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Using dynamicarrays, implement a polynomial class with polynomial addition, subtraction, and multiplication.

Using dynamicarrays, implement a polynomial class with polynomial addition, subtraction, and multiplication.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Use C++

Using dynamicarrays, implement a polynomial class with polynomial addition, subtraction, and multiplication.
Implement addition and subtraction functions first. 
Multiplication function –extra point

## Polynomial Class Implementation The image provides a code snippet for implementing a Polynomial class in C++ and explains its structure with diagrams illustrating how to handle polynomial expressions dynamically. ### Code Explanation: ```cpp class Polynomial { public: Polynomial(); Polynomial(int d); Polynomial(int* c, int d); int getDegree(); int* getCoef(); friend Polynomial add(Polynomial x, Polynomial y); friend Polynomial subtract(Polynomial x, Polynomial y); // friend Polynomial multiply(Polynomial x, Polynomial y); // extra point private: int* coef; int degree; }; ``` - **Constructors:** - `Polynomial()`: Default constructor. - `Polynomial(int d)`: Initializes a polynomial with a specific degree `d`. - `Polynomial(int* c, int d)`: Initializes with coefficients `c` and degree `d`. - **Methods:** - `int getDegree()`: Returns the degree of the polynomial. - `int* getCoef()`: Returns the coefficients array. - **Friend Functions:** - `add(Polynomial x, Polynomial y)`: Adds two polynomials. - `subtract(Polynomial x, Polynomial y)`: Subtracts one polynomial from another. - `multiply(Polynomial x, Polynomial y)`: (Commented out) Multiplies two polynomials. ### Note: > *If needed, you can add additional member functions.* ### Diagram Explanation: - **Object A:** - Polynomial: \( A = 4x^7 + 5x^6 + 3x^3 + 2x^1 + 8x^0 \) - Degree: 7 - Coefficients Array: `[8, 0, 2, 0, 0, 3, 0, 5, 4]` - **Object B:** - Polynomial: \( B = 6x^8 + 3x^6 + 4x^5 + 8x^3 + 3x^1 + 2x^0 \) - Degree: 8 - Coefficients Array: `[2, 0, 3, 0, 0, 0, 3, 0, 6]` ### Graphs Explanation: - **Dynamic Array:** - Both objects use a dynamic array
Transcribed Image Text:## Polynomial Class Implementation The image provides a code snippet for implementing a Polynomial class in C++ and explains its structure with diagrams illustrating how to handle polynomial expressions dynamically. ### Code Explanation: ```cpp class Polynomial { public: Polynomial(); Polynomial(int d); Polynomial(int* c, int d); int getDegree(); int* getCoef(); friend Polynomial add(Polynomial x, Polynomial y); friend Polynomial subtract(Polynomial x, Polynomial y); // friend Polynomial multiply(Polynomial x, Polynomial y); // extra point private: int* coef; int degree; }; ``` - **Constructors:** - `Polynomial()`: Default constructor. - `Polynomial(int d)`: Initializes a polynomial with a specific degree `d`. - `Polynomial(int* c, int d)`: Initializes with coefficients `c` and degree `d`. - **Methods:** - `int getDegree()`: Returns the degree of the polynomial. - `int* getCoef()`: Returns the coefficients array. - **Friend Functions:** - `add(Polynomial x, Polynomial y)`: Adds two polynomials. - `subtract(Polynomial x, Polynomial y)`: Subtracts one polynomial from another. - `multiply(Polynomial x, Polynomial y)`: (Commented out) Multiplies two polynomials. ### Note: > *If needed, you can add additional member functions.* ### Diagram Explanation: - **Object A:** - Polynomial: \( A = 4x^7 + 5x^6 + 3x^3 + 2x^1 + 8x^0 \) - Degree: 7 - Coefficients Array: `[8, 0, 2, 0, 0, 3, 0, 5, 4]` - **Object B:** - Polynomial: \( B = 6x^8 + 3x^6 + 4x^5 + 8x^3 + 3x^1 + 2x^0 \) - Degree: 8 - Coefficients Array: `[2, 0, 3, 0, 0, 0, 3, 0, 6]` ### Graphs Explanation: - **Dynamic Array:** - Both objects use a dynamic array
The image contains information about polynomial expressions and their operations. Here's the transcription suitable for an educational website: --- **Polynomial Operations Example** We are given two polynomials, \( A \) and \( B \), and we will explore their addition and subtraction. **Polynomial A:** \[ A = 4x^7 + 5x^6 + 3x^3 + 2x^1 + 8x^0 \] - **Object A:** - Coefficients: \( [0, 0, 0, 3, 0, 0, 5, 4] \) - Degree: 7 **Polynomial B:** \[ B = 6x^8 + 3x^6 + 4x^5 + 8x^3 + 3x^1 + 2x^0 \] - **Object B:** - Coefficients: \( [2, 3, 0, 8, 0, 4, 3, 0, 6] \) - Degree: 8 **Addition of Polynomials (A + B):** The result of adding polynomials \( A \) and \( B \) is: \[ 6x^8 + 4x^7 + 8x^6 + 4x^5 + 11x^3 + 5x^1 + 10x^0 \] - Combined Coefficients: \( [10, 5, 0, 11, 0, 4, 8, 4, 6] \) - Resulting Degree: 8 **Subtraction of Polynomials (A - B):** The result of subtracting polynomial \( B \) from \( A \) is: \[ 6x^8 + 4x^7 + 2x^6 - 4x^5 - 5x^3 - x^1 + 6x^0 \] - Combined Coefficients: \( [6, -1, 0, -5, 0, -4, 2, 4, 6] \) - Resulting Degree: 8 **Explanation of the Tables:** The tables display the coefficients for each power of x, starting from \( x^0 \) up to \( x^8 \), where applicable. The degree
Transcribed Image Text:The image contains information about polynomial expressions and their operations. Here's the transcription suitable for an educational website: --- **Polynomial Operations Example** We are given two polynomials, \( A \) and \( B \), and we will explore their addition and subtraction. **Polynomial A:** \[ A = 4x^7 + 5x^6 + 3x^3 + 2x^1 + 8x^0 \] - **Object A:** - Coefficients: \( [0, 0, 0, 3, 0, 0, 5, 4] \) - Degree: 7 **Polynomial B:** \[ B = 6x^8 + 3x^6 + 4x^5 + 8x^3 + 3x^1 + 2x^0 \] - **Object B:** - Coefficients: \( [2, 3, 0, 8, 0, 4, 3, 0, 6] \) - Degree: 8 **Addition of Polynomials (A + B):** The result of adding polynomials \( A \) and \( B \) is: \[ 6x^8 + 4x^7 + 8x^6 + 4x^5 + 11x^3 + 5x^1 + 10x^0 \] - Combined Coefficients: \( [10, 5, 0, 11, 0, 4, 8, 4, 6] \) - Resulting Degree: 8 **Subtraction of Polynomials (A - B):** The result of subtracting polynomial \( B \) from \( A \) is: \[ 6x^8 + 4x^7 + 2x^6 - 4x^5 - 5x^3 - x^1 + 6x^0 \] - Combined Coefficients: \( [6, -1, 0, -5, 0, -4, 2, 4, 6] \) - Resulting Degree: 8 **Explanation of the Tables:** The tables display the coefficients for each power of x, starting from \( x^0 \) up to \( x^8 \), where applicable. The degree
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