10个重要的算法C语言实现源代码

10个重要的算法C语言实现源代码：拉格朗日，牛顿插值，高斯，龙贝格，牛顿迭代，牛顿-科特斯，雅克比，秦九昭，幂法，高斯塞德尔

1.拉格朗日插值多项式，用于离散数据的拟合

1#include

2 #include

3 #include

4float lagrange(float *x,float *y,float xx,int n) /*拉格朗日插值算法*/

5 { int i,j;

6float *a,yy=0.0; /*a作为临时变量，记录拉格朗日插值多项式*/

7 a=(float *)malloc(n*sizeof(float));

8for(i=0;i<=n-1;i++)

9 { a[i]=y[i];

10for(j=0;j<=n-1;j++)

11if(j!=i) a[i]*=(xx-x[j])/(x[i]-x[j]);

12 yy+=a[i];

13 }

14 free(a);

15return yy;

16}

17main()

18{ int i,n;

19float x[20],y[20],xx,yy;

20 printf("Input n:");

21 scanf("%d",&n);

22if(n>=20) {printf("Error!The value of n must in (0,20)."); getch();return1;}

23if(n<=0) {printf("Error! The value of n must in (0,20)."); getch(); return1;}

25 { printf("x[%d]:",i);

26 scanf("%f",&x[i]);

27 }

28 printf("\n");

29for(i=0;i<=n-1;i++)

30 { printf("y[%d]:",i);scanf("%f",&y[i]);}

31 printf("\n");

32 printf("Input xx:");

33 scanf("%f",&xx);

34 yy=lagrange(x,y,xx,n);

35 printf("x=%f,y=%f\n",xx,yy);

36 getch();

37}

38

2.牛顿插值多项式，用于离散数据的拟合

1#include

2#include

3#include

4void difference(float *x,float *y,int n)

5{ float *f;

6int k,i;

7 f=(float *)malloc(n*sizeof(float));

8for(k=1;k<=n;k++)

9 { f[0]=y[k];

11 f[i+1]=(f[i]-y[i])/(x[k]-x[i]);

12 y[k]=f[k];

13 }

14return;

15}

16main()

17{ int i,n;

18float x[20],y[20],xx,yy;

19 printf("Input n:");

20 scanf("%d",&n);

21if(n>=20) {printf("Error! The value of n must in (0,20)."); getch(); return1;}

22if(n<=0) {printf("Error! The value of n must in (0,20).");getch(); return1;} 23for(i=0;i<=n-1;i++)

24 { printf("x[%d]:",i);

25 scanf("%f",&x[i]);

26 }

27 printf("\n");

28for(i=0;i<=n-1;i++)

29 { printf("y[%d]:",i);scanf("%f",&y[i]);}

30 printf("\n");

31 difference(x,(float *)y,n);

32 printf("Input xx:");

33 scanf("%f",&xx);

34 yy=y[20];

35for(i=n-1;i>=0;i--) yy=yy*(xx-x[i])+y[i];

36 printf("NewtonInter(%f)=%f",xx,yy);

37 getch();

38}

39

3.高斯列主元消去法,求解其次线性方程组

1#include

2#include

3#define N 20

4int main()

5{ int n,i,j,k;

6int mi,tmp,mx;

7float a[N][N],b[N],x[N];

8 printf("\nInput n:");

9 scanf("%d",&n);

10if(n>N)

11 { printf("The input n should in(0,N)!\n");

12 getch();

13return1;

14 }

15if(n<=0)

16 { printf("The input n should in(0,N)!\n");

17 getch();

18return1;

19 }

20 printf("Now input a(i,j),i,j=0%d:\n",n-1); 21for(i=0;i

22 { for(j=0;j

23 scanf("%f",&a[i][j]);}

24 printf("Now input b(i),i,j=0%d:\n",n-1); 25for(i=0;i

26 scanf("%f",&b[i]);

27for(i=0;i

28 { for(j=i+1,mi=i,mx=fabs(a[i][j]);jmx)

30 { mi=j;

