bzoj 3473 字符串 - 后缀数组 - 树状数组

题目传送门

  传送门

题目大意

  给定n个字符串,询问每个字符串有多少子串(不包括空串)是所有n个字符串中至少k个字符串的子串

  先用奇怪的字符把所有字符串连接起来。

  建后缀树,数每个节点的子树内包含多少属于不同串的后缀。

  数这个东西,可以将每个串的后缀(被奇怪的字符分割开的地方认为它属于不同后缀)按dfs序排序,然后简单容斥就能统计出来。

  对于每个后缀,有贡献的是一个前缀,然后直接统计就行了。

Code

 /**
* bzoj
* Problem#3473
* Accepted
* Time: 788ms
* Memory: 41208k
*/
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
using namespace std;
typedef bool boolean; template <typename T>
void pfill(T* pst, const T* ped, T val) {
for ( ; pst != ped; *(pst++) = val);
} const int N = 2e5 + ;
const int bzmax = ; typedef class SparseTable {
public:
int n;
int *ar;
int log2[N];
int f[N][bzmax]; SparseTable() { } void init(int n, int* ar) {
this->n = n;
this->ar = ar;
log2[] = ;
for (int i = ; i <= n; i++)
log2[i] = log2[i >> ] + ;
for (int i = ; i < n; i++)
f[i][] = ar[i];
for (int j = ; j < bzmax; j++)
for (int i = ; i + ( << j) - < n; i++)
f[i][j] = min(f[i][j - ], f[i + ( << (j - ))][j - ]);
} int query(int l, int r) {
int d = log2[r - l + ];
// int rt = min(f[l][d], f[r - (1 << d) + 1][d]);
// cerr << l << " " << r << " " << rt << '\n';
return min(f[l][d], f[r - ( << d) + ][d]);
}
}SparseTable; typedef class Pair3 {
public:
int x, y, id; Pair3() { }
Pair3(int x, int y, int id):x(x), y(y), id(id) { }
}Pair3; typedef class SuffixArray {
protected:
Pair3 T1[N], T2[N];
int cnt[N]; public:
int n;
char *str;
int sa[N], rk[N], hei[N];
SparseTable st; void set(int n, char* str) {
this->n = n;
this->str = str;
memset(sa, , sizeof(sa));
memset(rk, , sizeof(rk));
memset(hei, , sizeof(hei));
} void radix_sort(Pair3* x, Pair3* y) {
int m = max(n, );
memset(cnt, , sizeof(int) * m);
for (int i = ; i < n; i++)
cnt[x[i].y]++;
for (int i = ; i < m; i++)
cnt[i] += cnt[i - ];
for (int i = ; i < n; i++)
y[--cnt[x[i].y]] = x[i]; memset(cnt, , sizeof(int) * m);
for (int i = ; i < n; i++)
cnt[y[i].x]++;
for (int i = ; i < m; i++)
cnt[i] += cnt[i - ];
for (int i = n - ; ~i; i--)
x[--cnt[y[i].x]] = y[i];
} void build() {
for (int i = ; i < n; i++)
rk[i] = str[i];
for (int k = ; k <= n; k <<= ) {
for (int i = ; i + k < n; i++)
T1[i] = Pair3(rk[i], rk[i + k], i);
for (int i = n - k; i < n; i++)
T1[i] = Pair3(rk[i], , i);
radix_sort(T1, T2);
int diff = ;
rk[T1[].id] = ;
for (int i = ; i < n; i++)
rk[T1[i].id] = (T1[i].x == T1[i - ].x && T1[i].y == T1[i - ].y) ? (diff) : (++diff);
if (diff == n)
break;
}
for (int i = ; i < n; i++)
sa[--rk[i]] = i;
} void get_height() {
for (int i = , j, k = ; i < n; i++, (k) ? (k--) : ()) {
if (rk[i]) {
j = sa[rk[i] - ];
while (i + k < n && j + k < n && str[i + k] == str[j + k]) k++;
hei[rk[i]] = k;
}
}
} void init_st() {
st.init(n, hei);
} int lcp(int x1, int x2) {
if (x1 == x2)
return n - x1 + ;
x1 = rk[x1], x2 = rk[x2];
if (x1 > x2)
swap(x1, x2);
return st.query(x1 + , x2);
} int compare(int l1, int r1, int l2, int r2) {
int len_lcp = lcp(l1, l2);
int len1 = r1 - l1 + , len2= r2 - l2 + ;
if (len_lcp >= len1 && len_lcp >= len2)
return ;
if (len_lcp < len1 && len_lcp < len2)
return (str[l1 + len_lcp] < str[l2 + len_lcp]) ? (-) : ();
return (len_lcp >= len1) ? (-) : ();
} int query(int u, int v) { // u, v -> sa
if (u == v)
return n - sa[u];
return st.query(u + , v);
} const int& operator [] (int p) {
return sa[p];
} const int& operator () (int p) {
return hei[p];
}
} SuffixArray; typedef class IndexedTree {
public:
int s;
int *a; IndexedTree() { }
