字符串算法总结

字符串算法总结

1、KMP

求字符串匹配

luogu 3375 KMP字符串匹配

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
char A[1000010], B[1010];
int next[1010];
int main()
{
    scanf("%s %s", A, B);
    int lena = strlen(A), lenb = strlen(B);
    for(int i=1, j=0; i < lenb; i++){
        while(j>0 && B[i]!=B[j])  j = next[j-1];
        if(B[i] == B[j])  next[i] = ++j;
    }
    for(int i=0, j=0; i < lena; i++){
        while(j>0 && A[i]!=B[j])  j = next[j-1];
        if(A[i] == B[j])  ++j;
        if(j == lenb){
            printf("%d\n", i-lenb+2);
        }
    }
    for(int i = 0; i < lenb; i++)  printf("%d ", next[i]);
    return 0;
}

2、Manacher

求最长回文子串

POJ 3974 Palindrome

#include<iostream>
#include<cstring> 
#include<cstdio>
using namespace std;
char S[100010], H[100010];
int G[100010], mx, ans, len, id;
int main()
{
    scanf("%s", S);
    len = strlen(S);
    H[0] = '$'; H[1] = '#';
    for(int i = 0; i < len; i++){
        H[i*2+2] = S[i];
        H[i*2+3] = '#';
    }
    len = len * 2 + 2;
    H[len] = '\0';
    for(int i = 1; i < len; i++){
        if(i < mx)  G[i] = min(G[id*2-i], G[id]+id-i);
        else G[i] = 1;
        while(H[i-G[i]] == H[i+G[i]])  G[i]++;
        if(mx < G[i]+i){
            mx = G[i] + i;
            id = i;
        }
        ans = max(ans, G[i]-1);
    }
    printf("%d", ans);
    return 0;
}

3、最小表示法

判断字符串是否循环同构

luogu 1709 Hidden Password

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
int len;
char S[5000010];
int Work(){    
    int i = 0, j = 1;
    while(i<len && j<len){  
        int k = 0;  
        while(S[(i+k)%len]==S[(j+k)%len] && k<len)  k++;  
        if(k==len)  return min(i, j);  
        if(S[(i+k)%len] > S[(j+k)%len])  i = i+k+1;
        else j = j+k+1;
        if(i == j)  j++;
    } 
    return min(i, j);
}     
int main()
{
    scanf("%d", &len);
    for(int i = 0; i < len; i++)  cin >> S[i];
    printf("%d", Work());
    return 0;
}

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未完待续