This documentation is automatically generated by online-judge-tools/verification-helper
#include "string/suffix_tree.hpp"
#include "string/suffix_array.hpp"
#include "seq/cartesian_tree.hpp"
#include "graph/base.hpp"
// https://twitter.com/maspy_stars/status/1565901414236205057?s=20&t=S2Tu6ayozHcakxai8dmh4g
// 各ノードは、suffix array での長方形領域と見なして、
// グラフおよび、領域データを作る。
// sample: test/my_test/suffix_tree.test.cpp
template <typename SUFFIX>
pair<Graph<int, 1>, vc<tuple<int, int, int, int>>> suffix_tree(SUFFIX& X) {
auto SA = X.SA;
auto ISA = X.ISA;
auto LCP = X.LCP;
vc<tuple<int, int, int, int>> dat;
vc<pair<int, int>> edges;
int N = len(SA);
if (N == 1) {
Graph<int, 1> G(2);
G.add(0, 1);
G.build();
dat.eb(0, 1, 0, 0), dat.eb(0, 1, 0, 1);
return {G, dat};
}
dat.eb(0, N, 0, 0);
CartesianTree<int, true> CT(LCP);
auto dfs = [&](auto& dfs, int p, int idx, int h) -> void {
int L = CT.range[idx].fi;
int R = CT.range[idx].se + 1;
int hh = LCP[idx];
if (h < hh) {
edges.eb(p, len(dat));
p = len(dat);
dat.eb(L, R, h, hh);
}
if (CT.lch[idx] == -1) {
if (hh < N - SA[idx]) {
edges.eb(p, len(dat));
dat.eb(idx, idx + 1, hh, N - SA[idx]);
}
} else {
dfs(dfs, p, CT.lch[idx], hh);
}
if (CT.rch[idx] == -1) {
if (hh < N - SA[idx + 1]) {
edges.eb(p, len(dat));
dat.eb(idx + 1, idx + 2, hh, N - SA[idx + 1]);
}
} else {
dfs(dfs, p, CT.rch[idx], hh);
}
};
int r = CT.root;
if (LCP[r] > 0) {
edges.eb(0, 1);
dat.eb(0, N, 0, LCP[r]);
dfs(dfs, 1, r, LCP[r]);
} else {
dfs(dfs, 0, r, 0);
}
Graph<int, 1> G(len(dat));
for (auto&& [a, b]: edges) G.add(a, b);
G.build();
return {G, dat};
}
#line 1 "string/suffix_tree.hpp"
#line 2 "string/suffix_array.hpp"
#line 2 "alg/monoid/min.hpp"
template <typename E>
struct Monoid_Min {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
static constexpr X unit() { return infty<E>; }
static constexpr bool commute = true;
};
#line 1 "ds/sparse_table/sparse_table.hpp"
// 冪等なモノイドであることを仮定。disjoint sparse table より x 倍高速
template <class Monoid>
struct Sparse_Table {
using MX = Monoid;
using X = typename MX::value_type;
int n, log;
vvc<X> dat;
Sparse_Table() {}
Sparse_Table(int n) { build(n); }
template <typename F>
Sparse_Table(int n, F f) {
build(n, f);
}
Sparse_Table(const vc<X>& v) { build(v); }
void build(int m) {
build(m, [](int i) -> X { return MX::unit(); });
}
void build(const vc<X>& v) {
build(len(v), [&](int i) -> X { return v[i]; });
}
template <typename F>
void build(int m, F f) {
n = m, log = 1;
while ((1 << log) < n) ++log;
dat.resize(log);
dat[0].resize(n);
FOR(i, n) dat[0][i] = f(i);
FOR(i, log - 1) {
dat[i + 1].resize(len(dat[i]) - (1 << i));
FOR(j, len(dat[i]) - (1 << i)) {
dat[i + 1][j] = MX::op(dat[i][j], dat[i][j + (1 << i)]);
}
}
}
X prod(int L, int R) {
if (L == R) return MX::unit();
if (R == L + 1) return dat[0][L];
