Codeforces 432D Prefixes and Suffixes(KMP+dp)

题目连接：Codeforces 432D Prefixes and Suffixes

题目大意：给出一个字符串，求全部既是前缀串又是后缀串的字符串出现了几次。

解题思路：依据性质能够依据KMP算法求出全部的前后缀串，然后利用dp求解，dp[i]表示从1到i这个子串出现过的次数。转移方程dp[jump[i]]+=dp[i]。随意一个dp[i]的初始状态应该是1。

#include <cstdio>
#include <cstring>

const int N = 1e5+5;

int n, jump[N], c, r[N], dp[N];
char str[N];

void getJump() {
    int k = 0;
    n = strlen(str+1);
    for (int i = 2; i <= n; i++) {
        while (k && str[i] != str[k+1])
            k = jump[k];

        if (str[i] == str[k+1])
            k++;
        jump[i] = k;
    }
}

int main () {
    scanf("%s", str+1);
    getJump();

    c = 0;
    for (int i = jump[n]; i; i = jump[i]) {
        r[c] = i;
        c++;
    }

    memset(dp, 0, sizeof(dp));
    for (int i = n; i; i--) {
        dp[i]++;
        dp[jump[i]] += dp[i];
    }

    printf("%d
", c+1);
    for (int i = c-1; i >= 0; i--)
        printf("%d %d
", r[i], dp[r[i]]);
    printf("%d %d
", n, dp[n]);
    return 0;
}