minimum of values in range [1, 5] is = 2 **Time complexity:**The creation of a tree has an O (n) time complexity. There are 2n-1 nodes overall, and the tree creation process only computes each node's value once. The query's time complexity is O (Logn). We process no more than two nodes at each level to query a range minimum, and the total number of levels is O (Logn).**Auxiliary Space:**n additional room has been taken, therefore,O(N)
Next TopicSegment Tree - Sum of given Range |

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