31 mx=fabs(a[j][i]);

32 }

33if(i

34 { tmp=b[i];b[i]=b[mi];b[mi]=tmp;

35for(j=i;j

36 { tmp=a[i][j];

37 a[i][j]=a[mi][j];

38 a[mi][j]=tmp;

39 }

40 }

41for(j=i+1;j

42 { tmp=-a[j][i]/a[i][i];

43 b[j]+=b[i]*tmp;

44for(k=i;k

45 a[j][k]+=a[i][k]*tmp;

46 }

47 }

48 x[n-1]=b[n-1]/a[n-1][n-1];

49for(i=n-2;i>=0;i--)

50 { x[i]=b[i];

51for(j=i+1;j

52 x[i]-=a[i][j]*x[j];

53 x[i]/=a[i][i];

54 }

55for(i=0;i

56 printf("Answer:\n x[%d]=%f\n",i,x[i]);

57 getch();

58return0;

59}

60

61

62#include

63#include

64#define NUMBER 20

65#define Esc 0x1b

66#define Enter 0x0d

67

68float A[NUMBER][NUMBER+1] ,ark; 69int flag,n;

70exchange(int r,int k);

71float max(int k);

72message();

73

74main()

75{

76float x[NUMBER];

77int r,k,i,j;

78char celect;

79 clrscr();

80

81 printf("\n\nUse Gauss.");

82 printf("\n\n1.Jie please press Enter.");

83 printf("\n\n2.Exit press Esc.");

84 celect=getch();

85if(celect==Esc)

86 exit(0);

87 printf("\n\n input n=");

88 scanf("%d",&n);

89 printf(" \n\nInput matrix A and B:");

90for(i=1;i<=n;i++)

91 {

92 printf("\n\nInput a%d1--a%d%d and b%d:",i,i,n,i); 93

94for(j=1;j<=n+1;j++) scanf("%f",&A[i][j]);

95 }

96for(k=1;k<=n-1;k++)

97 {

98 ark=max(k);

99if(ark==0)

100 {

101 printf("\n\nIt's wrong!");message();

102 }

103else if(flag!=k)

104 exchange(flag,k);

105for(i=k+1;i<=n;i++)

106for(j=k+1;j<=n+1;j++)

107 A[i][j]=A[i][j]-A[k][j]*A[i][k]/A[k][k]; 108 }

109 x[n]=A[n][n+1]/A[n][n];

110for( k=n-1;k>=1;k--)

111 {

112float me=0;

113for(j=k+1;j<=n;j++)

114 {

115 me=me+A[k][j]*x[j];

116 }

117 x[k]=(A[k][n+1]-me)/A[k][k]; 118 }

119for(i=1;i<=n;i++)

120 {

121 printf(" \n\nx%d=%f",i,x[i]);

122 }

123 message();

124}

125

126exchange(int r,int k)

127{

128int i;

129for(i=1;i<=n+1;i++)

130 A[0][i]=A[r][i];

131for(i=1;i<=n+1;i++)

132 A[r][i]=A[k][i];

133for(i=1;i<=n+1;i++)

134 A[k][i]=A[0][i];

135}

136

137float max(int k)

138{

139int i;

140float temp=0;

141for(i=k;i<=n;i++)

142if(fabs(A[i][k])>temp)

143 {

144 temp=fabs(A[i][k]);

145 flag=i;

146 }

147return temp;

148}

149

150message()

151{

152 printf("\n\n Go on Enter ,Exit press Esc!");

153switch(getch())

154 {

155case Enter: main();

156case Esc: exit(0);

157default:{printf("\n\nInput error!");message();} 158 }

159}

4.龙贝格求积公式，求解定积分

1#include

2#include

3#define f(x) (sin(x)/x)

4#define N 20

5#define MAX 20

6#define a 2

7#define b 4

8#define e 0.00001

9float LBG(float p,float q,int n) 10{ int i;

11float sum=0,h=(q-p)/n;

12for (i=1;i

13 sum+=f(p+i*h);

14 sum+=(f(p)+f(q))/2;

