关于KMP的应用几例

信息竞赛中，KMP大概是字符串方面最经典的算法了。参考了部分代码，KMP的写法大概有两种

1. 在原有字符串上进行KMP

#include <bits/stdc++.h>
using namespace std;

const int S = 1000010;
int kmp[S], len_a, len_b, j;
char a[S], b[S];

int main() {
    scanf("%s", a + 1);
    scanf("%s", b + 1);
    len_a = strlen(a + 1);
    len_b = strlen(b + 1);
    for (int i = 2; i <= len_b; i++) {
        while (j && b[i] != b[j + 1]) j = kmp[j];
        if (b[j + 1] == b[i]) j++;
        kmp[i] = j;
    }
    j = 0;
    for (int i = 1; i <= len_a; i++) {
        while (j > 0 && b[j + 1] != a[i]) j = kmp[j];
        if (b[j + 1] == a[i]) j++;
        if (j == len_b) {
            printf("%d\n", i - len_b + 1);
            j = kmp[j];
        }
    }
    for (int i = 1; i <= len_b; i++)
        printf("%d ", kmp[i]);
    printf("\n");
    return 0;
}

2. 在嫁接字符串上进行KMP

#include <bits/stdc++.h>
using namespace std;

const int N = 100010, M = 1000010;
int pi[M + N], n, m;

void prefix(string s) {
    int len = s.length();
    for (int i = 1; i < len; i++) {
        int j = pi[i - 1];
        while (j > 0 && s[i] != s[j]) j = pi[j - 1];
        if (s[i] == s[j]) j++;
        pi[i] = j;
    }
}

int main() {
    string s, t;
    cin >> s >> t;
    n = s.length(), m = t.length();
    prefix(s + " " + t);
    for (int i = n + 1; i <= n + m; i++)
        if (pi[i] == n) printf("%d ", i - 2 * n);
    printf("\n");

    return 0;
}

至于KMP算法的解释，个人认为OI-Wiki上提供的解释很详尽
KMP算法的一般应用一般是字符串匹配