【bzoj1009】: [HNOI2008]GT考试 字符串-kmp-矩阵乘法-DP

【bzoj1009】: [HNOI2008]GT考试

先用kmp写个暴力

/* http://www.cnblogs.com/karl07/ */
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;
char s[25];
int n,m,p,fail[25],f[1000][25];

void kmp(){
    fail[1]=0;
    for (int i=2;i<=m;i++){
        fail[i]=fail[i-1];
        if (s[fail[i-1]]==s[i-1]) fail[i-1]=fail[fail[i-1]];
        while (s[fail[i]]!=s[i-1] && fail[i]) fail[i]=fail[fail[i]];
        fail[i]++;
    }
}

int main(){
    scanf("%d%d%d",&n,&m,&p);
    scanf("%s",s+1);
    kmp();
    f[0][0]=1;
    for (int i=1;i<=n;i++){
        for (int j=0;j<m;j++){
            for (int k='0',now=j+1;k<='9';k++,now=j+1){
                while (k!=s[now] && now) now=fail[now];
                f[i][now]=(f[i][now]+f[i-1][j])%p;
            }
        }
    }
    int ans=0;
    for (int i=0;i<m;i++){
        ans=(ans+f[n][i])%p;
    }
    printf("%d
",ans);
    return 0;
}

然后对着转移方程yy一下矩阵就好辣

/* http://www.cnblogs.com/karl07/ */
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;
char s[25];
int n,m,p,fail[25];
struct MAT{
    int m[25][25];
    int x,y;
}m1,m2;

MAT operator * (const MAT &a,const MAT &b){
    MAT c;
    c.x=b.x,c.y=a.y;
    for (int i=1;i<=c.x;i++){
        for (int j=1;j<=c.y;j++){
            c.m[i][j]=0;
            for (int k=1;k<=b.y;k++){
                c.m[i][j]=(c.m[i][j]+a.m[k][j]*b.m[i][k])%p;
            }
        }
    } 
    return c;
}

int sum(MAT a){
    int ans=0;
    for (int i=1;i<=a.x;i++){
        for (int j=1;j<=a.y;j++){
            ans=(ans+a.m[i][j])%p;
        }
    }
    return ans;
}

void kmp(){
    fail[1]=0;
    for (int i=2;i<=m;i++){
        fail[i]=fail[i-1];
        if (s[fail[i-1]]==s[i-1]) fail[i-1]=fail[fail[i-1]];
        while (s[fail[i]]!=s[i-1] && fail[i]) fail[i]=fail[fail[i]];
        fail[i]++;
    }
}

MAT qpow(int x){
    for (;x;x=(x>>1),m2=m2*m2) if (x&1) m1=m1*m2;
    return m1;
}

int main(){
    scanf("%d%d%d",&n,&m,&p);
    scanf("%s",s+1);
    kmp();
    m1.x=m;m1.y=1;m1.m[1][1]=1;
    m2.x=m2.y=m;
    for (int i=2;i<=m;i++) m1.m[i][1]=0;
    for (int i=1;i<=m;i++) for (int j=1;j<=m;j++) m2.m[i][j]=0;
    for (int j=0;j<m;j++){
        for (int k='0',now=j+1;k<='9';k++,now=j+1){
            while (k!=s[now] && now)now=fail[now]; 
            m2.m[now+1][j+1]++;
        }
    }
    printf("%d
",sum(qpow(n)));
    return 0;
}

 为什么感觉自己的kmp写的好奇怪。。