Data Structures and Algorithms (DSA) in C++ Last Updated : 24 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Data Structures and Algorithms (DSA) are fundamental part of computer science that allow you to store, organize, and process data in ways that maximize performance. This tutorial will guide you through the important data structures and key algorithms using C++ programming language.Why Learn DSA Using C++?C++ is a powerful and high-performance programming language used for system/software development and game programming. Learning DSA using C++ instead of any other languages have many advantages such as:Learning DSA in C++ gives you a deep understanding of lower-level memory management which improves your understanding of the data structure.C++ is widely used in competitive programming due to its speed and rich set of libraries.C++ allows you to implement data structures as classes, making your code closer to the real implementations of data structures.Knowledge of DSA in C++ is versatile can be transferred to other languages, as many modern languages are built on similar syntax.Learn Data Structures and Algorithms using C++Mastering DSA concepts in C++ will improve your problem-solving abilities and also prepare you for technical interviews, competitive programming, and real-world software development. Whether you're a beginner or an experienced, this guide is designed to provide you with a strong foundation in one of the most essential areas of computer science.Asymptotic Analysis of AlgorithmsAsymptotic analysis of algorithms is a method used to evaluate the performance and efficiency of an algorithm. It evaluates how the execution time or memory requirements of an algorithm grow as the input size increases.Asymptotic NotationBest, Average and Worst CasesAnalysis of LoopsAnalysis of RecursionBit ManipulationBit manipulation involves performing operations directly on binary digits (bits) to optimize different operations.Extract bits in C++Setting bits in C++Clearing bits in C++Toggling bits in C++Counting Set bits in C++ArraysAn array is a data structure that holds a sequence of elements of the same type in a fixed size, stored together in memory, and accessed by their position or index.1D Array in C++Multidimensional Arrays in C++Searching AlgorithmsSearching algorithms are used to find a particular element in a data structure like linked list, arrays, etc.Linear Search in C++Sentinel Linear Search in C++Binary Search in C++Ternary Search in C++Sorting AlgorithmsSorting algorithms provides efficient ways to arrange the given data structure in desired order.Selection Sort in C++Bubble Sort in C++Insertion Sort in C++Merge Sort in C++Quick Sort in C++Iterative Quick Sort in C++Heap Sort in C++Radix Sort in C++Counting Sort in C++Bucket Sort in C++HashingHashing is a technique used to map data of any size to fixed-size values, known as hash codes. It is widely used in for fast data retrieval, encryption, and implementing efficient data structures like hash tables.Direct Address Tables in C++Hashing Functions in C++Hash Tables in C++Collision Resolving in C++Separate ChainingOpen AddressingString AlgorithmsString algorithms deal with the manipulation and processing of sequences of characters. Common tasks include searching, matching patterns, and modifying strings.String Pattern Searching in C++Rabin Karp in C++Knuth-Morris-Pratt in C++Boyer-Moore in C++Longest Common Subsequence in C++Longest Palindromic Subsequence in C++Linked ListsA linked list is a data structure that holds a sequence of elements called nodes. Here, each node contains a value and a pointer to the next node in the sequence.There are 3 types of linked list:Singly Linked List in C++Doubly Linked List in C++Circular Linked List in C++StacksA stack is a linear data structure that follows the Last-In-First-Out (LIFO) principle where elements are added and removed from the top (from one side). Stacks are not implemented independently, instead they are implemented over other data structure.Stack Implementation Using Arrays in C++Stack Implementation Using Linked List in C++QueuesA queue is a linear data structure that follows the First-In-First-Out(FIFO) principle where elements are added at the rear (one end) and removed from the front (other end). Just like stacks, queues are also implemented over other data structures.Queue Implementation Using Arrays in C++Queue Implementation Using Linked Lists in C++Circular Queue in C++Double-Ended Queue (Deque) in C++TreesA tree is a hierarchical data structure consisting of nodes where each node contains a data field and reference (or pointer) to its child nodes. A tree in C is represented by a pointer to the root node (topmost node in the tree).Binary Tree in C++Tree TraversalBFS Tree Traversal in C++DFS Tree Traversal in C++Binary Search Tree (BST) in C++Self-Balancing BST in C++AVL Tree in C++Red-Black Tree in C++B-Tree in C++B+ Tree in C++Advanced Tree Data StructuresSegment Tree in C++Trie (Prefix Tree) in C++K-D Tree in C++HeapsA heap is a specialized tree-based data structure that satisfies the heap property: In a