bài tập môn phương pháp tính cho sinh viên khoa công nghệ thông tin

Bài tập môn phương pháp tính cho sinh viên khoa công nghệ thông tin

1.bảng nội suy ayken và giá trị

#include<stdio.h>
#include<conio.h>
#define max 100
void nhap (float a[max],int n)
{
int i;
for (i=1;i<=n;i++)
{
printf("a[%d]=",i);
scanf("%f",&a[i]);
}
}
void xuat (float a[max],int n)
{
int i;
for (i=1;i<=n;i++)
printf("%f",a[i]);
}
main()
{
int i,j,n;
float x[max],y[max],a[max][max],c;
char tl;
while (1)
{
printf("nhap so nguyen duong n=");

scanf("%d",&n);
printf("\n nhap he so x[i] \n");
nhap (x,n);
xuat (x,n);
printf("\n nhap he so y[i] \n");
nhap (y,n);
xuat (y,n);
printf("\n nhap he so c can tinh c=");
scanf("%f",&c);
for (i=1;i<=n;i++)
{
a[i][0]=x[i];
a[i][1]=y[i];
printf("%f",a[i][0]);
printf("%f",a[i][1]);
for (j=2;j<=i;j++)
{
a[i][j]=(a[j-1][j-1]*(x[i]-c)-a[i][j-1]*(x[j-1]-c))/(x[i]-x[j-1]);
printf("%f",a[i][j]);
}
printf("\n");
}
printf("\n vay gia tri can tinh la %.3f",a[n][n]);
printf("\n ban co muon tiep tuc khong (c/k)?\n");
tl=getch();
if (tl=='k'||tl=='K')
break;
}
}

2.phương pháp bình phương bé nhất
#include<stdio.h>
#include<conio.h>
#include<math.h>
void nhap (float a[10],int n)
{
int i;
for (i=1;i<=n;i++)
{
printf("a[%d]=",i);
scanf("%f",&a[i]);
}
}
void xuat (float a[10],int n)
{
int i;
for (i=1;i<=n;i++)
printf("%.3f",a[i]);
}
void hoanvi (float *a,float *b)
{
float tmp;
tmp=*a;
*a=*b;
*b=tmp;
}
void doidong (float a[10][10],int n,int p,int q)
{
int k;

if (p<=n&&q<=n&&p!=q)
for (k=1;k<=n+1;k++)
hoanvi (&a[p][k],&a[q][k]);
}
float det (float a[10][10])
{
int i,j,k;
float m,s=1;
for (i=1;i<=3;i++)
{
if (a[i][i]==0)
{
for (k=i+1;k<=3;k++)
if (a[k][i]!=0)
doidong (a,3,i,k);
}
for (j=i+1;j<=3;j++)
{
m=-a[j][i]/a[i][i];
for (k=i;k<=3;k++)
a[j][k]+=a[i][k]*m;
}
s*=a[i][i];
}
return s;
}
void giaihephuongtrinh (float b[10][10],float c[10][10],float d[10][10],float e[10][10])
{
float p,q,r,l;
p=det (b);

q=det (c);
r=det (d);
l=det (e);
if (p==0)
printf("\n he phuong trinh vo nghiem \n");
else
{
printf("\n nghiem thu nhat cua he la %.3f",q/p);
printf("\n nghiem thu hai cua he la %.3f",r/p);
printf("\n nghiem thu ba cua he la %.3f",l/p);
printf("\nvay ket qua can tim la:y=%.3f+%.3f*x+%.3f*x*x",q/p,r/p,l/p);
}
}
main()
{
int n,i;
printf("nhap n=");
scanf("%d",&n);
float x[10],y[10],b[10][10],c[10][10],d[10][10],e[10][10];
float x1=0,xx=0,y1=0,yy=0,xxx=0,xxxx=0,xxy=0,xy=0;
nhap (x,n);
xuat (x,n);
printf("\n");
nhap (y,n);
xuat (y,n);
for (i=1;i<=n;i++)
{
x1+=x[i];
y1+=y[i];
xx+=x[i]*x[i];

