C++ Tutorial Index

C++ Tutorial C++ History C++ Installation C++ First Program C++ cin and cout C++ Data type C++ Variable C++ operator C++ Keywords

C++ Control Statements

C++ If C++ Nested if C++ If-else C++ If-else-if C++ Switch C++ Break C++ Continue C++ Goto C++ For loop C++ While loop C++ Do while loop

C++ Functions

C++ Call by Value C++ Call by Reference C++ Recursion Function C++ Inline function C++ Friend function

C++ Arrays

Single dimension array Two dimension array

C++ Strings

C++ Strings

C++ Inheritance

C++ Inheritance Single level Inheritance Multilevel Inheritance Multiple Inheritance Hierarchical Inheritance Hybrid Inheritance

C++ Polymorphism

C++ Polymorphism C++ Overloading C++ Overriding C++ Virtual Function

C++ Pointers

C++ Pointers C++ this pointer

C++ Exception Handling

C++ Exception Handling

C++ Constructors

C++ Constructors Default Constructor Parameterize Constructor Copy constructor Constructor Overloading Destructor

C++ File Handling

C++ File Handling C++ Writing to file C++ Reading file C++ Close file

Miscellaneous

C Vs C++ C++ Comments C++ Data Abstraction C++ Identifier C++ Memory Management C++ Storage Classes C++ Void Pointer C++ Array To Function C++ Expressions C++ Features C++ Interfaces C++ Encapsulation std::min in C++ External merge sort in C++ Remove duplicates from sorted array in C++ Precision of floating point numbers Using these functions floor(), ceil(), trunc(), round() and setprecision() in C++ C++ References C++ Friend Functions C++ Mutable keyword Unary Operators in C++ Initialize Array of objects with parameterized constructors in C++ Differences between #define & const in C/C++ C++ Program to Implement Shell Sort C++ Program to Implement Merge Sort Storage Classes in C Vector resize() in C++ Passing by Reference Vs. Passing by the pointer in C++ Free vs delete() in C++ goto statement in C and C++ C++ program to read string using cin.getline() C++ String Concatenation Heap Sort in C++ Swap numbers in C++ Input Iterators in C++ Fibonacci Series in C++ C ++ Program: Alphabet Triangle and Number Triangle C++ Program: Matrix Multiplication C++ Program to Print Fibonacci Triangle Stack in C++ Maps in C++ Queue in C++ C++ Bitset C++ Algorithms Priority Queue in C++ C++ Multimap C++ Deque Function Pointer in C++ Sizeof() Operators in C++ C++ array of Pointers free() Vs delete in C Timsort Implementation Using C++ CPP Templates C++ Aggregation C++ Enumeration C++ Math Functions C++ Object Class C++ Queue Initialize Vector in C++ Vector in C++ C++ STL Components Function overloading in C++ C++ Maximum Index Problem C++ find missing in the second array C++ Program to find the product array puzzle C++ Program To Find Largest Subarray With 0 Sum C++ Program To Move All Zeros To The End Of The Array C++ Program to find the element that occurs once C++ Program to find the largest number formed from an array Constructor Vs Destructor C++ Namespaces C++ OOPs Concept C++ Static C++ Structs C++ Try-Catch C++ User Defined Exceptions C++ Virtual Destructor C++ vs C# Malloc() and new in C++ Palindrome Number Program in C++ Snake Code in C++ Splitting a string in C++ Structure Vs Class in C++ Virtual Function Vs Pure Virtual Function C++ Bidirectional Iterators C++ Forward Iterators C++ Iterators C++ Output Iterators C++ Range-based For Loop Converting string into integer in C++ LCM Program in C++ Type conversion in C++ Add two numbers using the function in C++ Advantage and disadvantage friend function C++ Armstrong Number Program in C++ ATM machine program in C++ using functions Binary to Decimal in C++ Bit Manipulation in C++ C++ Constructor C++ Dijkstra Algorithm Using the Priority Queue C++ int into String C++ Signal Handling Decimal to Binary in C++ Decimal to Hexadecimal in C++ Decimal to Octal in C++ Factorial Program in C++ Function in C++ Hexadecimal to Decimal in C++ Octal to Decimal in C++ Reverse a Number in C++ Structure Vs Class in C++ C++ Forward Iterators C++ Output Iterators C++ Prime number program Char Array to String in C++ Constructor Overloading in C++ Default arguments in C++ Different Ways to Compare Strings in C++ Dynamic Binding in C++ Program to convert infix to postfix expression in C++ SET Data Structure in C++ Upcasting and Downcasting in C++ Reverse an Array in C++ Fast Input and Output in C++ Delete Operator in C++ Copy elision in C++ C++ Date and Time C++ Bitwise XOR Operator Array of sets in C++ Binary Operator Overloading in C++ Binary Search in C++ Implementing the sets without C++ STL containers Scope Resolution Operator in C++ Smart pointers in C++ Types of polymorphism in C++ Exception Handling in C++ vs Java Const Keyword in C++ Type Casting in C++ Static keyword in C++ vs Java Inheritance in C++ vs Java How to concatenate two