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#include "string/prefix_substring_LCS.hpp"
#include "ds/wavelet_matrix/wavelet_matrix.hpp" // https://codeforces.com/blog/entry/111625 struct Prefix_Substring_LCS { int N, M; vc<Wavelet_Matrix<int, 0>> WM; template <typename STRING> Prefix_Substring_LCS(STRING S, STRING T) { build(S, T); } template <typename STRING> void build(STRING S, STRING T) { N = len(S), M = len(T); vv(int, dph, N + 1, M + 1); vv(int, dpv, N + 1, M + 1); FOR(j, M + 1) dph[0][j] = j; FOR(i, 1, N + 1) FOR(j, 1, M + 1) { bool same = S[i - 1] == T[j - 1]; int a = dph[i - 1][j], b = dpv[i][j - 1]; dph[i][j] = (same ? b : max(a, b)); dpv[i][j] = (same ? a : min(a, b)); } FOR(i, N + 1) { WM.eb(Wavelet_Matrix<int, 0>(dph[i])); } } // LCS(S[0:n], T[L:R]) int query(int n, int L, int R) { return WM[n].count(L + 1, R + 1, 0, L + 1); } };
#line 1 "ds/bit_vector.hpp" struct Bit_Vector { vc<pair<u32, u32>> dat; Bit_Vector(int n) { dat.assign((n + 63) >> 5, {0, 0}); } void set(int i) { dat[i >> 5].fi |= u32(1) << (i & 31); } void build() { FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi); } // [0, k) 内の 1 の個数 int rank(int k, bool f = 1) { auto [a, b] = dat[k >> 5]; int ret = b + popcnt(a & ((u32(1) << (k & 31)) - 1)); return (f ? ret : k - ret); } }; #line 2 "alg/monoid/add.hpp" template <typename E> struct Monoid_Add { using X = E; using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return x + y; } static constexpr X inverse(const X &x) noexcept { return -x; } static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; } static constexpr X unit() { return X(0); } static constexpr bool commute = true; }; #line 3 "ds/wavelet_matrix/wavelet_matrix.hpp" // 座圧するかどうかを COMPRESS で指定する // xor 的な使い方をする場合には、コンストラクタで log を渡すこと template <typename T, bool COMPRESS, typename Monoid = Monoid_Add<T>> struct Wavelet_Matrix { using MX = Monoid; using X = typename MX::value_type; static_assert(MX::commute); int N, lg; vector<int> mid; vector<Bit_Vector> bv; vc<T> key; bool set_log; vvc<X> cumsum; Wavelet_Matrix() {} // 和を使わないなら、SUM_data は空でよい Wavelet_Matrix(vc<T> A, vc<X> SUM_data = {}, int log = -1) { build(A, SUM_data, log); } void build(vc<T> A, vc<X> SUM_data = {}, int log = -1) { N = len(A), lg = log, set_log = (log != -1); if (N == 0) { lg = 0; return; } bool MAKE_SUM = !(SUM_data.empty()); vc<X>& S = SUM_data; if (COMPRESS) { assert(!set_log); key.reserve(N); vc<int> I = argsort(A); for (auto&& i: I) { if (key.empty() || key.back() != A[i]) key.eb(A[i]); A[i] = len(key) - 1; } key.shrink_to_fit(); } if (lg == -1) lg = __lg(max<ll>(MAX(A), 1)) + 1; mid.resize(lg); bv.assign(lg, Bit_Vector(N)); if (MAKE_SUM) cumsum.assign(1 + lg, vc<X>(N + 1, MX::unit())); S.resize(N); vc<T> A0(N), A1(N); vc<X> S0(N), S1(N); FOR_R(d, -1, lg) { int p0 = 0, p1 = 0; if (MAKE_SUM) { FOR(i, N) { cumsum[d + 1][i + 1] = MX::op(cumsum[d + 1][i], S[i]); } } if (d == -1) break; FOR(i, N) { bool f = (A[i] >> d & 1); if (!f) { if (MAKE_SUM) S0[p0] = S[i]; A0[p0++] = A[i]; } if (f) { if (MAKE_SUM) S1[p1] = S[i]; bv[d].set(i), A1[p1++] = A[i]; } } mid[d] = p0; bv[d].build(); swap(A, A0), swap(S, S0); FOR(i, p1) A[p0 + i] = A1[i], S[p0 + i] = S1[i]; } } // xor した結果で [a, b) に収まるものを数える int count(int L, int R, T a, T b, T xor_val = 0) { return prefix_count(L, R, b, xor_val) - prefix_count(L, R, a, xor_val); } int count(vc<pair<int, int>> segments, T a, T b, T xor_val = 0) { int res = 0; for (auto&& [L, R]: segments) res += count(L, R, a, b, xor_val); return res; } // xor