yy+=y[i]*y[i];
xy+=x[i]*y[i];
xxx+=x[i]*x[i]*x[i];
xxxx+=x[i]*x[i]*x[i]*x[i];
xxy+=x[i]*x[i]*y[i];
}
b[1][1]=n;
b[1][2]=x1;
b[1][3]=xx;
b[2][1]=x1;
b[2][2]=xx;
b[2][3]=xxx;
b[3][1]=xx;
b[3][2]=xxx;
b[3][3]=xxxx;
c[1][1]=y1;
c[1][2]=x1;
c[1][3]=xx;
c[2][1]=xy;
c[2][2]=xx;
c[2][3]=xxx;
c[3][1]=xxy;
c[3][2]=xxx;
c[3][3]=xxxx;
d[1][1]=n;
d[1][2]=y1;
d[1][3]=xx;
d[2][1]=x1;
d[2][2]=xy;
d[2][3]=xxx;

d[3][1]=xx;
d[3][2]=xxy;
d[3][3]=xxxx;
e[1][1]=n;
e[1][2]=x1;
e[1][3]=y1;
e[2][1]=x1;
e[2][2]=xx;
e[2][3]=xy;
e[3][1]=xx;
e[3][2]=xxx;
e[3][3]=xxy;
giaihephuongtrinh (b,c,d,e);
getch();
}


3.đệ qui quay lui
#include<stdio.h>
#include<conio.h>
#include<math.h>
int count;
int x[3];
void out (int x[])
{
int i;
printf("\n%d\t",++count);
for ( i = 1; i <= 3; i++ )
printf("%d", x[i] );
}

void thu(int i, int x[])
{
int j;
if (i==1)
{
for (j=1; j<=5; j++)
{
x[i]=j;
thu(i+1,x);
}
}
if (i==2)
{
for (j=1;j<=5;j++)
{
x[i]=j;
thu(i+1,x);
}
}
if (i==3)
{
for (j=1;j<=5;j++)
{
x[i]=j;
out (x);
}
}
}
main()
{

thu (1,x);
getch();
}


4.tính định thức ma trận
#include<stdio.h>
#include<conio.h>
#include<math.h>
//tinh dinh thuc cua ma tran

void nhap (float a[10],int n)
{
int i;
for (i=1;i<=n;i++)
{
printf("a[%d]=",i);
scanf("%f",&a[i]);
}
}

void xuat (float a[10],int n)
{
int i;
for (i=1;i<=n;i++)
printf("%.3f",a[i]);
}

void hoanvi (float *a,float *b)
{

float tmp;
tmp=*a;
*a=*b;
*b=tmp;
}

void doidong (float a[10][10],int n,int p,int q)
{
int k;
if (p<=n&&q<=n&&p!=q)
for (k=1;k<=n+1;k++)
hoanvi (&a[p][k],&a[q][k]);
}

float det (float a[10][10])
{
int i,j,k;
float m,s=1;
for (i=1;i<=3;i++)
{
if (a[i][i]==0)
{
for (k=i+1;k<=3;k++)
if (a[k][i]!=0)
doidong (a,3,i,k);
}
for (j=i+1;j<=3;j++)
{
m=-a[j][i]/a[i][i];
for (k=i;k<=3;k++)

a[j][k]+=a[i][k]*m;
}
s*=a[i][i];
}
return s;
}

main()
{
int n,i;
printf("nhap n=");
scanf("%d",&n);
float x[10],y[10],b[10][10],c[10][10],d[10][10],e[10][10];
float x1=0,xx=0,y1=0,yy=0,xxx=0,xxxx=0,xxy=0,xy=0;
nhap (x,n);
xuat (x,n);
printf("\n");
nhap (y,n);
xuat (y,n);
for (i=1;i<=n;i++)
{
x1+=x[i];
y1+=y[i];
xx+=x[i]*x[i];
yy+=y[i]*y[i];
xy+=x[i]*y[i];
xxx+=x[i]*x[i]*x[i];
xxxx+=x[i]*x[i]*x[i]*x[i];
xxy+=x[i]*x[i]*y[i];
}