15return(h*sum);

16}

17void main()

18 { int i;

19int n=N,m=0;

20float T[MAX+1][2];

21 T[0][1]=LBG(a,b,n);

22 n*=2;

23for(m=1;m

24 { for(i=0;i

25 T[i][0]=T[i][1];

26 T[0][1]=LBG(a,b,n);

27 n*=2;

28for(i=1;i<=m;i++)

29 T[i][1]=T[i-1][1]+(T[i-1][1]-T[i-1][0])/(pow(2,2*m)-1); 30if((T[m-1][1]T[m][1]-e))

31 { printf("Answer=%f\n",T[m][1]); getch();

32return ;

33 }

34 }

35 }

36

5.牛顿迭代公式，求方程的近似解

1#include

2#include

3#include

4#define N 100

5#define PS 1e-5

6#define TA 1e-5

7float Newton(float (*f)(float),float(*f1)(float),float x0 ) 8{ float x1,d=0;

9int k=0;

10do

11 { x1= x0-f(x0)/f1(x0);

12if((k++>N)||(fabs(f1(x1))

13 { printf("\nFailed!");

14 getch();

15 exit();

16 }

17 d=(fabs(x1)<1?x1-x0:(x1-x0)/x1);

18 x0=x1;

19 printf("x(%d)=%f\n",k,x0);

20 }

21while((fabs(d))>PS&&fabs(f(x1))>TA) ; 22return x1;

23}

24float f(float x)

25{ return x*x*x+x*x-3*x-3; }

26float f1(float x)

27{ return3.0*x*x+2*x-3; }

28void main()

29{ float f(float);

30float f1(float);

31float x0,y0;

32 printf("Input x0: ");

33 scanf("%f",&x0);

34 printf("x(0)=%f\n",x0);

35 y0=Newton(f,f1,x0);

36 printf("\nThe root is x=%f\n",y0);

37 getch();

38}

6. 牛顿-科特斯求积公式，求定积分

1#include

2#include

3int NC(a,h,n,r,f)

5float h;

6int n,f;

7float *r;

8{ int nn,i;

9float ds;

10if(n>1000||n<2)

11 { if (f)

12 printf("\n Faild! Check if 1

13return(-1);

14}

15if(n==2)

16{ *r=0.5*((*a)[0]+(*a)[1])*(h);

17return(0);

18}

19if (n-4==0)

20 { *r=0;

21*r=*r+0.375*(h)*((*a)[n-4]+3*(*a)[n-3]+3*(*a)[n-2]+(*a)[n-1]); 22return(0);

23}

24if(n/2-(n-1)/2<=0)

25nn=n;

26else

27nn=n-3;

28ds=(*a)[0]-(*a)[nn-1];

29for(i=2;i<=nn;i=i+2)

30ds=ds+4*(*a)[i-1]+2*(*a)[i];

31*r=ds*(h)/3;

33*r=*r+0.375*(h)*((*a)[n-4]+3*(*a)[n-3]+3*(*a)[n-2]+(*a)[n-1]); 34return(0);

35}

36main()

37{

38float h,r;

39int n,ntf,f;

40int i;

41float a[16];

42printf("Input the x[i](16):\n");

43for(i=0;i<=15;i++)

44 scanf("%d",&a[i]);

45h=0.2;

46f=0;

47ntf=NC(a,h,n,&r,f);

48if(ntf==0)

49 printf("\nR=%f\n",r);

50else

51 printf("\n Wrong!Return code=%d\n",ntf);

52 getch();

53}

7.雅克比迭代，求解方程近似解

1#include

2#include

3#define N 20

4#define MAX 100

5#define e 0.00001

6int main()

7{ int n;

8int i,j,k;

9float t;

10float a[N][N],b[N][N],c[N],g[N],x[N],h[N];

11 printf("\nInput dim of n:"); scanf("%d",&n);

12if(n>N)

13 { printf("Faild! Check if 0

15 {printf("Faild! Check if 0

16 printf("Input a[i,j],i,j=0…%d:\n",n-1);

