【BZOJ4698】[SDOI2008]Sandy的卡片

题面

flag倒了。

bzoj

洛谷

题解

首先题目的区间加很丑对吧，

将每个串差分一下，就可以转化为

求：

给定\(N\)个串，求他们的最长公共子串。

怎么办呢，按照后缀数组常用套路

我们用不同的未曾用过的字符将这些串连接起来

我们将\(lcp\)大于\(mid\)的串分组

如果一组内串的个数大于等于\(N\)个，就证明可以\(return\;1\)

否则若没有一组大于等于\(N\)返回\(0\)

代码

#include <iostream>

#include <cstdio>

#include <cstdlib>

#include <cstring>

#include <cmath>

#include <algorithm>

using namespace std;

inline int gi() {

    register int data = 0, w = 1;

    register char ch = 0;

    while (!isdigit(ch) && ch != '-') ch = getchar();

    if (ch == '-') w = -1, ch = getchar();

    while (isdigit(ch)) data = 10 * data + ch - '0', ch = getchar();

    return w * data;

}

const int MAX_N = 2e6 + 5;

int N, T, a[MAX_N], b[MAX_N], vis[MAX_N];

int sa[MAX_N], rnk[MAX_N], lcp[MAX_N];

void GetSA() {

#define cmp(i, j, k) (y[i] == y[j] && y[i + k] == y[j + k])

    static int x[MAX_N], y[MAX_N], bln[MAX_N];

    int M = 1e6;

    for (int i = 1; i <= N; i++) bln[x[i] = a[i]]++;

    for (int i = 1; i <= M; i++) bln[i] += bln[i - 1];

    for (int i = N; i >= 1; i--) sa[bln[x[i]]--] = i;

    for (int k = 1; k <= N; k <<= 1) {

        int p = 0;

        for (int i = 0; i <= M; i++) y[i] = 0;

        for (int i = N - k + 1; i <= N; i++) y[++p] = i;

        for (int i = 1; i <= N; i++) if (sa[i] > k) y[++p] = sa[i] - k;

        for (int i = 0; i <= M; i++) bln[i] = 0;

        for (int i = 1; i <= N; i++) bln[x[y[i]]]++;

        for (int i = 1; i <= M; i++) bln[i] += bln[i - 1];

        for (int i = N; i >= 1; i--) sa[bln[x[y[i]]]--] = y[i];

        swap(x, y); x[sa[1]] = p = 1;

        for (int i = 2; i <= N; i++) x[sa[i]] = cmp(sa[i], sa[i - 1], k) ? p : ++p;

        if (p >= N) break;

        M = p;

    }

}

void GetLcp() {

    for (int i = 1; i <= N; i++) rnk[sa[i]] = i;

    for (int i = 1, j = 0; i <= N; i++) {

        if (j) --j;

        while (a[i + j] == a[sa[rnk[i] - 1] + j]) ++j;

        lcp[rnk[i]] = j;

    }

}

int col[MAX_N], tot;

bool check(int v) {

    ++tot; int cnt = 0;

    for (int i = 1; i <= N; i++) {

        if (lcp[i] < v) ++tot, cnt = 0;

        if (col[vis[sa[i]]] != tot) col[vis[sa[i]]] = tot, ++cnt;

        if (cnt == T) return 1;

    }

    return 0;

}

const int dlt = 5e4;

int main () {

    T = gi();

    for (int i = 1; i <= T; i++) {

        int m = gi();

        for (int j = 1; j <= m; j++) b[j] = gi();

        for (int j = 1; j <= m; j++) b[j] = b[j + 1] - b[j] + dlt;

        for (int j = 1; j < m; j++) a[++N] = b[j], vis[N] = i;

        a[++N] = i + 5e5;

    }

    GetSA(); GetLcp();

    int l = 0, r = N, ans = 0;

    while (l <= r) {

        int mid = (l + r) >> 1;

        if (check(mid)) l = mid + 1, ans = mid;

        else r = mid - 1;

    }

    printf("%d\n", ans + 1);

    return 0;

}