int k = topbit(R - L - 1);
return MX::op(dat[k][L], dat[k][R - (1 << k)]);
}
template <class F>
int max_right(const F check, int L) {
assert(0 <= L && L <= n && check(MX::unit()));
if (L == n) return n;
int ok = L, ng = n + 1;
while (ok + 1 < ng) {
int k = (ok + ng) / 2;
bool bl = check(prod(L, k));
if (bl) ok = k;
if (!bl) ng = k;
}
return ok;
}
template <class F>
int min_left(const F check, int R) {
assert(0 <= R && R <= n && check(MX::unit()));
if (R == 0) return 0;
int ok = R, ng = -1;
while (ng + 1 < ok) {
int k = (ok + ng) / 2;
bool bl = check(prod(k, R));
if (bl) ok = k;
if (!bl) ng = k;
}
return ok;
}
};
#line 5 "string/suffix_array.hpp"
// 辞書順 i 番目の suffix が j 文字目始まりであるとき、
// SA[i] = j, ISA[j] = i
// |S|>0 を前提(そうでない場合 dummy 文字を追加して利用せよ)
template <bool USE_LCP_QUERY = 0>
struct Suffix_Array {
vc<int> SA;
vc<int> ISA;
vc<int> LCP;
Sparse_Table<Monoid_Min<int>> seg;
// DisjointSparse<Monoid_Min<int>> seg;
Suffix_Array(string& s) {
assert(len(s) > 0);
char first = 127, last = 0;
for (auto&& c: s) {
chmin(first, c);
chmax(last, c);
}
SA = calc_suffix_array(s, first, last);
calc_LCP(s);
if (USE_LCP_QUERY) seg.build(LCP);
}
Suffix_Array(vc<int>& s) {
assert(len(s) > 0);
SA = calc_suffix_array(s);
calc_LCP(s);
if (USE_LCP_QUERY) seg.build(LCP);
}
// lcp(S[i:], S[j:])
int lcp(int i, int j) {
static_assert(USE_LCP_QUERY);
int n = len(SA);
if (i == n || j == n) return 0;
if (i == j) return n - i;
i = ISA[i], j = ISA[j];
if (i > j) swap(i, j);
return seg.prod(i, j);
}
// S[i:] との lcp が n 以上であるような半開区間
pair<int, int> lcp_range(int i, int n) {
static_assert(USE_LCP_QUERY);
i = ISA[i];
int a = seg.min_left([&](auto e) -> bool { return e >= n; }, i);
int b = seg.max_right([&](auto e) -> bool { return e >= n; }, i);
return {a, b + 1};
}
// -1: S[L1:R1) < S[L2, R2)
// 0: S[L1:R1) = S[L2, R2)
// +1: S[L1:R1) > S[L2, R2)
int compare(int L1, int R1, int L2, int R2) {
int N = len(SA);
int n1 = R1 - L1, n2 = R2 - L2;
int n = lcp(L1, L2);
if (n == n1 && n == n2) return 0;
if (n == n1) return -1;
if (n == n2) return 1;
return (ISA[L1 + n] > ISA[L2 + n] ? 1 : -1);
}
private:
void induced_sort(const vc<int>& vect, int val_range, vc<int>& SA,
const vc<bool>& sl, const vc<int>& lms_idx) {
vc<int> l(val_range, 0), r(val_range, 0);
for (int c: vect) {
if (c + 1 < val_range) ++l[c + 1];
++r[c];
}
partial_sum(l.begin(), l.end(), l.begin());
partial_sum(r.begin(), r.end(), r.begin());
fill(SA.begin(), SA.end(), -1);
for (int i = (int)lms_idx.size() - 1; i >= 0; --i)
SA[--r[vect[lms_idx[i]]]] = lms_idx[i];
for (int i: SA)
if (i >= 1 && sl[i - 1]) SA[l[vect[i - 1]]++] = i - 1;
fill(r.begin(), r.end(), 0);
for (int c: vect) ++r[c];
partial_sum(r.begin(), r.end(), r.begin());
for (int k = (int)SA.size() - 1, i = SA[k]; k >= 1; --k, i = SA[k])
