KMP算法

KMP算法

常见题型：

• 类型1：匹配子字符串在母串中第几个位置开始出现。

• 类型2：子串在母串中出现了几次（可以有重复的）。

  子串：AZA

  母串：AZAZAZA

  sum = 3；

• 类型3：母串中最多有几个子串。

• 类型4：需要再补几个字符能构成一个类似手链那样循环相同的。

  abca ->2

  abcde->5

  aaa->0

• 类型5：给出一字符串，找出由2个或2个以上相同的子字符串组成的前缀，输出前缀长度及其相同的子字符串数。

• 类型6：最小循环节有几个。

• 类型7：

类型一

匹配子字符串在母串中第几个位置开始出现

题目名称： Number Sequence

#include 
#include 
#include 
using namespace std;

int n;
int a[1000005];
int b[10005];
int nextp[10005];
int temp1;
int temp2;
/*--------------------------------------------------------*/
void getnext()
{
    int len = temp2;
    int i = 0;
    int j = -1;
    nextp[0] =-1;
    while (i<len)
    {
        if(j==-1||b[i]==b[j])
            nextp[++i] = ++j;
        else j = nextp[j];
    }
     
}
void kmp()
{
    getnext();
    int i = 0;
    int j = 0;
    while (i<temp1&&j<temp2)
    {
        if(j==-1||a[i]==b[j])
        {
            i++;
            j++;
        }
        else
            j = nextp[j];
        
    }
    if(j==temp2)
        printf("%d\n",i-j+1);
    else printf("-1\n");
    
}
/*--------------------------------------------------------*/
int main()
{
    scanf("%d",&n);
    while (n--)
    {
        memset(a,0,sizeof(a));
        memset(b,0,sizeof(b));
        memset(nextp,0,sizeof(nextp));
        
        scanf("%d %d", &temp1, &temp2);
        for (int i = 0; i < temp1; i++)
            scanf("%d", &a[i]);
        for (int i = 0; i < temp2; i++)
            scanf("%d", &b[i]);
        
        kmp();
    }
    

}

类型二

子串在母串中出现了几次（可以有重复的）

题目名称：Oulipo

#include 
#include 
#include 

using namespace std;

int n;
int count = 0;
char a[1000005];
char b[10005];
int nextt[10005];
int len1,len2;
/*-----------------------------------------*/
void getnext()
{
    int i = 0;
    int j = -1;
    nextt[0] = -1;
    while (i<len2)
    {
        if(j==-1||b[i]==b[j])
            nextt[++i] = ++j;
        else  j = nextt[j]; 
    }
    
}
void kmp()
{
    getnext();
    int i = 0;
    int j = 0;
    while (i<len1)
    {
        if(j==-1||a[i]==b[j])
        {
            i++;
            j++;
        }
        else j = nextt[j];
        if(j==len2)
        {
            count++;
            j = nextt[j];
        }
    }
    
}
/*-----------------------------------------*/
int main()
{
    scanf("%d",&n);
    getchar();
    while (n--)
    {
        memset(a,0,sizeof(a));
        memset(b,0,sizeof(b));
        memset(nextt,0,sizeof(nextt));

        count = 0;
        
        scanf("%s",b);
        scanf("%s",a);
        len1 = strlen(a);
        len2 = strlen(b);
        //printf("%d\n%d\ndd",len1,len2)
        kmp();
        printf("%d\n",count);


    }
    
}

类型三

母串中最多有几个子串。

题目名称：剪花布条

#include 
#include 
#include 
using namespace std;
char a[1005];
char b[1005];
int nextt[1005];
int len1,len2;
int count = 0;
/*------------------------------------------------------------------*/
void getnext()
{
    int i =0;
    int j =-1;
    nextt[0]=-1;
    while (i<len2)
    {
        if(j==-1||b[i]==b[j])
        nextt[++i] = ++j;
        else  j = nextt[j];
    }
    
    
}
void kmp()
{
    getnext();
    int i = 0;
    int j = 0;
    while (i<len1)
    {
       if(j==-1||a[i]==b[j])
       {
           i++;
           j++;
       }
       else j = nextt[j];
       if(j==len2)
       {
           count++;
           j = 0;
       }
    }
    printf("%d\n",count);
    
