博客园

KMP字符匹配算法+Romberg数值求积分+Simpson求积分

KMP字符匹配算法：（具体理论知识参见 严蔚敏的《数据结构（C语言版）》字符串那一章节）

代码：

  1 //index_kmp.c
  2 //KPM搜索算法
  3 //
  4 #include <stdio.h>
  5 #include <string.h>
  6 
  7 //---串的定长顺序存储表示－－－－－
  8 #define MAXSTRLEN 255  //用户可在255以内定义最大串长
  9 typedef unsigned char SString[MAXSTRLEN + 1];//0号单元存放串的长度
 10 
 11 int index_KMP(SString S, SString T, int pos);
 12 void get_next(SString T, int next[]);
 13 //接收char * 类型的字符串，以便测试
 14 int get_index(char * Sstr, char * Tstr, int pos);
 15 
 16 int main()
 17 {
 18     SString S = "xabcdefghijklmn",
 19             T = "xghi";
 20     char a[2] = "12";
 21     sprintf(a,"%c%c",15,3);
 22     printf("%c\n%c\n",T[0],T[1]);
 23     S[0] = a[0];
 24     T[0] = a[1];
 25     printf("S = %s\n",&S[1]);
 26     printf("T = %s\n",&T[1]);
 27     printf("S[0] = %d\n",S[0]);
 28     printf("T[0] = %d\n",T[0]);
 29     int index = index_KMP(S, T, 1);
 30     printf("k1 = %d\n", index);
 31     char * Sstr = "abcdefghijklmn",
 32          * Tstr = "ghi";
 33     index = get_index(Sstr, Tstr, 1);
 34     printf("k2 = %d\n", index);
 35     return 0;
 36 }
 37 
 38 //
 39 //接收char * 类型的字符串，以便测试
 40 int get_index(char * Sstr, char * Tstr, int pos)
 41 {
 42     SString S,T;
 43     sprintf(S,"%c%s",strlen(S),Sstr);
 44     sprintf(T,"%c%s",strlen(T),Tstr);    
 45     return index_KMP(S, T, 1);
 46 }
 47 
 48 int index_KMP(SString S, SString T, int pos)
 49 {
 50     int i = pos,
 51         j = 1;
 52     int next[MAXSTRLEN + 1];
 53     get_next(T, next);
 54     while (i <= S[0] && j <= T[0])
 55     {
 56         if (j == 0 || S[i] == T[j])
 57         {
 58             ++i;
 59             ++j;
 60         }
 61         else
 62         {
 63             j = next[j];//不匹配，j回溯
 64         }
 65     }
 66     if (i <= S[0])
 67     {
 68         return i-T[0];
 69     }
 70     else
 71     {
 72         return 0;
 73     }
 74 }
 75 void get_next(SString T, int next[])
 76 {
 77     int i = 1,
 78         j = 0;
 79     next[1] = 0;
 80     printf("T[0] = %d\n",T[0]);
 81     while (i < T[0])
 82     {
 83         if (j == 0 || T[i] == T[j])
 84         {
 85             ++i;
 86             ++j;
 87             if (T[i] != T[j])
 88             {
 89                 next[i] = j;
 90             }
 91             else
 92             {
 93                 next[i] = next[j];
 94             }
 95             printf("%d : %d ",i,next[i]);
 96         }
 97         else
 98         {
 99             j = next[j];//回溯查找匹配个数
100         }
101     }
102     printf("\n");
103 }

我是在Linux下平台完成的，所以写了个简单的makefile

obj = index_kmp.o

index:$(obj)
    cc -o index $(obj)