max-heap, each parent node is greater than or equal to its child nodes. In a min-heap, each parent node is less than or equal to its child nodes.Binary Heap in C++Min Heap in C++Max Heap in C++Priority Queue in C++Binomial Heap in C++Fibonacci Heap in C++GraphsGraph is a data structure that is made up of nodes (also called vertices) connected to each other using edges. Graphs are commonly used in networking, social networks, and various algorithms like pathfinding and traversal.Classification of GraphsGraph Representation in C++Adjacency Matrix in C++Adjacency List in C++Graph Traversal in C++Breadth First Search (BFS) Traversal in C++Depth-First Search (DFS) Traversal in C++Graph Cycle Detection in C++Minimum Spanning Trees in C++Prim's Algorithm in C++Kruskal's Algorithm in C++Shortest Path Algorithms in C++Dijkstra's Algorithm in C++Floyd-Warshall Algorithm in C++Bellman-Ford Algorithm in C++Johnson Algorithm in C++Strongly Connected Components (SCC) in C++Kosaraju’s Algorithm in C++Tarjan’s Algorithm in C++Topological Sorting of Graphs in C++DFS-based Topological Sorting in C++ Kahn’s Algorithm in C++Greedy AlgorithmsGreedy algorithms are a class of algorithms that make the choices by selecting the best available option at each step (i.e. local optimum) in the hope that it will lead to a global optimum solution.Following are some standard Greedy algorithms with their implementation in C++:Fractional Knapsack in C++Activity Selection Problem in C++Job Sequencing Problem in C++Huffman Coding in C++Divide and Conquer AlgorithmsDivide and Conquer algorithms divides a problem into smaller subproblems, solves each subproblem independently, and then combines their solutions to provide the final solution of the original problem. These algorithms depend mainly on recursion.Following are some standard Divide and Conquer algorithms:Tower of Hanoi in C++Convex Hull in C++Closest Pair of Points in C++Karatsuba Algorithm for Fast Multiplication in C++Strassen’s Algorithm for Matrix Multiplication in C++Backtracking AlgorithmsBacktracking algorithms solve problems by exploring all possible solutions and backtracking when a solution path fails to meet the problem's conditions.Following are some standard backtracking algorithms:Knight’s Tour Problem in C++Rat in a Maze in C++N-Queen Problem in C++Sudoku in C++Dynamic Programming AlgorithmsDynamic Programming algorithms involve solving the problems by breaking them down into smaller overlapping subproblems and storing the solutions to these subproblems to avoid repeated calculations.Following are some standard Dynamic Programming algorithms:Rod Cutting Problem in C++Coin Change Problem in C++Edit Distance in C++0-1 Knapsack in C++Longest Increasing Subsequence in C++Partition Equal Subset Sum in C++Subset Sum Problem in C++Maximum Subarray Sum in C++Minimum Cost Path in C++Maximum Product Subarray in C++What's next?Now that you have a strong foundation in DSA with C++, you can explore more advanced topics such as advanced graph algorithms and design patterns. Keep challenging yourself with complex problems, contribute to open-source projects, or even start preparing for competitive programming contests. Your journey in mastering DSA has just begun! Comment More infoAdvertise with us Next Article Introduction to C++ Programming Language A abhishekcpp Follow Improve Article Tags : C++ Tutorials CPP-DSA Practice Tags : CPP Similar Reads C++ Programming Language C++ is a computer programming language developed by Bjarne Stroustrup as an extension of the C language. It is known for is fast speed, low level memory management and is often taught as first programming language. It provides:Hands-on application of different programming concepts.Similar syntax to 5 min read C++ OverviewIntroduction to C++ Programming LanguageC++ is a general-purpose programming language that was developed by Bjarne Stroustrup as an enhancement of the C language to add object-oriented paradigm. It is considered as a middle-level language as it combines features of both high-level and low-level languages. It has high level language featur 3 min read Features of C++C++ is a general-purpose programming language that was developed as an enhancement of the C language to include an object-oriented paradigm. It is an imperative and compiled language. C++ has a number of features, including:Object-Oriented ProgrammingMachine IndependentSimpleHigh-Level LanguagePopul 5 min read History of C++The C++ language is an object-oriented programming language & is a combination of both low-level & high-level language - a Middle-Level Language. The programming language was created, designed & developed by a Danish Computer Scientist - Bjarne Stroustrup at Bell Telephone Laboratories ( 7 min read Interesting Facts about C++C++ is a general-purpose, object-oriented programming language. It supports generic programming and low-level memory manipulation. Bjarne Stroustrup (Bell Labs) in 1979, introduced the C-With-Classes, and in 1983 with the C++. Here are some awesome facts about C++ that may interest you: The name of 2 min read Setting up C++ Development