if (i >= 1 && !sl[i - 1]) { SA[--r[vect[i - 1]]] = i - 1; }
}
vc<int> SA_IS(const vc<int>& vect, int val_range) {
const int n = vect.size();
vc<int> SA(n), lms_idx;
vc<bool> sl(n);
sl[n - 1] = false;
for (int i = n - 2; i >= 0; --i) {
sl[i] = (vect[i] > vect[i + 1] || (vect[i] == vect[i + 1] && sl[i + 1]));
if (sl[i] && !sl[i + 1]) lms_idx.push_back(i + 1);
}
reverse(lms_idx.begin(), lms_idx.end());
induced_sort(vect, val_range, SA, sl, lms_idx);
vc<int> new_lms_idx(lms_idx.size()), lms_vec(lms_idx.size());
for (int i = 0, k = 0; i < n; ++i)
if (!sl[SA[i]] && SA[i] >= 1 && sl[SA[i] - 1]) {
new_lms_idx[k++] = SA[i];
}
int cur = 0;
SA[n - 1] = cur;
for (size_t k = 1; k < new_lms_idx.size(); ++k) {
int i = new_lms_idx[k - 1], j = new_lms_idx[k];
if (vect[i] != vect[j]) {
SA[j] = ++cur;
continue;
}
bool flag = false;
for (int a = i + 1, b = j + 1;; ++a, ++b) {
if (vect[a] != vect[b]) {
flag = true;
break;
}
if ((!sl[a] && sl[a - 1]) || (!sl[b] && sl[b - 1])) {
flag = !((!sl[a] && sl[a - 1]) && (!sl[b] && sl[b - 1]));
break;
}
}
SA[j] = (flag ? ++cur : cur);
}
for (size_t i = 0; i < lms_idx.size(); ++i) lms_vec[i] = SA[lms_idx[i]];
if (cur + 1 < (int)lms_idx.size()) {
auto lms_SA = SA_IS(lms_vec, cur + 1);
for (size_t i = 0; i < lms_idx.size(); ++i) {
new_lms_idx[i] = lms_idx[lms_SA[i]];
}
}
induced_sort(vect, val_range, SA, sl, new_lms_idx);
return SA;
}
vc<int> calc_suffix_array(const string& s, const char first = 'a',
const char last = 'z') {
vc<int> vect(s.size() + 1);
copy(begin(s), end(s), begin(vect));
for (auto& x: vect) x -= (int)first - 1;
vect.back() = 0;
auto ret = SA_IS(vect, (int)last - (int)first + 2);
ret.erase(ret.begin());
return ret;
}
vc<int> calc_suffix_array(const vc<int>& s) {
vc<int> ss = s;
UNIQUE(ss);
vc<int> vect(s.size() + 1);
copy(all(s), vect.begin());
for (auto& x: vect) x = LB(ss, x) + 1;
vect.back() = 0;
auto ret = SA_IS(vect, MAX(vect) + 2);
ret.erase(ret.begin());
return ret;
}
template <typename STRING>
void calc_LCP(const STRING& s) {
int n = s.size(), k = 0;
ISA.resize(n);
LCP.resize(n);
for (int i = 0; i < n; i++) ISA[SA[i]] = i;
for (int i = 0; i < n; i++, k ? k-- : 0) {
if (ISA[i] == n - 1) {
k = 0;
continue;
}
int j = SA[ISA[i] + 1];
while (i + k < n && j + k < n && s[i + k] == s[j + k]) k++;
LCP[ISA[i]] = k;
}
LCP.resize(n - 1);
}
};
#line 1 "seq/cartesian_tree.hpp"
/*
辞書順で高さを unique して、木にしている。
極大長方形アルゴリズムで線形時間構築。
*/
template <typename T, bool IS_MIN>
struct CartesianTree {
int n;
vc<T>& A;
vc<pair<int, int>> range;
vc<int> lch, rch, par;
int root;
CartesianTree(vc<T>& A) : n(len(A)), A(A) {
range.assign(n, {-1, -1});
lch.assign(n, -1);
rch.assign(n, -1);
par.assign(n, -1);
if (n == 1) {
range[0] = {0, 1};
root = 0;
return;
}
auto is_sm = [&](int i, int j) -> bool {