17for(i=0;i

18for(j=0;j

19 scanf("%f",&a[i][j]);

20 printf("Input c[i],i=0…%d:\n",n-1);

21for(i=0;i

22scanf("%f",&c[i]);

23for(i=0;i

24for(j=0;j

25 { b[i][j]=-a[i][j]/a[i][i]; g[i]=c[i]/a[i][i]; }

26for(i=0;i

27 { for(j=0;j

28 h[j]=g[j];

29 { for(k=0;k

30 { if(j==k) continue; h[j]+=b[j][k]*x[k]; }

31 }

33for(j=0;j

34if(t

35for(j=0;j

36 x[j]=h[j];

37if(t

38 { printf("x_i=\n");

39for(i=0;i

40printf("x[%d]=%f\n",i,x[i]);

41 getch();

42return0;

43 }

44 printf("after %d repeat , return\n",MAX);

45 getch();

46return1;

47 }

48 getch();

49}

50

8.秦九昭算法

1#include

2float qin(float a[],int n,float x)

3{ float r=0;

4int i;

5for(i=n;i>=0;i--)

6 r=r*x+a[i];

8}

9main()

10{ float a[50],x,r=0;

11int n,i;

12do

13 { printf("Input frequency:");

14 scanf("%d",&n);

15 }

16while(n<1);

17 printf("Input value:");

18for(i=0;i<=n;i++)

19 scanf("%f",&a[i]);

20 printf("Input frequency:");

21 scanf("%f",&x);

22 r=qin(a,n,x);

23 printf("Answer:%f",r);

24 getch();

25}

26

9.幂法

1#include

2#include

3#define N 100

4#define e 0.00001

5#define n 3

6float x[n]={0,0,1};

7float a[n][n]={{2,3,2},{10,3,4},{3,6,1}};

8float y[n];

9main()

10{ int i,j,k;

11float xm,oxm;

12 oxm=0;

13for(k=0;k

14 { for(j=0;j

15 { y[j]=0;

16for(i=0;i

17 y[j]+=a[j][i]*x[i];

18 }

19 xm=0;

20for(j=0;j

21if(fabs(y[j])>xm) xm=fabs(y[j]);

22for(j=0;j

23 y[j]/=xm;

24for(j=0;j

25 x[j]=y[j];

26if(fabs(xm-oxm)

27 { printf("max:%f\n\n",xm);

28 printf("v[i]:\n");

29for(k=0;k

31 }

32 oxm=xm;

33 }

34 getch();

35}

36

10.高斯塞德尔

1#include

2#include

3#define N 20

4#define M 99

5float a[N][N];

6float b[N];

7int main()

8{ int i,j,k,n;

9float sum,no,d,s,x[N];

10 printf("\nInput dim of n:");

11 scanf("%d",&n);

12if(n>N)

13 { printf("Faild! Check if 0

14return1;

15 }

16if(n<=0)

17 { printf("Faild! Check if 0

18 printf("Input a[i,j],i,j=0…%d:\n",n-1);

19for(i=0;i

20for(j=0;j

21 scanf("%f",&a[i][j]);

22 printf("Input b[i],i=0…%d:\n",n-1);

23for(i=0;i

24for(i=0;i

25 k=0;

26 printf("\nk=%dx=",k);

27for(i=0;i

28do

29 { k++;

30if(k>M){printf("\nError!\n”);getch();} 31break;

32 }

33 no=0.0;

34for(i=0;i

35 { s=x[i];

36 sum=0.0;

37for(j=0;j

38if (j!=i) sum=sum+a[i][j]*x[j];

39 x[i]=(b[i]-sum)/a[i][i];

40 d=fabs(x[i]-s);

41if (no

42 }

43 printf("\nk=%2dx=",k);

44for(i=0;i

45}

46while (no>=0.1e-6);

47if(no<0.1e-6)

48{ printf("\n\n answer=\n");

49 printf("\nk=%d",k);

50for (i=0;i

51 printf("\n x[%d]=%12.8f",i,x[i]);