EnvironmentC++ runs on lots of platforms like Windows, Linux, Unix, Mac, etc. If you do not want to set up a local environment you can also use online IDEs for compiling your program.Using Online IDEIDE stands for an integrated development environment. IDE is a software application that provides facilities to 8 min read Difference between C and C++C++ is often viewed as a superset of C. C++ is also known as a "C with class" This was very nearly true when C++ was originally created, but the two languages have evolved over time with C picking up a number of features that either weren't found in the contemporary version of C++ or still haven't m 3 min read C++ BasicsUnderstanding First C++ ProgramThe "Hello World" program is the first step towards learning any programming language and is also one of the most straightforward programs you will learn. It is the basic program that demonstrates the working of the coding process. All you have to do is display the message "Hello World" on the outpu 4 min read C++ Basic SyntaxSyntax refers to the rules and regulations for writing statements in a programming language. They can also be viewed as the grammatical rules defining the structure of a programming language.The C++ language also has its syntax for the functionalities it provides. Different statements have different 4 min read C++ CommentsComments in C++ are meant to explain the code as well as to make it more readable. Their purpose is to provide information about code lines. When testing alternative code, they can also be used to prevent execution of some part of the code. Programmers commonly use comments to document their work.Ex 3 min read Tokens in CIn C programming, tokens are the smallest units in a program that have meaningful representations. Tokens are the building blocks of a C program, and they are recognized by the C compiler to form valid expressions and statements. Tokens can be classified into various categories, each with specific r 4 min read C++ KeywordsKeywords are the reserved words that have special meanings in the C++ language. They are the words that have special meaning in the language. C++ uses keywords for a specifying the components of the language, such as void, int, public, etc. They can't be used for a variable name, function name or an 2 min read Difference between Keyword and Identifier in CIn C, keywords and identifiers are basically the fundamental parts of the language used. Identifiers are the names that can be given to a variable, function or other entity while keywords are the reserved words that have predefined meaning in the language.The below table illustrates the primary diff 3 min read C++ Variables and ConstantsC++ VariablesIn C++, variable is a name given to a memory location. It is the basic unit of storage in a program. The value stored in a variable can be accessed or changed during program execution.Creating a VariableCreating a variable and giving it a name is called variable definition (sometimes called variable 4 min read Constants in CIn C programming, const is a keyword used to declare a variable as constant, meaning its value cannot be changed after it is initialized. It is mainly used to protect variables from being accidentally modified, making the program safer and easier to understand. These constants can be of various type 4 min read Scope of Variables in C++In C++, the scope of a variable is the extent in the code upto which the variable can be accessed or worked with. It is the region of the program where the variable is accessible using the name it was declared with.Let's take a look at an example:C++#include <iostream> using namespace std; // 7 min read Storage Classes in C++ with ExamplesC++ Storage Classes are used to describe the characteristics of a variable/function. It determines the lifetime, visibility, default value, and storage location which helps us to trace the existence of a particular variable during the runtime of a program. Storage class specifiers are used to specif 6 min read Static Keyword in C++The static keyword in C++ has different meanings when used with different types. In this article, we will learn about the static keyword in C++ along with its various uses.In C++, a static keyword can be used in the following context:Table of ContentStatic Variables in a FunctionStatic Member Variab 5 min read C++ Data Types and LiteralsC++ Data TypesData types specify the type of data that a variable can store. Whenever a variable is defined in C++, the compiler allocates some memory for that variable based on the data type with which it is declared as every data type requires a different amount of memory.C++ supports a wide variety of data typ 7 min read Literals in CIn C, Literals are the constant values that are assigned to the variables. Literals represent fixed values that cannot be modified. Literals contain memory but they do not have references as variables. Generally, both terms, constants, and literals are used interchangeably. For example, “const int = 4 min read Derived Data Types in C++The data types that are derived from the primitive or built-in datatypes are