if (IS_MIN) return (A[i] < A[j]) || (A[i] == A[j] && i < j);
return (A[i] > A[j]) || (A[i] == A[j] && i < j);
};
vc<int> st;
FOR(i, n) {
while (!st.empty() && is_sm(i, st.back())) {
lch[i] = st.back();
st.pop_back();
}
range[i].fi = (st.empty() ? 0 : st.back() + 1);
st.eb(i);
}
st.clear();
FOR_R(i, n) {
while (!st.empty() && is_sm(i, st.back())) {
rch[i] = st.back();
st.pop_back();
}
range[i].se = (st.empty() ? n : st.back());
st.eb(i);
}
FOR(i, n) if (lch[i] != -1) par[lch[i]] = i;
FOR(i, n) if (rch[i] != -1) par[rch[i]] = i;
FOR(i, n) if (par[i] == -1) root = i;
}
// (l, r, h)
tuple<int, int, T> maximum_rectangle(int i) {
auto [l, r] = range[i];
return {l, r, A[i]};
}
// (l, r, h)
T max_rectangle_area() {
assert(IS_MIN);
T res = 0;
FOR(i, n) {
auto [l, r, h] = maximum_rectangle(i);
chmax(res, (r - l) * h);
}
return res;
}
ll count_subrectangle(bool baseline) {
assert(IS_MIN);
ll res = 0;
FOR(i, n) {
auto [l, r, h] = maximum_rectangle(i);
ll x = (baseline ? h : h * (h + 1) / 2);
res += x * (i - l + 1) * (r - i);
}
return res;
}
};
#line 2 "graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
if (len(used_e) != M) used_e.assign(M, 0);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e: (*this)[V[i]]) {
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid: history) used_e[eid] = 0;
G.build();
return G;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 5 "string/suffix_tree.hpp"
// https://twitter.com/maspy_stars/status/1565901414236205057?s=20&t=S2Tu6ayozHcakxai8dmh4g
// 各ノードは、suffix array での長方形領域と見なして、
// グラフおよび、領域データを作る。
// sample: test/my_test/suffix_tree.test.cpp
template <typename SUFFIX>
pair<Graph<int, 1>, vc<tuple<int, int, int, int>>> suffix_tree(SUFFIX& X) {
auto SA = X.SA;
auto ISA = X.ISA;
auto LCP = X.LCP;
vc<tuple<int, int, int, int>> dat;
vc<pair<int, int>> edges;
int N = len(SA);
if (N == 1) {
Graph<int, 1> G(2);
G.add(0, 1);
G.build();
dat.eb(0, 1, 0, 0), dat.eb(0, 1, 0, 1);
return {G, dat};
}
dat.eb(0, N, 0, 0);
CartesianTree<int, true> CT(LCP);
auto dfs = [&](auto& dfs, int p, int idx, int h) -> void {
int L = CT.range[idx].fi;
int R = CT.range[idx].se + 1;
int hh = LCP[idx];
if (h < hh) {
edges.eb(p, len(dat));
p = len(dat);
dat.eb(L, R, h, hh);
}
if (CT.lch[idx] == -1) {
if (hh < N - SA[idx]) {
edges.eb(p, len(dat));
dat.eb(idx, idx + 1, hh, N - SA[idx]);
}
} else {
dfs(dfs, p, CT.lch[idx], hh);
}
if (CT.rch[idx] == -1) {
if (hh < N - SA[idx + 1]) {
edges.eb(p, len(dat));
dat.eb(idx + 1, idx + 2, hh, N - SA[idx + 1]);
}
} else {
dfs(dfs, p, CT.rch[idx], hh);
}
};
int r = CT.root;
if (LCP[r] > 0) {
edges.eb(0, 1);
dat.eb(0, N, 0, LCP[r]);
dfs(dfs, 1, r, LCP[r]);
} else {
dfs(dfs, 0, r, 0);
}
Graph<int, 1> G(len(dat));
for (auto&& [a, b]: edges) G.add(a, b);
G.build();
return {G, dat};
}