prefix_substring_lcs.hpp¶
对固定串的每个前缀，求它与另一串指定子串的最长公共子序列长度。
Complexity: Time: \(O(M N + (K N + Q) \log (N + 1) + M + N + Q)\). Space: \(O(M + N + Q)\). \(M / N\) are the largest nontrivial queried prefix/right boundary, \(K\) the number of such prefixes, and \(Q\) the total query count.
Source: Library Checker
AC 记录：prefix_substring_lcs。
Implementation¶
当前头文件，省略 include guard；依赖见 #include。
// SPDX-License-Identifier: Apache-2.0
// Adapted from Library Checker, with changes for libra.
// Sources and license: third_party/README.md.
/// @complexity Time: O(M N + (K N + Q) log(N + 1) + M + N + Q).
/// Space: O(M + N + Q). M/N are the largest nontrivial queried prefix/right
/// boundary, K the number of such prefixes, and Q the total query count.
#include "atcoder/fenwicktree.hpp"
#include <algorithm>
#include <cassert>
#include <numeric>
#include <vector>
namespace noya {
struct prefix_substring_lcs_query {
int pre;
int l;
int r;
};
/// @brief Answer LCS lengths between prefixes of one sequence and substrings
/// of another. The dynamic-programming grid is represented by its seaweed
/// permutation: after adding one symbol of the first sequence, a single scan
/// swaps boundary endpoints exactly where equality or crossing changes the
/// next LCS row. For a fixed prefix, the LCS deficit of [left, right) equals
/// the number of j < right with to[j] >= left.
/// Sweeping right and counting endpoint positions with a Fenwick tree answers
/// every query assigned to that prefix without storing the quadratic DP table.
template <class FirstSequence, class SecondSequence>
std::vector<int>
prefix_substring_lcs(const FirstSequence &a, const SecondSequence &b,
const std::vector<prefix_substring_lcs_query> &qs) {
int n1 = int(a.size());
int n2 = int(b.size());
int qn = int(qs.size());
std::vector<int> ans(qn);
std::vector<std::vector<int>> by;
int width = 0;
for (int id = 0; id < qn; id++) {
auto [pre, l, r] = qs[id];
assert(0 <= pre && pre <= n1);
assert(0 <= l && l <= r && r <= n2);
if (pre != 0 && l != r) {
if (int(by.size()) < pre) by.resize(pre);
by[pre - 1].push_back(id);
width = std::max(width, r);
}
}
if (width == 0) return ans;
std::vector<int> to(width);
std::iota(to.begin(), to.end(), 0);
std::vector<std::vector<int>> byr(width);
int remaining = width;
for (int pos = 0; pos < int(by.size()); pos++) {
int old = -1;
for (int po1 = 0; po1 < width; po1++) {
if (a[pos] == b[po1] || to[po1] < old) {
std::swap(to[po1], old);
}
}
remaining -= old != -1;
if (remaining == 0) { // b[0:width] is now a subsequence of a[0:pos+1].
for (int id = 0; id < qn; id++) {
if (qs[id].pre >= pos + 1) ans[id] = qs[id].r - qs[id].l;
}
break;
}
if (by[pos].empty()) continue;
int last = 0;
for (int id : by[pos]) {
byr[qs[id].r - 1].push_back(id);
last = std::max(last, qs[id].r);
}
atcoder::fenwick_tree<int> act(last); // to[r] <= r, so last also bounds updates.
int cnt = 0;
for (int r = 0; r < last; r++) {
if (to[r] != -1) {
act.add(to[r], 1);
cnt++;
}
for (int id : byr[r]) {
int l = qs[id].l;
int len = qs[id].r - l;
ans[id] = len - (cnt - act.sum(0, l));
}
byr[r].clear();
}
}
return ans;
}
} // namespace noya
// NOYA_PREFIX_SUBSTRING_LCS_HPP
#ifndef NOYA_PREFIX_SUBSTRING_LCS_HPP
#define NOYA_PREFIX_SUBSTRING_LCS_HPP 1
// SPDX-License-Identifier: Apache-2.0
// Adapted from Library Checker, with changes for libra.
// Sources and license: third_party/README.md.
/// @complexity Time: O(M N + (K N + Q) log(N + 1) + M + N + Q).
/// Space: O(M + N + Q). M/N are the largest nontrivial queried prefix/right
/// boundary, K the number of such prefixes, and Q the total query count.
#include "atcoder/fenwicktree.hpp"
#include <algorithm>
#include <cassert>
#include <numeric>
#include <vector>
namespace noya {
struct prefix_substring_lcs_query {
int pre;
int l;
int r;
};
/// @brief Answer LCS lengths between prefixes of one sequence and substrings
/// of another. The dynamic-programming grid is represented by its seaweed
/// permutation: after adding one symbol of the first sequence, a single scan
/// swaps boundary endpoints exactly where equality or crossing changes the
/// next LCS row. For a fixed prefix, the LCS deficit of [left, right) equals
/// the number of j < right with to[j] >= left.