$(obj):index_kmp.c
    cc -c index_kmp.c

clean:
    rm index index_kmp.o

下面的两个代码是《数值分析》的内容，具体理论知识详见 求积分的那一章节


Simpson求积分 

 1 //simpsom.c
 2 //使用辛普森求积公式
 3 //区间[a,b]分为n等分
 4 //h=(b-a)/n;
 5 //x(k)=a+k*h;
 6 //x(k+1/2)=x(k)+h/2;
 7 //Sn=(h/6)*( f(a) + 4*sum(f(x(k)＋1/2)) + 2*sum(f(x(k))) + f(b) );
 8 //Rn =(-(b-a)/180 ) * (h/2)^4 * f''''(n)
 9 //
10 
11 #include <stdio.h>
12 #include <math.h>
13 
14 float simpson(float a, float b, int n);
15 float f(float x);
16 
17 int main()
18 {
19     float a=1,b=10,n=10;
20     float Sn = simpson(a,b,n);
21     printf("%f\n", Sn);
22 }
23 
24 float simpson(float a, float b, int n)
25 {
26     float h = (b-a)/n;
27     float sum4 = 0,//序数为4的求和项
28           sum2 = 0;//序数为2的求和项
29     float xk = a,
30           xk2 = xk + h/2;
31     sum4 = f(xk2);
32     int k;
33     for (k=1; k <= n-1; k++)
34     {
35         xk = a + k*h;
36         xk2 = xk + h/2;
37         sum4 += f(xk2);
38         sum2 += f(xk);
39     }
40     sum4 *= 4;
41     sum2 *= 2;
42     float Sn = (h/6) * (f(a) + sum4 + sum2 + f(b));
43     return Sn;
44 }
45 
46 //被积函数
47 float f(float x)
48 {
49   return x*x*x;
50 }

Romberg数值求积分

 1//Romberg.c
 2 //使用龙贝格算法求积分
 3 //
 4 
 5 #include <stdio.h>
 6 #include <math.h>
 7 #include <stdlib.h>
 8 
 9 //T[k][m]表示积分表
10 float * romberg(float a, float b, int k, int m, float (* f)(float x));
11 //测试函数
12 float f(float x);
13 
14 //测试函数
15 float f(float x)
16 {
17     return pow(x,1.5);
18 }
19 
20 
21 int main()
22 {
23     float a = 0, b = 1;
24     int k = 6, m = 6;
25     float * T = romberg(a,b,k,m,f);
26     int i,j;
27     for (i = 0; i<k; i++)
28     {
29         printf("k=");
30         for (j = 0; j<=i; j++)
31         {
32             printf("%d  %f  ",i,T[i*m+j]);
33         }
34         printf("\n");        
35     }
36     free(T);
37     T = NULL;
38     return 0;
39 }
40 
41 //T[k][m]表示积分表
42 float * romberg(float a, float b, int k, int m, float (* f)(float x))
43 {
44     float * T;
45     T = (float *)malloc(k*m*sizeof(float));
46     T[0] = (b-a)*(f(a) + f(b))/2;
47     int kk;
48     for (kk = 1; kk <= k; kk++)
49     {
50         int j;
51         float sum = 0;        
52         for (j = 0; j <= pow(2.0,kk-1) - 1; j++)
53         {
54             sum += f(a + (2*j+1)*(b-a)/pow(2.0,kk));
55         }
56         sum *= (b-a)/pow(2.0,kk);
57         //printf("%f\n", sum);
58         T[kk*m+0] = T[(kk-1)*m+0]/2 + sum;
59         int mm;
60         for (mm = 1; mm <= m; mm++)
61         {
62             T[kk*m+mm] = (pow(4.0,mm)*T[kk*m+mm-1] - T[(kk-1)*m+mm-1]) / (pow(4.0,mm) - 1);
63         }
64 
65     }
66     return T;
67 }

makefile 还是很好用的

Romberg: Romberg.o
    cc -lm -o Romberg
Romberg.o: Romberg.c
    cc -c Romberg.c
clean:
    rm *.o Romberg



以上代码均在GCC下编译运行通过。

posted @ 2011-10-18 00:23  涵曦  阅读(868)  评论(0)  编辑  收藏  举报