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SA例题

题面

对于串 \(S\) 的两个子串 \(A\) 和 \(B\) ，满足 \(k = |A| = |B|\)，\(\exists c \forall i\, a_i + c=b_i\)，且 \(A\) 和 \(B\) 在原串中没有重叠，求最大的满足条件的 \(k\)

先考虑 \(\forall i\, a_i=b_i\) 的情况，二分 \(k\) ，如果在\(height\)上存在一段满足 \(\forall L \le i \le R \,height_i\ge k\)，且存在 \(SA[p_1]-SA[p_2] \ge k\)，说明 \(k\) 满足条件

接下来将上述做法用在原数组的差分数组上即可，注意判定时条件要改为\(SA[p_1]-SA[p_2] > k\)，且要在第一个字符前添加特殊字符，否则判定时可能出问题

#include<cstdio>
using namespace std;

const int MAXN = 5001;
int str[MAXN], sa[MAXN], rank[MAXN], ht[MAXN], buc[MAXN];

void Swap(int*& a, int*& b){
    int *tmp = a; a = b; b = tmp;
}

void getSA(int s[], int len){
    int *rk = rank, *tp = ht;
    int crd = 180, p;
    for (int i = 1; i <= len; ++i)
        rk[i] = s[i], tp[i] = i;
    for (int i = 0; i <= crd; ++i) 
        buc[i] = 0;
    for (int i = 1; i <= len; ++i)
        ++buc[rk[i]];
    for (int i = 1; i <= crd; ++i)
        buc[i] += buc[i - 1];
    for (int i = len; i >= 1; --i)
        sa[buc[rk[tp[i]]]--] = tp[i];
    for (int w = 1; p != len; w <<= 1, crd = p){
        p = 0;
        for (int i = len - w + 1; i <= len; ++i)
            tp[++p] = i;
        for (int i = 1; i <= len; ++i)
            if (sa[i] > w)
                tp[++p] = sa[i] - w;
        for (int i = 0; i <= crd; ++i) 
            buc[i] = 0;
        for (int i = 1; i <= len; ++i)
            ++buc[rk[i]];
        for (int i = 1; i <= crd; ++i)
            buc[i] += buc[i - 1];
        for (int i = len; i >= 1; --i)
            sa[buc[rk[tp[i]]]--] = tp[i];
        Swap(rk, tp);
        rk[sa[1]] = p = 1;
        for (int i = 2; i <= len; ++i)
            rk[sa[i]] = tp[sa[i]] == tp[sa[i - 1]] && tp[sa[i] + w] == tp[sa[i - 1] + w] ? p : ++p;
    } 
    for (int i = 1; i <= len; ++i)
        rank[sa[i]] = i;
}

void getHeight(int s[], int len){
    ht[1] = 0;
    for (int i = 1, j = 0, pos; i <= len; ++i, --j){
        if (rank[i] == 1)
            continue;
        if (j < 0)
            j = 0;
        pos = sa[rank[i] - 1];
        while (s[i + j] == s[pos + j] && i + j <= len && pos + j <= len)
            ++j;
        ht[rank[i]] = j;
    }
}

bool judge(int k, int len){
    int lp, rp;
    for (int i = 1, j; i < len;){
        if (ht[i + 1] >= k){
            lp = rp = sa[i];
            j = i + 1;
            while (ht[j] >= k && j <= len){
                if (sa[j] < lp)
                    lp = sa[j];
                if (sa[j] > rp)
                    rp = sa[j];
                ++j;
            }
            if (rp - lp > k)
                return 1;
            i = j;
        }
        else 
            ++i;
    }
    return 0;
}

int main(){
    int slen;
    scanf("%d", &slen);
    for (int i = 1, pre = 89, tmp; i <= slen; ++i){
        scanf("%d", &tmp);
        str[i] = tmp - pre + 89; pre = tmp;
    }
    getSA(str, slen);
    getHeight(str, slen);
    int L = 1, R = slen >> 1, mid;
    while (L + 1 < R){
        mid = L + R >> 1;
        if (judge(mid, slen))
            L = mid;
        else
            R = mid;
    }
    int ans;
    if (judge(R, slen))
        ans = R;
    else 
        ans = L;
    if (ans < 4)
        printf("0");
    else
        printf("%d", ans + 1);
    return 0;
}