strings in C++ Programs to Print Pyramid Patterns in C++ swap() function in C++ Structure of C++ Program Stringstream in C++ and its applications rand() and srand() in C / C++ C++ Ternary Operator C++ Scope of Variables While Loop Examples in C++ Star pattern in C++ using For Loops For Loop Examples in C++ Do-While Loop Examples in C++ Top 5 IDEs for C++ That You Should Try Once Assertions in C/C++ C++ Convert Int to String Continue in C++ While loop Diamond Pattern in C++ using For Loop How to Reverse a String in C++ using Do-While Loop How to Reverse a String in C++ using For Loop How to Reverse a String in C++ using While Loop Infinite loop in C++ Loops in C++ Returning Multiple Values from a Function using Tuple and Pair in C++ wcscpy(), wcslen(), wcscmp() Functions in C++ Auto keyword in C++ C++ 11 vs C++ 14 vs C++ 17 C++ STL (Standard Template Library) Differences Between C Structures and C++ Structures Divide by Zero Exception in C++ Dynamic Constructor in C++ Dynamic Memory Allocation in C++ Find the Size of Array in C/C++ without using sizeof() function Floating Point Operations and Associativity in C, C++ and Java Hello World Program in C++ How to create a table in C++ How to Setup Environment for C++ Programming on Mac Implementation of a Falling Matrix in C++ Message Passing in C++ Pointer to Object in C++ Templates in C++ vs Generics in Java Ways to Copy a Vector in C++ What does Buffer Flush mean in C++ sort() function in C++ Structure Sorting (By Multiple Rules) in C++ Similarities between C++ and Java std::distance in C++ Array program in C++ C++ Tricks for Competitive Programming Desired Capabilities in Selenium Web Driver in C++ Socket Programming in C++ Template Specialization in C++ Classes and Objects in C++ Convex hull Algorithm in C++ DES in C++ C++ vardiac() function Difference between Two Sets in C++ Difference between Exit and Return Structured Binding in C++ Differences between Local and Global Variable Bitwise Operator vs Logical Operator Difference between OOP and POP in C++ Fork in C++ Functors in C++ How to call a void function in C++ How to create a directory or folder in C/C++ How to create a library in C++ How to create a stack in C++ How to create the Processes with Fork in C++ How to Handle Divide by Zero Exception in C++ Lambda Expression in C++ Pattern programs in C++ Roadmap to C++ Programming Substring in C++ Virtual base class in C++ Bits stdc++.h in C++ Top 14 Best Free C++ IDE (Editor & Compiler) for Windows in 2022 Bitmasking in C++ Auto Keyword in C++ Features of OOPS in C++ Hospital Management Project in C++ How to Declare Unordered Sets in C++ How to Sort an Array in C++ Include Guards in C++ Iostream in C++ Method overriding in C++ How to run program in turbo c++ How to Use Getline in C++ Leap Year Program in C++ Naming Convention in C++ New Operator in C++ Nullptr in C++ Object Slicing in C++ Principles of Object-Oriented Programming in C++ Processing strings using std string stream in C++ Pure Virtual Function in C++ With Example Program Random Number Generator in C++ Singleton Design Pattern in C++ Size_t Data Type in C++ Skyline Problem in C++ System() function in C++ Web Development in C++ Data Hiding in C++ Difference between exit() and _Exit() in C++ Hashing in C++ Object in C++ Sum of all Elements between k1’th and k2’th Smallest Elements Virtual class in C++ Vector Size in C++ Top best IDEs for C/C++ Developers in 2022 Tensorflow in C++ Sliding Window Technique in C++ Reverse String Word-Wise in C++ Returning a Function Pointer from a Function in C/C++ RTTI in C++ Pthreads or POSIX Threads in C++ Reserved Keywords in C++ Passing a Vector to a function in C++ 10 Best C and C++ Books for Beginners & Advanced Programmers Add two numbers represented by two arrays in C++ Array of Object in C++ C++ Program For FCFS Containership in C++ Counting Frequencies of Array Elements in C++ Decltype type Specifier in C++ Dynamic _Cast in C++ Difference between int main() and int main(void) in C/C++ Depth First Search Program to Traverse a Graph in C++ Features and Use Of Pointers in C/C++ Fread Function in C++ Programming Fscanf Function in The C++ Functions in C++ With Types and Examples Gmtime Function in C/C++ How is Multiset Implemented in C++ How to Build a Program in C++ How to Declare a 2d Array Dynamically in C++ inheritance Program in C++ int Max and int Min in C/C++ is It Fine to Write Void Main Or Main in C/C++ How to create a button in C++ abs() function in C++ Compile Time Polymorphism in C++ Division in C++ Factorial of a Number in C++ using while Loop Multiset in C++ 4 Pillars of OOPs Approach in C++ Backtracking Time Complexity in C++ C++ Global Variable C++ Pipe Tutorial Observer Design Pattern in C++ Private Inheritance in C++ Pthread in C++ Parameters SDL