Newton.c

#include "stdio.h"
#include "stdlib.h"
#include "math.h"

float calculateX(float xFrom, float i, float step) {
    return xFrom + i * step;
}
float yFormula(float x) {
    return exp(-(x - 2) * (x - 2));
}

char* getQ(float x0, float h) {
    int bufLen = snprintf(0, 0, "(x - %f)/%f", x0, h);
    char* buf = (char*)malloc(bufLen + 1);
    snprintf(buf, bufLen + 1, "(x - %f)/%f", x0, h);
    return buf;
}

float calculateYDelta(float xFrom, float step, int power, int i) {
    if (power <= 1)
        return yFormula(calculateX(xFrom, i, step));
    else
        return calculateYDelta(xFrom, step, power - 1, i) - calculateYDelta(xFrom, step, power - 1, i + 1);
}

void printNewton1(float xFrom, float step, int n, char* q) {
    printf("P(x) = %f", calculateYDelta(xFrom, step, 0, 0));
    float fact = 1;
    for (int i = 1; i <= n; i++) {
        fact *= i;
        float yDelta = calculateYDelta(xFrom, step, i, 0);
        if (yDelta < 0) {
            yDelta *= -1;
            printf(" - ");
        }
        else
            printf(" + ");
        printf("%f(%s)", yDelta / fact, q);
        for (int j = 2; j <= i; j++)
            printf("(%s - %d)", q, j - 1);
    }
}

void printNewton2(float xFrom, float step, int n, char* q) {
    printf("P(x) = %f", calculateYDelta(xFrom, step, 0, n));
    float fact = 1;
    for (int i = 1; i <= n; i++) {
        fact *= i;
        float yDelta = calculateYDelta(xFrom, step, i, n - i);
        if (yDelta < 0) {
            yDelta *= -1;
            printf(" - ");
        }
        else
            printf(" + ");
        printf("%f(%s)", yDelta / fact, q);
        for (int j = 2; j <= i; j++)
            printf("(%s + %d)", q, j - 1);
    }
}

int main(int argc, char** argv) {
    float xFrom = 2;
    float xTo = 4;
    float step = 0.2;

    int n = (int)((xTo - xFrom) / step);

    char* q = getQ(xFrom, step);
    printNewton1(xFrom, step, n, q);
    free(q);

    printf("\n");

    q = getQ(xTo, step);
    printNewton2(xFrom, step, n, q);
    free(q);

    return 0;
}