b[1][1]=n;
b[1][2]=x1;
b[1][3]=xx;
b[2][1]=x1;
b[2][2]=xx;
b[2][3]=xxx;
b[3][1]=xx;
b[3][2]=xxx;
b[3][3]=xxxx;
printf("\n dinh thuc cua ma tran la %.3f",det (b));
getch();
}

5.floy trong toán rời rạc
#include<stdio.h>
#include<conio.h>

main()
{
int n,i,j,k,sum=0,a[10][10],d[10][10],p[10][10];

//Nhap mt trong so n*n

printf("Nhap n: "); scanf("%d",&n);
printf("\nNhap mang: \n");
for(i=1;i<=n;i++)
for(j=1;j<=n;j++) {scanf("%d",&a[i][j]); sum+=a[i][j];}

for(i=1;i<=n;i++)
for(j=1;j<=n;j++)

if(a[i][j]==0) a[i][j]=sum; // cho 0 = vocung = sum

for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
{
d[i][j]=a[i][j];
p[i][j]=i;
}
for(k=1;k<=n;k++)
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
if(i!=j && d[i][j]>d[i][k]+d[k][j])
{
d[i][j]=d[i][k]+d[k][j];
p[i][j]=p[k][j];}
printf("\nMa tran a\n");
for(i=1;i<=n;i++)
{ printf("\n");
for(j=1;j<=n;j++) printf("\t%d",a[i][j]);
}
printf("\nMa tran d\n");
for(i=1;i<=n;i++)
{ printf("\n");
for(j=1;j<=n;j++) printf("\t%d",d[i][j]);
}
printf("\nMa tran p\n");
for(i=1;i<=n;i++)
{ printf("\n");
for(j=1;j<=n;j++) printf("\t%d",p[i][j]);
}

getch();
}

6.giải phương trình bằng phương pháp gauss
#include<stdio.h>
#include<conio.h>
#include<math.h>
void nhap (float a[][10],int n)
{
int i,j;
float x;
for (i=1;i<=n;i++)
for (j=1;j<=n+1;j++)
{
printf("a[%d][%d]=",i,j);
scanf("%f",&x);
a[i][j]=x;
}
}
void xuat (float a[][10],int n)
{
int i,j;
for (i=1;i<=n;i++)
{
printf("\n");
for (j=1;j<=n+1;j++)
printf("%f",a[i][j]);
}
}
void hoanvi (float *a,float *b)

{
float tmp;
tmp=*a;
*a=*b;
*b=tmp;
}
void doidong (float a[][10],int n,int p,int q)
{
int k;
if (p<=n&&q<=n&&p!=q)
for (k=1;k<=n+1;k++)
hoanvi (&a[p][k],&a[q][k]);
}
void make (float a[][10],float x[10],int n)
{
int i,j,k;
float m,s;
for (i=1;i<=n;i++)
{
if (a[i][i]==0)
{
for (k=i+1;k<=n;k++)
if (a[k][i]!=0)
doidong (a,n,i,k);
}
for (j=i+1;j<=n+1;j++)
{
m=-a[j][i]/a[i][i];
for (k=i;k<=n+1;k++)
a[j][k]+=a[i][k]*m;