library in C++ with Examples Pointers in C++ Abstract Factory Design Pattern in C++ Ascending order in C++ How the value is passed in C++ Call by Pointer in C++ Constexpr in C++ Deadlock in C++ Design Patterns in C++ Factory Method for Designing Pattern in C++ How to calculate size of string in C++ Name Mangling and extern in C++ Preventing Object Copy in C++ Program that produces different results in C and C++ Quick Sort in C++ Single Handling in C++ Type difference of Character literals in C VS C++ Use of Inheritance in C++ User-defined literals in C++ Vector methods in C++ Void * in C and C++ Zombie and Orphan Process in C++ Isprint() in C++ List and Vector in C++ List iterators in C++ Merging Two Vectors in C++ Sleep function in C++ Stoi function in C++ String erase() in C++ String Trim in C++ When should we write own Assignment operator in C++ C++ tcp client server example C++ tcp server example Early Binding and Late Binding in C++ Factory Design Pattern in C++ Fisher-Yates shuffle algorithm in C++ For Auto in C++ Group anagrams in C++ How to convert binary string to int in C++ How to convert string to float in C++ How to remove space from string in C++ How to use pair in C++ How to use the string find() in C++ Dynamic Casting in C++ 2D Vector Initialization in C++ C++ GUI Visual Studio C++ IPC C++ Macro Function Example C++ Permutation Overloading Stream Insertion in C++ Overloading array Index operator in C++ Operators that cannot be overloaded in C++ Operator overloading in C++ isprint() function in c++ Is_trivial function in C++ Is assignment operator Inherited in C++ div() function in C++ Default Assignment Operator and References in C++ Copy Constructor vs Assignment Operator in C++ Conversion Operator in C++ Array sum in C++ STL C++ Define Macro C++ Design C++ Factory Pattern TCP Client Server Example in C++ Convert String to Uppercase in C++ exit() and _Exit() in C and C++ Initializer list in C++ Iterator invalidation in C++ Lower bound in C++ Modulus of Two float numbers or double number Pass by value in C++ Set insert function in C++ Std partition_point in C++ Unary Operator Overloading in C++ Using Default Arguments with Virtual Functions Virtual Functions and Runtime Polymorphism What is endl in C++ What is Unary Operator Overloading in C++ Which operators cannot be overloaded in C++ C++ Program to Divide the String Into N equal Parts Gray Code to Binary Code in C++ How to get the value of pi in C++ Multimap value_comp() function in C++ Vector of Vectors in C++ Naïve Bayes Algorithm in C++ Minimum Cost Path Problem in C++ 10 C++ Programming Tricks You Should Know btowc() function in C++ forward_list::cend() in C++ Unordered_multimap max_load_factor() function in C++ Cpp_int in c++ Dynamic Objects in C++ FLOCK() FUNCTION IN C++ Generate Random Double Numbers in C++ How to Assign Infinity to a Number in C++ Jump statements in C++ Multipath inheritance in C++ Out of Range Exception in C++ Size of Class in C++ Size of string in C++ std::binary_negate in c++ Thread_local in C++ Tokenizing a String in C++ Ancestors of a Node in Binary Search Tree C++ program for Double to String Conversion C++ Program to Demonstrate Use of Formatting Flags on Float Output Clamp in C++ K-Dimensional Tree in C++ Mutable Lambda in C++ Power Set in C++ Program to Find Sum of Geometric Progression Std::Back_inserter in C++ Strpbrk() function in C++ Size of int in C++ TYPES OF MANIPULATORS IN C++ Double colon in C++ How to sort vector in C++ How to use Setprecision in C++ How to write a Vector in C++ Insertion in Splay Tree in C++ Merge Sort Algorithm in C++ Printing a Character using ASCII value in C++ Regex in C++ Size of Data Types in C++ Abstract Factory Design Pattern in C++ Sqrtf() function in C++ Static Casting in C++ Using Range in Switch Case in C++ wcstoimax() and wcstoumax() function in C++ What is float in C++ What is the Diamond Problem in C++ Best way to learn C++ ios setstate() function in C++ Nested Namespace in C++ Single Inheritance in C++ std::fixed, std::scientific, std::hexfloat, std::defaultfloat in C++ StringStream in C++ for Decimal to Hexadecimal and back The OFFSETOF() macro in C++ Difference between std::next and std::advance in C++ Hiding of all overloaded methods with same name in base class in C++ C++ program to concatenate two strings using operator overloading Difference between array::fill() and array::swap() in C++ Difference between Friend Function and Virtual Function in C++ Semaphores in C++ Seekg in C++ UDP server- client implementattion in C++ What is long long in C++ CSV file management using C++ Toggle bits of a number except first and last bits in C++ Trailing Return Type C++ 11 Binary search implementation in C++ Different Versions of C++ What is Cascading in C++ Background Colour in C++