referred to as Derived Data Types. They are generally the data types that are created from the primitive data types and provide some additional functionality.In C++, there are four different derived data types:Table of Cont 4 min read User Defined Data Types in C++User defined data types are those data types that are defined by the user himself. In C++, these data types allow programmers to extend the basic data types provided and create new types that are more suited to their specific needs. C++ supports 5 user-defined data types:Table of ContentClassStructu 4 min read Data Type Ranges and Their Macros in C++Most of the times, in competitive programming, there is a need to assign the variable, the maximum or minimum value that data type can hold but remembering such a large and precise number comes out to be a difficult job. Therefore, C++ has certain macros to represent these numbers, so that these can 3 min read C++ Type ModifiersIn C++, type modifiers are the keywords used to change or give extra meaning to already existing data types. It is added to primitive data types as a prefix to modify their size or range of data they can store.C++ have 4 type modifiers which are as follows:Table of Contentsigned Modifierunsigned Mod 4 min read Type Conversion in C++Type conversion means converting one type of data to another compatible type such that it doesn't lose its meaning. It is essential for managing different data types in C++. Let's take a look at an example:C++#include <iostream> using namespace std; int main() { // Two variables of different t 4 min read Casting Operators in C++The casting operators is the modern C++ solution for converting one type of data safely to another type. This process is called typecasting where the type of the data is changed to another type either implicitly (by the compiler) or explicitly (by the programmer).Let's take a look at an example:C++# 5 min read C++ OperatorsOperators in C++C++ operators are the symbols that operate on values to perform specific mathematical or logical computations on given values. They are the foundation of any programming language.Example:C++#include <iostream> using namespace std; int main() { int a = 10 + 20; cout << a; return 0; }Outpu 9 min read C++ Arithmetic OperatorsArithmetic Operators in C++ are used to perform arithmetic or mathematical operations on the operands (generally numeric values). An operand can be a variable or a value. For example, ‘+’ is used for addition, '-' is used for subtraction, '*' is used for multiplication, etc. Let's take a look at an 4 min read Unary Operators in CIn C programming, unary operators are operators that operate on a single operand. These operators are used to perform operations such as negation, incrementing or decrementing a variable, or checking the size of a variable. They provide a way to modify or manipulate the value of a single variable in 5 min read Bitwise Operators in CIn C, bitwise operators are used to perform operations directly on the binary representations of numbers. These operators work by manipulating individual bits (0s and 1s) in a number.The following 6 operators are bitwise operators (also known as bit operators as they work at the bit-level). They are 6 min read Assignment Operators in CIn C, assignment operators are used to assign values to variables. The left operand is the variable and the right operand is the value being assigned. The value on the right must match the data type of the variable otherwise, the compiler will raise an error.Let's take a look at an example:C#include 4 min read C++ sizeof OperatorThe sizeof operator is a unary compile-time operator used to determine the size of variables, data types, and constants in bytes at compile time. It can also determine the size of classes, structures, and unions.Let's take a look at an example:C++#include <iostream> using namespace std; int ma 3 min read Scope Resolution Operator in C++In C++, the scope resolution operator (::) is used to access the identifiers such as variable names and function names defined inside some other scope in the current scope. Let's take a look at an example:C++#include <iostream> int main() { // Accessing cout from std namespace using scope // r 4 min read C++ Input/OutputBasic Input / Output in C++In C++, input and output are performed in the form of a sequence of bytes or more commonly known as streams.Input Stream: If the direction of flow of bytes is from the device (for example, Keyboard) to the main memory then this process is called input.Output Stream: If the direction of flow of bytes 5 min read cin in C++In C++, cin is an object of istream class that is used to accept the input from the standard input stream i.e. stdin which is by default associated with keyboard. The extraction operator (>>) is used along with cin to extract the data from the object and insert it to the given variable.Let's t 4 min read cout in C++In C++, cout is an object of the ostream class that is used to display output to the standard output device, usually the monitor. It is associated with the standard C output stream stdout. The insertion operator (<<) is used with cout to insert data into the output stream.Let's take a look at 2 min read Standard Error Stream Object - cerr in C++In C++, cerr is the standard error stream used to output the errors. It is an instance of the ostream class and is un-buffered, so it is used when we need to display the error message immediately and does not store the error message to display later. The 'c' in cerr refers to "character" and 'err' m 3 min read Manipulators in C++Manipulators are helping functions that can modify the input or output stream. They can be included in the I/O statement to alter the format parameters of a stream. They are defined inside <iomanip> and some are also defined inside <iostream> header file. For example, if we want to print 4 min read C++ Control StatementsDecision Making in C (if , if..else, Nested if, if-else-if )In C, programs can choose which part of the code to execute based on some condition. This ability is called decision making and the statements used for it are called conditional statements. These statements evaluate one or more conditions and make the decision whether to execute a block of code or n 7 min read C++ if StatementThe C++ if statement is the most simple decision-making statement. It is used to decide whether a certain statement or block of statements will be executed or not executed based on a certain condition. Let's take a look at an example:C++#include <iostream> using namespace std; int main() { int 3 min read C++ if else StatementThe if statement alone tells us that if a condition is true it will execute a block of statements and if the condition is false, it won’t. But what if we want to do something else if the condition is false. Here comes the C++ if else statement. We can use the else statement with if statement to exec 3 min read C++ if else if LadderIn C++, the if-else-if ladder helps the user decide from among multiple options. The C++ if statements are executed from the top down. As soon as one of the conditions controlling the if is true, the statement associated with that if is executed, and the rest of the C++ else-if ladder is bypassed. I 3 min read Switch Statement in C++In C++, the switch statement is a flow control statement that is used to execute the different blocks of statements based on the value of the given expression. It is a simpler alternative to the long if-else-if ladder.SyntaxC++switch (expression) { case value_1: // code to be executed. break; case v 5 min read Jump statements in C++Jump statements are used to manipulate the flow of the program if some conditions are met. It is used to terminate or continue the loop inside a program or to stop the execution of a function.In C++, there is four jump statement:Table of Contentcontinue Statementbreak Statementreturn Statementgoto S 4 min read C++ LoopsIn C++ programming, sometimes there is a need to perform some operation more than once or (say) n number of times. For example, suppose we want to print "Hello World" 5 times. Manually, we have to write cout for the C++ statement 5 times as shown.C++#include <iostream> using namespace std; int 7 min read for Loop in C++In C++, for loop is an entry-controlled loop that is used to execute a block of code repeatedly for the given number of times. It is generally preferred over while and do-while loops in case the number of iterations is known beforehand.Let's take a look at an example:C++#include <bits/stdc++.h 6 min read Range-Based for Loop in C++In C++, the range-based for loop introduced in C++ 11 is a version of for loop that is able to iterate over a range. This range can be anything that is iteratable, such as arrays, strings and STL containers. It provides a more readable and concise syntax compared to traditional for loops.Let's take 3 min read C++ While LoopIn C++, the while loop is an entry-controlled loop that repeatedly executes a block of code as long as the given condition remains true. Unlike the for loop, while loop is used in situations where we do not know the exact number of iterations of the loop beforehand as the loop execution is terminate 3 min read C++ do while LoopIn C++, the do-while loop is an exit-controlled loop that repeatedly executes a block of code at least once and continues executing as long as a given condition remains true. Unlike the while loop, the do-while loop guarantees that the loop body will execute at least once, regardless of whether the 4 min read C++ FunctionsFunctions in C++A Function is a reusable block of code designed to perform a specific task. It helps break large programs into smaller, logical parts. Functions make code cleaner, easier to understand, and more maintainable.Just like in other languages, C++ functions can take inputs (called parameters), execute a b 8 min read return Statement in C++In C++, the return statement returns the flow of the execution to the function from where it is called. This statement does not mandatorily need any conditional statements. As soon as the statement is executed, the flow of the program stops immediately and returns the control from where it was calle 4 min read Parameter Passing