}
}
printf("\n he phuong trinh sau khi bien doi la:\n",s);
xuat (a,n);
for (i=n;i>=1;i )
{
s=a[i][n+1];
for (k=i+1;k<=n;k++)
s-=a[i][k]*x[k];
if (a[i][i]!=0)
x[i]=s/a[i][i];
}
printf("\n vay ngiem cua he phuong trinh la: \n");
for (i=1;i<=n;i++)
printf("%.3f",x[i]);
}
main()
{
int n;
float a[10][10],x[10];
char tl;
while (1)
{
printf("nhap bac cua ma tran n=");
scanf("%d",&n);
printf("cac he so cua ma tran la:\n");
nhap (a,n);
xuat (a,n);
make (a,x,n);
printf("\n ban co muon tiep tuc khong (c/k)?\n");

tl=getch();
if (tl=='k'||tl=='K')
break;
}
}

7.giải hệ phương trình 2 ẩn
#include<stdio.h>
#include<conio.h>
#include<math.h>
void giaihephuongtrinh (float a,float b,float c,float d,float e,float f)
{
float i,k,m,l;
i=a*e-b*d;
k=c*e-b*f;
m=a*f-c*d;
if (i==0)
printf("he phuong trinh vo nghiem");
else
{
printf("\ngia tri cua a la la %.3f\n",k/i);
printf("\ngia tri cua b la %.3f",m/i);
l=exp (k/i);
printf("\n vay ham can tim la y=%.3f*emu%.3f",l,m/i);
}
}
main()
{
float a,b,c,d,e,f;
giaihephuongtrinh (1,2,3,5,6,4);

getch ();
}

8.giải hệ phương trình
#include<stdio.h>
#include<conio.h>
#include<math.h>
void nhap (float a[][10],int n)
{
int i,j;
float x;
for (i=1;i<=n;i++)
for (j=1;j<=n;j++)
{
printf("a[%d][%d]=",i,j);
scanf("%f",&x);
a[i][j]=x;
}
}
void xuat (float a[][10],int n)
{
int i,j;
for (i=1;i<=n;i++)
{
printf("\n");
for (j=1;j<=n;j++)
printf("%f",a[i][j]);
}
}
void hoanvi (float *a,float *b)

{
float tmp;
tmp=*a;
*a=*b;
*b=tmp;
}
void doidong (float a[][10],int n,int p,int q)
{
int k;
if (p<=n&&q<=n&&p!=q)
for (k=1;k<=n+1;k++)
hoanvi (&a[p][k],&a[q][k]);
}
float det (float a[10][10],int n)
{
int i,j,k;
float m,s=1;
for (i=1;i<=n;i++)
{
if (a[i][i]==0)
{
for (k=i+1;k<=n;k++)
if (a[k][i]!=0)
doidong (a,n,i,k);
}
for (j=i+1;j<=n;j++)
{
m=-a[j][i]/a[i][i];
for (k=i;k<=n;k++)
a[j][k]+=a[i][k]*m;

}
s*=a[i][i];
}
return s;
}
void giaihephuongtrinh (float b[10][10],float c[10][10],float d[10][10],float e[10][10],int n)
{
float p,q,r,l;
p=det (b,n);
q=det (c,n);
r=det (d,n);
l=det (e,n);
if (p==0)
printf("\n he phuong trinh vo nghiem \n");
else
{
printf("\n nghiem thu nhat cua he la %.3f",q/p);
printf("\n nghiem thu hai cua he la %.3f",r/p);
printf("\n nghiem thu ba cua he la %.3f",l/p);
}
}
main()
{
int n;
float b[10][10],c[10][10],d[10][10],e[10][10];
printf("nhap bac cua ma tran n=");
scanf("%d",&n);
printf("cac he so cua ma tran la:\n");
nhap (b,n);
xuat (b,n);

printf("\n");
nhap (c,n);
xuat (c,n);
printf("\n");
nhap (d,n);
xuat (d,n);
printf("\n");
nhap (e,n);
xuat (e,n);
printf("\n");
giaihephuongtrinh (b,c,d,e,n);
getch();
}

9.in bảng hoocner
#include<stdio.h>
#include<conio.h>
void nhap (float a[10],int n)
{
int i;
for (i=0;i<=n;i++)
{
printf("a[%d]=",i);
scanf("%f",&a[i]);