Maximum sum Bi-tonic sub-sequence in C++
2024-05-03 04:47:22

Maximum sum Bi-tonic sub-sequence in C++

Introduction of Bi-tonic Subsequence:

A sequence of elements within an array that follows a particular pattern, which first increasing and then decreasing, is referred to as a bi-tonic subsequence in C++. Formally speaking, a subsequence arr[i1], arr[i2],..., arr[ik] of an array arr[] of size n is deemed bi-tonic if and only if:

  • i1 < i2 < ... < ik (elements maintain their relative order in the array)
  • arr[i1] <= arr[i2] <= ... <= arr[ik-1] >= arr[ik] (elements increase and then decrease)

Problem Statement:

Finding the Maximum Sum Bi-tonic Subsequence:

Finding the bi-tonic subsequence with the largest sum of its elements within a given array is the issue we are trying to solve. This issue has applications in several fields, such as:

  • Analysis of the stock market (finding peak-and-dip patterns).
  • Signal processing: identifying upward and downward trends.
  • Optimization issues (determining the best schedules or distribution of resources).

Problem Definition

Given: A n-integer array arr[].

  • The task is to find the bi-tonic subsequence's maximum sum inside arr[].
  • The maximum sum of a bi-tonic subsequence is the output.

Constraints:

  • Positive and negative integers can be contained in the array arr[].
  • There might or might not be a bi-tonic subsequence in the array.
  • The output should be 0 (or any suitable value indicating no such subsequence) if there is no bi-tonic subsequence.

Input and Output Requirements:

Input:

  • An array arr[] of n integers represents the data to be analyzed.
  • The number n represents the array's size.

