void readPolynom(int **p, int *n) {
    printf("Give the degree of the polynom -> ");
    scanf("%d", n);

    // Allocate memory for coefficients (degree + 1 elements)
    *p = (int *)malloc((*n + 1) * sizeof(int));
    if (*p == NULL) {
        printf("Memory allocation failed!\n");
        exit(1);
    }

    for(int i = 0; i <= *n; i++) {
        printf("P[%d] = ", i);
        scanf("%d", (*p + i));
    }
}

void writePolynom(int *p, int *n) {
    printf("p(x) = %dx^0", p[0]);
    for(int i = 1; i <= *n; i++) {
        printf(" + %dx^%d", p[i], i);
    }
}

float valuePolynom(int *p, int *n, float x) {
    float value = p[0],
          aux = 1;

    for(int i = 1; i <= *n; ++i) {
        aux = aux * x;
        value += aux * p[i];
    }

    return value;
}

void derivatePolynom(int *p, int *n) {
    for(int i = 0; i < *n; i++) {
        p[i] = p[i + 1] * (i + 1);
    }
    (*n)--;
}

Polynomial Derivative Calculator

A C program that handles polynomial operations including reading coefficients, calculating derivatives, and evaluating polynomials at specific points.

Features

  • Read polynomial coefficients dynamically
  • Display polynomial in standard mathematical notation
  • Calculate first derivative of polynomials
  • Evaluate polynomials at given points
  • Dynamic memory management for polynomial coefficients

Technical Details

Functions

readPolynom(int **p, int *n)

  • Takes a pointer to pointer for coefficients array and pointer to degree
  • Dynamically allocates memory for coefficients
  • Reads polynomial degree and coefficients from user input
  • Error handling for memory allocation failures

writePolynom(int *p, int *n)

  • Displays polynomial in standard mathematical notation
  • Format: ax^0 + bx^1 + cx^2 + …
  • Takes coefficient array and degree as parameters

valuePolynom(int *p, int *n, float x)

  • Evaluates polynomial at a given point x
  • Uses Horner’s method for efficient computation
  • Returns float value of polynomial evaluation

derivatePolynom(int *p, int *n)

  • Calculates first derivative of the polynomial
  • Modifies original coefficient array
  • Updates polynomial degree (reduces by 1)

Usage

  1. Compile the program: 
    gcc polynomial.c -o polynomial
  2. Run the executable: 
    ./polynomial
  3. Follow the prompts:
    • Enter the degree of polynomial
    • Enter coefficients starting from constant term
    • Program will display:
      • Original polynomial
      • Its derivative
      • Value at x = 1.450

Example

Give the degree of the polynom -> 2
P[0] = 1
P[1] = 2
P[2] = 3

Original polynomial: p(x) = 1x^0 + 2x^1 + 3x^2
Derivative: p(x) = 2x^0 + 6x^1
p(1.450) = 8.273

Memory Management

The program uses dynamic memory allocation to handle polynomials of any degree:

  • Memory is allocated using malloc()
  • Proper memory deallocation using free()
  • Includes error checking for allocation failures

Technical Requirements

  • C compiler (gcc recommended)
  • Standard C libraries:
    • stdio.h
    • stdlib.h

Error Handling

The program includes basic error handling for:

  • Memory allocation failures
  • Invalid input validation (basic)

Limitations

  • Handles only integer coefficients
  • Calculates only first derivative
  • No input validation for polynomial degree limits