}
/*------------------------------------------------------------------*/
int main()
{
    while (1)
    {
        count = 0;
        memset(a,0,sizeof(a));
        memset(b,0,sizeof(b));
        memset(nextt,0,sizeof(nextt));
        scanf("%s",a);
        if(strcmp(a,"#")==0)break;
        scanf("%s",b);
        len1 = strlen(a);
        len2 = strlen(b);
        kmp();
    }
    

}

类型四

需要再补几个字符能构成一个类似手链那样循环相同的。

题目名称： Cyclic Nacklace

#include 
#include 
#include 

using namespace std;
int n;
char b[100005];
int len2;
int nextt[100005];
/*------------------------------------------------------------------*/
void getnext()
{
    int  j = -1;
    nextt[0] =-1;
    for(int i =0;i<len2;)
    {
        if(j == -1||b[i]==b[j])
            nextt[++i] = ++j;
        else j = nextt[j];    
    }
   
    

}
void result()
{
    getnext();
    int temp = len2 - nextt[len2];
    if ((len2%temp==0)&&(temp!=len2))
        printf("0\n");
    else
        printf("%d\n",temp-nextt[len2]%temp);
}
/*------------------------------------------------------------------*/
int main()
{
    scanf("%d",&n);
    while (n--)
    {
        //这是杭电的一道题，这里初始化会wa，具体原因不太清楚
        //memset(b,0,sizeof(b));
        //memset(nextt,0,sizeof(nextt));
        scanf("%s",b);
        len2 = strlen(b);
        result();
       
    }
    
}

类型五

给出一字符串，找出由2个或2个以上相同的子字符串组成的前缀，输出前缀长度及其相同的子字符串数。

题目名称： Period

#include 
#include 
#include 

using namespace std;

int c = 1;
char b[1000005];

int nextt[1000005];
int len2;
void getnext()
{
    
    int j  =-1;
    nextt[0] = -1;
    for(int i = 0;i<len2;)
    {
        if(j==-1||b[i]==b[j])
        nextt[++i] = ++j;
        else j = nextt[j];
        
        
    }

}
void result()
{
    getnext();
    

    for(int i = 2;i<=len2;i++)
    {
        if (nextt[i] != 0)
        {
            int temp = i -nextt[i];
            if(i%temp==0&&i/temp>1)
            printf("%d %d\n",i,i/temp);
        }
        
    }
    printf("\n");
}
int main()
{
    while (1)
    {
        memset(b,0,sizeof(b));
        memset(nextt,0,sizeof(nextt));
        scanf("%d", &len2);
        if (len2 == 0)
            break;
        scanf("%s",b);
        printf("Test case #%d\n", c);
        c++;
        result();
    }
}

类型六

最小循环节有几个。（必须是s=$a^n$的类型）

题目名称： Power Strings

#include 
#include 
#include 

using namespace std;


char b[1000005];
int len2;
int nextt[1000005];
void getnext()
{
    int j =-1;
    nextt[0]=-1;
    for(int i = 0;i<len2;)
    {
        if(j==-1||b[i]==b[j])
            nextt[++i] = ++j;
        else
        {
            j = nextt[j];
        }
    }
}
void result()
{
    getnext();
    int temp = len2 - nextt[len2];
    if(temp==len2||len2%temp!=0)printf("1\n");
    else
    {
        printf("%d\n",len2/temp);
    }

}
int main()
{
    while (1)
    {
        memset(b,0,sizeof(b));
        scanf("%s",b);
        if(strcmp(b,".")==0)
            break;
        len2 = strlen(b);
        result();
    }
    
}

类型七

题目名称：Seek the Name, Seek the Fame

#include 
#include 
#include 

using namespace std;

int num[1000005];
char b[1000005];
int len2;
int nextt[1000005];
int count = 0;
void getnext()
{
    int j =-1;
    nextt[0]=-1;
    for(int i = 0;i<len2;)
    {
        if(j==-1||b[i]==b[j])
            nextt[++i] = ++j;
        else
        {
            j = nextt[j];
        }
    }
}
void result()
{
    
    getnext();

    int t = nextt[len2];
    
    while (t!=-1)
    {
        num[count++] = t;
        t = nextt[t];
    }
 
    for(int i = count-2;i>=0;i--)
    printf("%d ",num[i]);
    printf("%d\n",len2);
  
    


}
int main()
{
    while (scanf("%s",b)!=EOF)
    {
      
        memset(nextt,0,sizeof(nextt));
        memset(num,0,sizeof(num));
        count = 0;
        len2 = strlen(b);
        result();
        memset(b,0,sizeof(b));  
    }
    
}