【hihoCoder 1466】后缀自动机六·重复旋律9
http://hihocoder.com/problemset/problem/1466
建出A串和B串的两个后缀自动机
对后缀自动机的每个状态求出sg值。
求出B串的\(sum(x)\),表示B有多少子串的sg值等于x(用拓扑序求)。
对A串的每个状态,求出B串有多少子串的sg值不等于这个状态的sg值,再按拓扑序递推一下。
接下来就类似SPOJ 7258这道题了
从A串开始走,按字典序从小到大,定住A串后,根据在A串停住的状态的sg值再在B串上按拓扑序递推一次求出当前状态往后可以走出多少不等于这个sg值的子串,再在B串上按字典序从小到大走定住B串。
注意空串也算子串。
时间复杂度\(O(n\log n)\),只有求sg函数排序是\(O(n\log n)\)的,其他操作都是\(O(n)\)的。
调了好几天,很恶心啊,把c[nn + 1] = -1;
打成c[nn + 1] == -1;
了。
要是开-Wall就没这种事了qwq
在周赛结束前10分钟才发现错误,然后改过来A了233
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N = 100003;
int tot = 0, cnt, cnt2;
struct State {
State *par, *go[26];
int val, sg; ll f;
} pool[N << 2], *id[N << 1], *tp[N << 1], *tp2[N << 1], *root_A, *root_B, *root, *last, *tmp;
State *newState(int num) {
pool[++tot].val = num;
pool[tot].par = 0;
pool[tot].sg = 0;
pool[tot].f = 0;
memset(pool[tot].go, 0, sizeof(pool[tot].go));
return id[++cnt] = &pool[tot];
}
void extend(int w) {
State *p = last;
State *np = newState(p->val + 1);
while (p && p->go[w] == 0)
p->go[w] = np, p = p->par;
if (p == 0) np->par = root;
else {
State *q = p->go[w];
if (q->val == p->val + 1) np->par = q;
else {
State *nq = newState(p->val + 1);
memcpy(nq->go, q->go, sizeof(nq->go));
nq->par = q->par;
q->par = np->par = nq;
while (p && p->go[w] == q)
p->go[w] = nq, p = p->par;
}
}
last = np;
}
char Sa[N], Sb[N], ansa[N], ansb[N];
int nn, c[N << 1], ansalen = 0, ansblen = 0;
ll sum[N], k;
void pre(int len) {
cnt2 = cnt;
for (int i = 1; i <= cnt; ++i) ++c[id[i]->val];
for (int i = 1; i <= len; ++i) c[i] += c[i - 1];
for (int i = cnt; i >= 1; --i) tp[c[id[i]->val]--] = id[i];
for (int i = cnt; i >= 1; --i) {
tp2[i] = tmp = tp[i];
nn = 0;
for (int w = 0; w < 26; ++w)
if (tmp->go[w]) {
tmp->f += tmp->go[w]->f;
c[++nn] = tmp->go[w]->sg;
}
++tmp->f;
stable_sort(c + 1, c + nn + 1);
if (c[1] != 0 || nn == 0) tmp->sg = 0;
else {
c[nn + 1] = -1;
for (int j = 1; j <= nn; ++j)
if (c[j] != c[j + 1] && c[j] + 1 != c[j + 1]) {
tmp->sg = c[j] + 1;
break;
}
}
}
}
void pre2(int len) {
memset(c, 0, sizeof(int) * (len + 1));
for (int i = 1; i <= cnt; ++i) ++c[id[i]->val];
for (int i = 1; i <= len; ++i) c[i] += c[i - 1];
for (int i = cnt; i >= 1; --i) tp[c[id[i]->val]--] = id[i];
for (int i = cnt; i >= 1; --i) {
tmp = tp[i];
nn = 0;
for (int w = 0; w < 26; ++w)
if (tmp->go[w]) {
tmp->f += tmp->go[w]->f;
c[++nn] = tmp->go[w]->sg;
}
stable_sort(c + 1, c + nn + 1);
if (c[1] != 0 || nn == 0) tmp->sg = 0;
else {
c[nn + 1] = -1;
for (int j = 1; j <= nn; ++j)
if (c[j] != c[j + 1] && c[j] + 1 != c[j + 1]) {
tmp->sg = c[j] + 1;
break;
}
}
tmp->f += sum[tmp->sg];
}
}
void work_B(int nu) {
for (int i = cnt2; i >= 1; --i) {
tmp = tp2[i]; tmp->f = 0;
for (int w = 0; w < 26; ++w)
if (tmp->go[w])
tmp->f += tmp->go[w]->f;
if (tmp->sg != nu) ++tmp->f;
}
tmp = root_B;
bool flag;
while (k) {
flag = false;
if (tmp->sg != nu) --k;
if (k == 0) {flag = true; break;}
for (int w = 0; w < 26; ++w)
if (tmp->go[w] && k)
if (tmp->go[w]->f >= k) {
flag = true;
tmp = tmp->go[w];
ansb[++ansblen] = 'a' + w;
break;
} else
k -= tmp->go[w]->f;
if (!flag) break;
}
if (!flag) puts("NO");
else {
for (int i = 1; i <= ansalen; ++i) putchar(ansa[i]); puts("");
for (int i = 1; i <= ansblen; ++i) putchar(ansb[i]); puts("");
}
}
int main() {
scanf("%lld%s%s", &k, Sa + 1, Sb + 1);
int lena = strlen(Sa + 1), lenb = strlen(Sb + 1);
cnt = 0;
root_B = root = last = newState(0);
for (int i = 1; i <= lenb; ++i)
extend(Sb[i] - 'a');
pre(lenb);
for (int i = 1; i <= cnt; ++i)
if (tp[i] != root_B) sum[tp[i]->sg] += tp[i]->val - tp[i]->par->val;
else ++sum[tp[i]->sg];
for (int i = 0; i <= lena; ++i)
sum[i] = root_B->f - sum[i];
cnt = 0;
root_A = root = last = newState(0);
for (int i = 1; i <= lena; ++i)
extend(Sa[i] - 'a');
pre2(lena);
tmp = root_A;
bool flag;
while (k) {
flag = false;
if (sum[tmp->sg] >= k) {
work_B(tmp->sg);
return 0;
}
k -= sum[tmp->sg];
for (int w = 0; w < 26; ++w)
if (tmp->go[w] && k)
if (tmp->go[w]->f >= k) {
flag = true;
ansa[++ansalen] = 'a' + w;
tmp = tmp->go[w];
break;
} else
k -= tmp->go[w]->f;
if (!flag) break;
}
puts("NO");
return 0;
}
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