した結果で、[L, R) の中で k>=0 番目と prefix sum pair<T, X> kth_value_and_sum(int L, int R, int k, T xor_val = 0) { assert(0 <= k && k <= R - L); if (L == R) return {infty<T>, MX::unit()}; if (k == R - L) { return {infty<T>, sum_all(L, R)}; } if (xor_val != 0) assert(set_log); assert(!cumsum.empty()); int cnt = 0; X sm = MX::unit(); T ret = 0; for (int d = lg - 1; d >= 0; --d) { bool f = (xor_val >> d) & 1; int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int c = (f ? (R - L) - (r0 - l0) : (r0 - l0)); if (cnt + c > k) { if (!f) L = l0, R = r0; if (f) L += mid[d] - l0, R += mid[d] - r0; } else { X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0)); cnt += c, ret |= T(1) << d, sm = MX::op(sm, s); if (!f) L += mid[d] - l0, R += mid[d] - r0; if (f) L = l0, R = r0; } } sm = MX::op(sm, get(0, L, L + k - cnt)); if (COMPRESS) ret = key[ret]; return {ret, sm}; } // xor した結果で、[L, R) の中で k>=0 番目と prefix sum pair<T, X> kth_value_and_sum(vc<pair<int, int>> segments, int k, T xor_val = 0) { assert(!cumsum.empty()); if (xor_val != 0) assert(set_log); int total_len = 0; for (auto&& [L, R]: segments) total_len += R - L; assert(0 <= k && k <= total_len); if (k == total_len) { return {infty<T>, sum_all(segments)}; } int cnt = 0; X sm = MX::unit(); T ret = 0; for (int d = lg - 1; d >= 0; --d) { bool f = (xor_val >> d) & 1; int c = 0; for (auto&& [L, R]: segments) { int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); c += (f ? (R - L) - (r0 - l0) : (r0 - l0)); } if (cnt + c > k) { for (auto&& [L, R]: segments) { int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); if (!f) L = l0, R = r0; if (f) L += mid[d] - l0, R += mid[d] - r0; } } else { cnt += c, ret |= T(1) << d; for (auto&& [L, R]: segments) { int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0)); sm = MX::op(sm, s); if (!f) L += mid[d] - l0, R += mid[d] - r0; if (f) L = l0, R = r0; } } } for (auto&& [L, R]: segments) { int t = min(R - L, k - cnt); sm = MX::op(sm, get(0, L, L + t)); cnt += t; } if (COMPRESS) ret = key[ret]; return {ret, sm}; } // xor した結果で、[L, R) の中で k>=0 番目 T kth(int L, int R, int k, T xor_val = 0) { if (xor_val != 0) assert(set_log); assert(0 <= k && k < R - L); int cnt = 0; T ret = 0; for (int d = lg - 1; d >= 0; --d) { bool f = (xor_val >> d) & 1; int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int c = (f ? (R - L) - (r0 - l0) : (r0 - l0)); if (cnt + c > k) { if (!f) L = l0, R = r0; if (f) L += mid[d] - l0, R += mid[d] - r0; } else { cnt += c, ret |= T(1) << d; if (!f) L += mid[d] - l0, R += mid[d] - r0; if (f) L = l0, R = r0; } } if (COMPRESS) ret = key[ret]; return ret; } T kth(vc<pair<int, int>> segments, int k, T xor_val = 0) { int total_len = 0; for (auto&& [L, R]: segments) total_len += R - L; assert(0 <= k && k < total_len); int cnt = 0; T ret = 0; for (int d = lg - 1; d >= 0; --d) { bool f = (xor_val >> d) & 1; int c = 0; for (auto&& [L, R]: segments) { int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); c += (f ? (R - L) - (r0 - l0) : (r0 - l0)); } if (cnt + c > k) { for (auto&& [L, R]: segments) { int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); if (!f) L = l0, R = r0; if (f) L += mid[d] - l0, R += mid[d] - r0; } } else { cnt += c, ret |= T(1) << d; for (auto&& [L, R]: segments) { int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); if (!f) L += mid[d] - l0, R += mid[d] - r0; if (f) L = l0, R = r0; } } } if (COMPRESS) ret = key[ret]; return ret; } // xor した結果で、[L, R) の中で中央値。 // LOWER = true:下側中央値、false:上側中央値 T median(bool UPPER, int L, int R, T xor_val = 0) { int n = R - L; int k = (UPPER ? n / 2 : (n - 1) / 2); return kth(L, R, k, xor_val); } T median(bool UPPER, vc<pair<int, int>> segments, T xor_val = 0) { int n = 0; for (auto&& [L, R]: segments) n += R - L; int k = (UPPER ? n / 2 : (n - 1) / 2); return kth(segments, k, xor_val); } // xor した結果で [k1, k2) 番目であるところの SUM_data の和 X sum(int L, int R, int k1, int k2, T xor_val = 0) { assert(0 <= k1 && k1 <= k2 && k2 <= R - L); if (k1 == k2) return MX::unit(); X add = prefix_sum(L, R, k2, xor_val); X sub = prefix_sum(L, R, k1, xor_val); return MX::op(add, MX::inverse(sub)); } X sum_all(int L, int R) { return get(lg, L, R); } X sum_all(vc<pair<int, int>> segments) { X sm = MX::unit(); for (auto&& [L, R]: segments) { sm = MX::op(sm, get(lg, L, R)); } return sm; } // check(cnt, prefix sum) が true となるような最大の (cnt, sum) template <typename F> pair<int, X> max_right(F check, int L, int R, T xor_val = 0) { assert(check(0, MX::unit())); if (xor_val != 0) assert(set_log); if (L == R) return {R - L, MX::unit()}; if (check(R - L, get(lg, L, R))) return {R - L, get(lg, L, R)}; int cnt = 0; X sm = MX::unit(); for (int d = lg - 1; d >= 0; --d) { bool f = (xor_val >> d) & 1; int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int c = (f ? (R - L) - (r0 - l0) : (r0 - l0)); X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0)); if (check(cnt + c, MX::op(sm, s))) { cnt += c, sm = MX::op(sm, s); if (f) L = l0, R = r0; if (!f) L += mid[d] - l0, R += mid[d] - r0; } else { if (!f) L = l0, R = r0; if (f) L += mid[d] - l0, R += mid[d] - r0; } } int k = binary_search( [&](int k) -> bool { return check(cnt + k, MX::op(sm, get(0, L, L + k))); }, 0, R - L); cnt += k; sm = MX::op(sm, get(0, L, L + k)); return {cnt, sm}; } private: inline X get(int d, int L, int R) { assert(!cumsum.empty()); return MX::op(MX::inverse(cumsum[d][L]), cumsum[d][R]); } // xor した結果で [0, x) に収まるものを数える int prefix_count(int L, int R, T x, T xor_val = 0) { if (xor_val != 0) assert(set_log); x = (COMPRESS ? LB(key, x) : x); if (x == 0) return 0; if (x >= (1 << lg)) return R - L; int cnt = 0; FOR_R(d, lg) { bool add = (x >> d) & 1; bool f = ((xor_val) >> d) & 1; int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int kf = (f ? (R - L) - (r0 - l0) : (r0 - l0)); if (add) { cnt += kf; if (f) { L = l0, R = r0; } if (!f) { L += mid[d] - l0, R += mid[d] - r0; } } else { if (!f) L = l0, R = r0; if (f) L += mid[d] - l0, R += mid[d] - r0; } } return cnt; } // xor した結果で [0, k) 番目のものの和 X prefix_sum(int L, int R, int k, T xor_val = 0) { return kth_value_and_sum(L, R, k, xor_val).se; } // xor した結果で [0, k) 番目のものの和 X prefix_sum(vc<pair<int, int>> segments, int k, T xor_val = 0) { return kth_value_and_sum(segments, k, xor_val).se; } }; #line 2 "string/prefix_substring_LCS.hpp" // https://codeforces.com/blog/entry/111625 struct Prefix_Substring_LCS { int N, M; vc<Wavelet_Matrix<int, 0>> WM; template <typename STRING> Prefix_Substring_LCS(STRING S, STRING T) { build(S, T); } template <typename STRING> void build(STRING S, STRING T) { N = len(S), M = len(T); vv(int, dph, N + 1, M + 1); vv(int, dpv, N + 1, M + 1); FOR(j, M + 1) dph[0][j] = j; FOR(i, 1, N + 1) FOR(j, 1, M + 1) { bool same = S[i - 1] == T[j - 1]; int a = dph[i - 1][j], b = dpv[i][j - 1]; dph[i][j] = (same ? b : max(a, b)); dpv[i][j] = (same ? a : min(a, b)); } FOR(i, N + 1) { WM.eb(Wavelet_Matrix<int, 0>(dph[i])); } } // LCS(S[0:n], T[L:R]) int query(int n, int L, int R) { return WM[n].count(L + 1, R + 1, 0, L + 1); } };