[ganselo]

Вот что получилось...

Код:

/**Dano n tochek. Postroit' mnogochlen prohodyashiy cherez dannie tochki.
(Postroenie interpolyacionnogo mnogochlena v yavnom vide. Metod Lagranja)
**/

#include <stdio.h>
#include <time.h>
#include <graphics.h>
#define N 10

int driver=DETECT, mode;
int n, xl=80, xr=620, yl=20, yr=430;
double a, b, max=-100000, min=100000;

double f(double *x, double *y, double X);
void OXY(double a, double b, double M, double m);
void tochki(double *x, double *y, double kx, double ky, double x0, double y0);
void graphic(double kx, double ky, double x0, double y0, double *x, double *y);

int main()
{
    int  i;
    double j, Y, kx, ky, x0, y0, m, M;
    printf ("Vvedite kol-vo tochek :");
    scanf ("%d", &n);
    double x[n], y[n];

    srand (time(NULL));
    for (i=0; i<n; i++)
    {
        x[i]=1+rand()%400;
        y[i]=1+rand()%400;
    }
    m=x[0];
    M=x[0];
    for (i=0; i<n; i++)
    {
        if (M<x[i]) M=x[i];
        if (m>x[i]) m=x[i];
    }
    a=m; b=M;

    initgraph(&driver, &mode, "");
    for (j=a; j<b; j=j+0.1)
    {
        if (f(x, y, j)>max) max=f(x, y, j);
        if (f(x, y, j)<min) min=f(x, y, j);
    }

    kx=(xr-xl)/(b-a);
    ky=(yr-yl)/(max-min);
    x0=xl-a*kx;
    y0=yr+min*ky;

    OXY(a, b, max, min);
    graphic(kx, ky, x0, y0, x, y);
    tochki(x, y, kx, ky, x0, y0);

    getch();
    closegraph();


return 0;
}


double f(double *x, double *y, double X)
{
    int i, j;
    double B, L=0;
    for(j=0; j<n; j++)
    {
        B=y[j];
        for(i=0; i<n; i++)
        {
            if(i!=j) B=B*(X - x[i])/(x[j] - x[i]);
        }
    L+=B;
    }
return L;
}

void OXY(double a, double b, double M, double m)
{
    int i;
    double x, y;
    char h[10];
    setcolor (9);
    rectangle (xl, yl, xr, yr);
    setcolor (7);
    for(i=0; i<=N; i++)
    {
        x=a+i*(b-a)/N;
        sprintf(h,"%.1f",x);
        outtextxy(xl+i*(xr-xl)/N-10,yr+10,h);
        y=M-i*(M-m)/N;
        sprintf(h,"%.1f",y);
        outtextxy(xl-70,yl+i*(yr-yl)/N-5,h);
    }
}

void tochki(double *x, double *y, double kx, double ky, double x0, double y0)
{
    double tx, ty;
    setcolor (5);
    for (int i=0; i<n; i++)
    {
        tx=x0+x[i]*kx;
        ty=y0-f(x, y, x[i])*ky;
        circle (tx, ty, 3);
        circle (tx, ty, 2);
        circle (tx, ty, 1);
    }
}

void graphic(double kx, double ky, double x0, double y0, double *x, double *y)
{
    double xm, ym;
    for (double j=a; j<b; j=j+0.01)
    {
        xm=x0+j*kx;
        ym=y0-f(x, y, j)*ky;
        putpixel(xm,ym,7);
    }
}