Techniques in CIn C, passing values to a function means providing data to the function when it is called so that the function can use or manipulate that data. Here:Formal Parameters: Variables used in parameter list in a function declaration/definition as placeholders. Also called only parameters.Actual Parameters 3 min read Difference Between Call by Value and Call by Reference in CFunctions can be invoked in two ways: Call by Value or Call by Reference. These two ways are generally differentiated by the type of values passed to them as parameters.The following table lists the differences between the call-by-value and call-by-reference methods of parameter passing.Call By Valu 4 min read Default Arguments in C++A default argument is a value provided for a parameter in a function declaration that is automatically assigned by the compiler if no value is provided for those parameters in function call. If the value is passed for it, the default value is overwritten by the passed value.Example:C++#include <i 5 min read Inline Functions in C++In C++, inline functions provide a way to optimize the performance of the program by reducing the overhead related to a function call. When a function is specified as inline the whole code of the inline function is inserted or substituted at the point of its call during the compilation instead of us 6 min read Lambda Expression in C++C++ 11 introduced lambda expressions to allow inline functions which can be used for short snippets of code that are not going to be reused. Therefore, they do not require a name. They are mostly used in STL algorithms as callback functions.Example:C++#include <iostream> using namespace std; i 4 min read C++ Pointers and ReferencesPointers and References in C++In C++ pointers and references both are mechanisms used to deal with memory, memory address, and data in a program. Pointers are used to store the memory address of another variable whereas references are used to create an alias for an already existing variable. Pointers in C++ Pointers in C++ are a 5 min read C++ PointersA pointer is a special variable that holds the memory address of another variable, rather than storing a direct value itself. Pointers allow programs to access and manipulate data in memory efficiently, making them a key feature for system-level programming and dynamic memory management. When we acc 8 min read Dangling, Void , Null and Wild Pointers in CIn C programming pointers are used to manipulate memory addresses, to store the address of some variable or memory location. But certain situations and characteristics related to pointers become challenging in terms of memory safety and program behavior these include Dangling (when pointing to deall 6 min read Applications of Pointers in CPointers in C are variables that are used to store the memory address of another variable. Pointers allow us to efficiently manage the memory and hence optimize our program. In this article, we will discuss some of the major applications of pointers in C. Prerequisite: Pointers in C. C Pointers Appl 4 min read Understanding nullptr in C++Consider the following C++ program that shows problem with NULL (need of nullptr) CPP // C++ program to demonstrate problem with NULL #include <bits/stdc++.h> using namespace std; // function with integer argument void fun(int N) { cout << "fun(int)"; return;} // Overloaded fun 3 min read References in C++In C++, a reference works as an alias for an existing variable, providing an alternative name for it and allowing you to work with the original data directly.Example:C++#include <iostream> using namespace std; int main() { int x = 10; // ref is a reference to x. int& ref = x; // printing v 5 min read Can References Refer to Invalid Location in C++?Reference Variables: You can create a second name for a variable in C++, which you can use to read or edit the original data contained in that variable. While this may not sound appealing at first, declaring a reference and assigning it a variable allows you to treat the reference as if it were the 2 min read Pointers vs References in C++Prerequisite: Pointers, References C and C++ support pointers, which is different from most other programming languages such as Java, Python, Ruby, Perl and PHP as they only support references. But interestingly, C++, along with pointers, also supports references. On the surface, both references and 5 min read Passing By Pointer vs Passing By Reference in C++In C++, we can pass parameters to a function either by pointers or by reference. In both cases, we get the same result. So, what is the difference between Passing by Pointer and Passing by Reference in C++?Let's first understand what Passing by Pointer and Passing by Reference in C++ mean:Passing by 5 min read When do we pass arguments by pointer?In C, the pass-by pointer method allows users to pass the address of an argument to the function instead of the actual value. This allows programmers to change the actual data from the function and also improve the performance of the program. In C, variables are passed by pointer in the following ca 5 min read Like