IndexedTree(int n) : s(n) {
a = new int[(s + )];
pfill(a + , a + n + , );
}
~IndexedTree() {
delete[] a;
} void add(int idx, int val) {
for ( ; idx <= s; idx += (idx & (-idx)))
a[idx] += val;
} int query(int idx) {
int rt = ;
for ( ; idx; idx -= (idx & (-idx)))
rt += a[idx];
return rt;
} int query(int l, int r) {
return query(r) - query(l - );
}
} IndexedTree; typedef class Graph {
protected:
int dfs_clock;
public:
vector<int>* g;
int *fa;
int *in, *out;
int *sz, *zson;
int *dep, *top; Graph() { }
Graph(vector<int>* g, int n) : dfs_clock(), g(g) {
fa = new int[(n + )];
in = new int[(n + )];
out = new int[(n + )];
sz = new int[(n + )];
zson = new int[(n + )];
dep = new int[(n + )];
top = new int[(n + )];
dfs1(, );
dfs2(, true);
}
~Graph() {
#define rem(__) delete[] __;
rem(fa) rem(in) rem(out) rem(sz) rem(zson) rem(dep) rem(top)
} void dfs1(int p, int fa) {
dep[p] = ((fa) ? (dep[fa] + ) : ());
in[p] = ++dfs_clock;
this->fa[p] = fa;
sz[p] = ;
int mx = -, id = -, e;
for (unsigned i = ; i < g[p].size(); i++) {
e = g[p][i];
dfs1(e, p);
sz[p] += sz[e];
if (sz[e] > mx)
mx = sz[e], id = e;
}
out[p] = dfs_clock;
zson[p] = id;
} void dfs2(int p, boolean ontop) {
top[p] = ((ontop) ? (p) : (top[fa[p]]));
if (~zson[p])
dfs2(zson[p], false);
for (int i = , e; i < (signed) g[p].size(); i++) {
e = g[p][i];
if (e == zson[p])
continue;
dfs2(e, true);
}
} int lca(int u, int v) {
while (top[u] ^ top[v]) {
if (dep[top[u]] < dep[top[v]])
swap(u, v);
u = fa[top[u]];
}
return (dep[u] < dep[v]) ? (u) : (v);
}
} Graph; #define pii pair<int, int> int n, L, K;
int id[N];
char str[N];
SuffixArray sa;
int endp[N >> ];
char _str[N >> ];
vector<int> endpos[N >> ]; inline void init() {
L = ;
scanf("%d%d", &n, &K);
for (int i = ; i <= n; i++) {
scanf("%s", _str);
if (i > ) {
id[L] = -;
str[L] = '#'; //"!@#$%^&*()-+"[i % 11];
L += ;
}
for (char* p = _str; *p; p++) {
id[L] = i;
str[L] = *p;
L++;
}
endp[i] = L;
}
sa.set(L, str);
sa.build();
sa.get_height();
sa.init_st();
} int cnt_node;
vector<int> g[N << ];
int d[N << ]; int build_suffix_tree(int l, int r) {
int curid = ++cnt_node;
d[curid] = sa.query(l, r);
if (l == r) {
int p = sa[l];
if (id[p] > )
endpos[id[p]].push_back(curid);
return curid;
}
for (int p = l, j, L, R, mid; p <= r; p = j + ) {
L = p, R = r;
char x = str[sa[p] + d[curid]];
while (L <= R) {
mid = (L + R) >> ;
if (str[sa[mid] + d[curid]] == x)
L = mid + ;
else
R = mid - ;
}
j = L - ;
L = build_suffix_tree(p, j);
g[curid].push_back(L);
}
return curid;
} int res[N << ];
void dfs(int p, Graph& G, IndexedTree& it) {
res[p] = (it.query(G.in[p], G.out[p]) >= K) ? (d[p]) : (res[G.fa[p]]);
for (int i = ; i < (signed) g[p].size(); i++) {
dfs(g[p][i], G, it);
}
} inline void solve() {
while (cnt_node)
g[cnt_node--].clear();
build_suffix_tree(, L - ); IndexedTree it (cnt_node);
Graph graph (g, cnt_node);
for (int i = ; i <= n; i++) {
it.add(graph.in[endpos[i][]], );
for (int j = ; j < (signed) endpos[i].size(); j++) {
it.add(graph.in[endpos[i][j]], );
int g = graph.lca(endpos[i][j], endpos[i][j - ]);
it.add(graph.in[g], -);
}
} dfs(, graph, it);
for (int i = , p, l; i <= n; i++) {
long long ans = ;
for (int j = ; j < (signed) endpos[i].size(); j++) {
p = endpos[i][j], l = d[p];
ans += min(endp[i] - (L - l), res[p]);
}
printf("%lld ", ans);
}
} int main() {
init();
solve();
return ;
}
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