/// Sweeping right and counting endpoint positions with a Fenwick tree answers
/// every query assigned to that prefix without storing the quadratic DP table.
template <class FirstSequence, class SecondSequence>
std::vector<int>
prefix_substring_lcs(const FirstSequence &a, const SecondSequence &b,
const std::vector<prefix_substring_lcs_query> &qs) {
int n1 = int(a.size());
int n2 = int(b.size());
int qn = int(qs.size());
std::vector<int> ans(qn);
std::vector<std::vector<int>> by;
int width = 0;
for (int id = 0; id < qn; id++) {
auto [pre, l, r] = qs[id];
assert(0 <= pre && pre <= n1);
assert(0 <= l && l <= r && r <= n2);
if (pre != 0 && l != r) {
if (int(by.size()) < pre) by.resize(pre);
by[pre - 1].push_back(id);
width = std::max(width, r);
}
}
if (width == 0) return ans;
std::vector<int> to(width);
std::iota(to.begin(), to.end(), 0);
std::vector<std::vector<int>> byr(width);
int remaining = width;
for (int pos = 0; pos < int(by.size()); pos++) {
int old = -1;
for (int po1 = 0; po1 < width; po1++) {
if (a[pos] == b[po1] || to[po1] < old) {
std::swap(to[po1], old);
}
}
remaining -= old != -1;
if (remaining == 0) { // b[0:width] is now a subsequence of a[0:pos+1].
for (int id = 0; id < qn; id++) {
if (qs[id].pre >= pos + 1) ans[id] = qs[id].r - qs[id].l;
}
break;
}
if (by[pos].empty()) continue;
int last = 0;
for (int id : by[pos]) {
byr[qs[id].r - 1].push_back(id);
last = std::max(last, qs[id].r);
}
atcoder::fenwick_tree<int> act(last); // to[r] <= r, so last also bounds updates.
int cnt = 0;
for (int r = 0; r < last; r++) {
if (to[r] != -1) {
act.add(to[r], 1);
cnt++;
}
for (int id : byr[r]) {
int l = qs[id].l;
int len = qs[id].r - l;
ans[id] = len - (cnt - act.sum(0, l));
}
byr[r].clear();
}
}
return ans;
}
} // namespace noya
#endif // NOYA_PREFIX_SUBSTRING_LCS_HPP
// SPDX-License-Identifier: Apache-2.0
// Adapted from Library Checker, with changes for libra.
// Sources and license: third_party/README.md.
/// @complexity Time: O(M N + (K N + Q) log(N + 1) + M + N + Q).
/// Space: O(M + N + Q). M/N are the largest nontrivial queried prefix/right
/// boundary, K the number of such prefixes, and Q the total query count.
#include <cassert>
#include <vector>
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
template <class T> struct fenwick_tree {
using U = internal::to_unsigned_t<T>;
public:
fenwick_tree() : _n(0) {}
explicit fenwick_tree(int n) : _n(n), data(n) {}
void add(int p, T x) {
assert(0 <= p && p < _n);
p++;
while (p <= _n) {
data[p - 1] += U(x);
p += p & -p;
}
}
T sum(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
return sum(r) - sum(l);
}
private:
int _n;
std::vector<U> data;
U sum(int r) {
U s = 0;
while (r > 0) {
s += data[r - 1];
r -= r & -r;
}
return s;
}
};
} // namespace atcoder
#include <algorithm>
#include <cassert>
#include <numeric>
#include <vector>
namespace noya {
struct prefix_substring_lcs_query {
int pre;
int l;
int r;
};
/// @brief Answer LCS lengths between prefixes of one sequence and substrings
/// of another. The dynamic-programming grid is represented by its seaweed
/// permutation: after adding one symbol of the first sequence, a single scan
/// swaps boundary endpoints exactly where equality or crossing changes the
/// next LCS row. For a fixed prefix, the LCS deficit of [left, right) equals
/// the number of j < right with to[j] >= left.
/// Sweeping right and counting endpoint positions with a Fenwick tree answers
/// every query assigned to that prefix without storing the quadratic DP table.
template <class FirstSequence, class SecondSequence>
std::vector<int>
prefix_substring_lcs(const FirstSequence &a, const SecondSequence &b,
const std::vector<prefix_substring_lcs_query> &qs) {
int n1 = int(a.size());
int n2 = int(b.size());
int qn = int(qs.size());
std::vector<int> ans(qn);
std::vector<std::vector<int>> by;
int width = 0;
for (int id = 0; id < qn; id++) {
auto [pre, l, r] = qs[id];
assert(0 <= pre && pre <= n1);
assert(0 <= l && l <= r && r <= n2);
if (pre != 0 && l != r) {
if (int(by.size()) < pre) by.resize(pre);
by[pre - 1].push_back(id);
width = std::max(width, r);
}
}
if (width == 0) return ans;
std::vector<int> to(width);
std::iota(to.begin(), to.end(), 0);
std::vector<std::vector<int>> byr(width);
int remaining = width;
for (int pos = 0; pos < int(by.size()); pos++) {
int old = -1;
for (int po1 = 0; po1 < width; po1++) {
if (a[pos] == b[po1] || to[po1] < old) {
std::swap(to[po1], old);
}
}
remaining -= old != -1;
if (remaining == 0) { // b[0:width] is now a subsequence of a[0:pos+1].
for (int id = 0; id < qn; id++) {
if (qs[id].pre >= pos + 1) ans[id] = qs[id].r - qs[id].l;
}
break;
}
if (by[pos].empty()) continue;
int last = 0;
for (int id : by[pos]) {
byr[qs[id].r - 1].push_back(id);
last = std::max(last, qs[id].r);
}
atcoder::fenwick_tree<int> act(last); // to[r] <= r, so last also bounds updates.
int cnt = 0;
for (int r = 0; r < last; r++) {
if (to[r] != -1) {
act.add(to[r], 1);
cnt++;
}
for (int id : byr[r]) {
int l = qs[id].l;
int len = qs[id].r - l;
ans[id] = len - (cnt - act.sum(0, l));
}
byr[r].clear();
}
}
return ans;
}
} // namespace noya
// NOYA_PREFIX_SUBSTRING_LCS_HPP