Output:

The maximum sum of a bi-tonic subsequence within arr[] is represented by a single integer.

For instance:

  • Input: arr[] = {1, 15, 51, 45, 33, 100, 12, 18, 9}, n = 9
  • Output: 194 (corresponding to the bi-tonic subsequence 1, 15, 51, 100, 18, 9)

Approach and Algorithm

Algorithm: Dynamic Programming

Steps:

Initialization:

  • First create two arrays: MSIBS[n] and MDSB[n].
    • The maximum sum of an increasing subsequence ending at the index i will be stored in MSIBS[i].
    • Starting at the index i, MDSB[i] will hold the maximum sum of a decreasing subsequence.
    • Set all other MSIBS and MDSB elements to 0 and MSIBS[0] to arr[0].

Calculate Increasing Subsequence Sums:

  • Iterate from i = 1 to n-1:
  • For each i, iterate from j = 0 to i-1:
  • If arr[i] > arr[j] and MSIBS[i] < MSIBS[j] + arr[i]:
  • Update MSIBS[i] with MSIBS[j] + arr[i].

Calculate Decreasing Subsequence Sums (in reverse order):

  • Iterate from i = n-2 to 0:
  • For each i, iterate from j = n-1 down to i+1:
  • If arr[i] > arr[j] and MDSB[i] < MDSB[j] + arr[i]:
  • Update MDSB[i] with MDSB[j] + arr[i].

Return maxSum.

Intuition:

  • Finding the maximum increasing and decreasing subsequences is the problem's decomposition.
  • For these subproblems, intermediate results are efficiently stored by MSIBS and MDSB.
  • Building the bi-tonic subsequence by layering increasing and decreasing parts is possible.
  • The right values from MSIBS and MDSB are combined to get the ultimate maximum sum.
  • Due to avoiding redundant calculations, dynamic programming results in O(n^2) time complexity.

Implementation in C++

#include <iostream>

#include <vector>

int maxSumBitonicSubsequence(const std::vector<int>& arr) {

    int n = arr.size();

    std::vector<int> MSIBS(n, 0);

    std::vector<int> MSDSB(n, 0);

    MSIBS[0] = arr[0];

    for (int i = 1; i < n; i++) {

        for (int j = 0; j < i; j++) {

            if (arr[i] > arr[j] && MSIBS[i] < MSIBS[j] + arr[i]) {

                MSIBS[i] = MSIBS[j] + arr[i];

            }

        }

    }

    MSDSB[n - 1] = arr[n - 1];

    for (int i = n - 2; i >= 0; i--) {

        for (int j = n - 1; j > i; j--) {

            if (arr[i] > arr[j] && MSDSB[i] < MSDSB[j] + arr[i]) {

                MSDSB[i] = MSDSB[j] + arr[i];

            }

        }

    }

    int maxSum = 0;

    for (int i = 0; i < n; i++) {

        int currentSum = MSIBS[i] + MSDSB[i] - arr[i];

        maxSum = std::max(maxSum, currentSum);

    }

    return maxSum;

}

int main() {

    std::vector<int> arr = {1, 15, 51, 45, 33, 100, 12, 18, 9};

    int n = arr.size();

    int maxSum = maxSumBitonicSubsequence(arr);

    std::cout << "Maximum sum bi-tonic subsequence: " << maxSum << std::endl;

    return 0;

}

Output:

Maximum sum Bi-tonic sub-sequence in C++

Time and Space Complexity

Time Complexity:

  • O(n^2) due to the nested loops used to compute MDSB and MSIBS.
  • There are n^2 operations because each loop iterates over n elements.

Space Complexity:

  • O(n), mostly due to using two auxiliary arrays, each with size n: MSIBS and MDSB.
  • Compared to n, additional space for variables and function calls is insignificant.

Enhancement for more expansive arrays:

  • Consider different strategies such as divide-and-conquer or more sophisticated dynamic programming methods that could lower the time complexity to O(n log n) or even O(n).
  • Space optimization: Investigate methods to reduce the space complexity to O(1) if space is a significant constraint. It may involve modifying the input array or employing a single auxiliary array.