DS Tutorial

DS Tutorial DS Introduction DS Algorithm Asymptotic Analysis DS Pointer DS Structure

DS Array

DS Array 2D Array

DS Linked List

Linked List Types of Linked List Singly Linked List Doubly Linked List Circular Linked List Circular Doubly List Skip list in DS

DS Stack

DS Stack Array Implementation Linked List Implementation

DS Queue

DS Queue Types of Queues Array Representation Linked List Representation Circular Queue Deque Priority Queue

DS Tree

DS Tree Binary Tree Binary Search Tree AVL Tree B Tree B+ Tree

DS Graph

DS Graph Graph Implementation BFS Algorithm DFS Algorithm Spanning Tree

DS Searching

Linear Search Binary Search

DS Sorting

Bubble Sort Bucket Sort Comb Sort Counting Sort Heap Sort Insertion Sort Merge Sort Quick Sort Radix Sort Selection Sort Shell Sort Bitonic Sort Cocktail Sort Cycle Sort Tim Sort

Differences

Misc

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

DS MCQ

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Maximum number of distinct nodes in a root-to-leaf path

Find the maximum number of distinct nodes in all root-to-leaf paths given a Binary Tree.

Examples

Input :   1
            /    \
           2      3
          / \    / \
        4   5  6   3
               \   \
                8   9 

Output : 4 
The root to leaf path with maximum distinct
nodes is 1-3-6-8.

Exploring all root to leaf paths is a simple solution. Count distinct nodes along each root-to-leaf path and return the maximum number.

Hashing is an efficient solution. We traverse the tree recursively, keeping track of the number of distinct nodes on the path from the root to the current node. We repeat for the left and right subtrees, returning the maximum of two values.

The implementation of the above idea is shown below.

Program in C++

// C++ program to find count of distinct nodes
// on a path with maximum distinct nodes.
#include <bits/stdc++.h>
using namespace std;

// A node of binary tree
struct Node {
	int data;
	struct Node *left, *right;
};

// A utility function to create a new Binary
// Tree node
Node* newNode(int data)
{
	Node* temp = new Node;
	temp->data = data;
	temp->left = temp->right = NULL;
	return temp;
}

int largestUinquePathUtil(Node* node, unordered_map<int, int> m)
{
	if (!node)
		return m.size();

	// put this node into hash
	m[node->data]++;

	int max_path = max(largestUinquePathUtil(node->left, m),
					largestUinquePathUtil(node->right, m));

	// remove current node from path "hash"
	m[node->data]--;

	// if we reached a condition where all duplicate value
	// of current node is deleted
	if (m[node->data] == 0)
		m.erase(node->data);

	return max_path;
}

// A utility function to find long unique value path
int largestUinquePath(Node* node)
{
	if (!node)
		return 0;

	// hash that store all node value
	unordered_map<int, int> hash;

	// return max length unique value path
	return largestUinquePathUtil(node, hash);
}

// Driver program to test above functions
int main()
{
	// Create binary tree shown in above figure
	Node* root = newNode(1);
	root->left = newNode(2);
	root->right = newNode(3);
	root->left->left = newNode(4);
	root->left->right = newNode(5);
	root->right->left = newNode(6);
	root->right->right = newNode(7);
	root->right->left->right = newNode(8);
	root->right->right->right = newNode(9);

	cout << largestUinquePath(root) << endl;

	return 0;
}

Output

Time Complexity : O (n)

Next TopicHashing - Open Addressing for Collision Handling

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