#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define PB push_back
#define LL long long
#define int LL
#define FOR(i,a,b) for (int i = (a); i <= (b); i++)
#define FORD(i,a,b) for (int i = (a); i >= (b); i--)
#define REP(i,n) FOR(i,0,(int)(n)-1)
#define st first
#define nd second
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
#define VI vector<int>
#define PII pair<int,int>
#define LD long double
struct EncodedWord {
vector<PII> runs;
int total = 0;
int length = 0;
};
EncodedWord read_encoded_word() {
int blocks = 0;
char first = 0;
cin >> blocks >> first;
EncodedWord word;
char current = first;
REP(i, blocks) {
int repetitions = 0;
cin >> repetitions;
word.runs.PB({current, repetitions});
word.total += (current == '(' ? repetitions : -repetitions);
word.length += repetitions;
current = (current == '(' ? ')' : '(');
}
return word;
}
string expand_word(const EncodedWord& word) {
string out;
out.reserve(SZ(word.runs) ? (size_t)word.length : 0);
for (auto [c, len] : word.runs) {
out.append((size_t)len, c);
}
return out;
}
int bracket_value(char c) {
return c == '(' ? 1 : -1;
}
pair<VI, vector<char>> build_prefix_info(const string& s) {
VI pref(SZ(s) + 1, 0);
vector<char> reachable_empty(SZ(s) + 1, false);
reachable_empty[0] = true;
FOR(i, 1, SZ(s)) {
pref[i] = pref[i - 1] + bracket_value(s[i - 1]);
reachable_empty[i] = reachable_empty[i - 1] && (pref[i] >= 0);
}
return {pref, reachable_empty};
}
int solve_unrolled(const EncodedWord& s_enc, const EncodedWord& t_enc) {
const string s = expand_word(s_enc);
const string t = expand_word(t_enc);
auto [pref_s, reachable_empty] = build_prefix_info(s);
vector<char> prev(SZ(s) + 1, false), cur(SZ(s) + 1, false);
int answer = 0;
REP(left, SZ(t)) {
prev = reachable_empty;
int fragment_balance = 0;
FOR(right, left, SZ(t) - 1) {
fragment_balance += bracket_value(t[right]);
cur[0] = prev[0] && (fragment_balance >= 0);
FOR(i, 1, SZ(s)) {
cur[i] = (pref_s[i] + fragment_balance >= 0) && (prev[i] || cur[i - 1]);
}
swap(prev, cur);
if (pref_s[SZ(s)] + fragment_balance == 0 && prev[SZ(s)]) {
++answer;
}
}
}
return answer;
}
bool use_unrolled_solver(const EncodedWord& s, const EncodedWord& t) {
if (s.length + t.length > 3000) return false;
return true;
}
int single_need(const vector<PII>& runs, int idx, VI& memo) {
if (idx >= SZ(runs)) {
return 0;
}
if (memo[idx] != -1) {
return memo[idx];
}
if (runs[idx].st == '(') {
memo[idx] = max(0LL, single_need(runs, idx + 1, memo) - runs[idx].nd);
return memo[idx];
}
return memo[idx] = runs[idx].nd + single_need(runs, idx + 1, memo);
}
int pair_need(const vector<PII>& a, const vector<PII>& b, int ia, int ib,
vector<VI>& memo, VI& memo_a, VI& memo_b) {
if (ia >= SZ(a)) {
return single_need(b, ib, memo_b);
}
if (ib >= SZ(b)) {
return single_need(a, ia, memo_a);
}
int& ans = memo[ia][ib];
if (ans != -1) {
return ans;
}
if (a[ia].st == '(' || b[ib].st == '(') {
int gain = 0;
int na = ia, nb = ib;
if (a[ia].st == '(') {
gain += a[na++].nd;
}
if (b[ib].st == '(') {
gain += b[nb++].nd;
}
return ans = max(0LL, pair_need(a, b, na, nb, memo, memo_a, memo_b) - gain);
}
return ans = min(a[ia].nd + pair_need(a, b, ia + 1, ib, memo, memo_a, memo_b),
b[ib].nd + pair_need(a, b, ia, ib + 1, memo, memo_a, memo_b));
}
int need_merge(const vector<PII>& a, const vector<PII>& b) {
vector<VI> memo(SZ(a), VI(SZ(b), -1));
VI memo_a(SZ(a), -1), memo_b(SZ(b), -1);
return pair_need(a, b, 0, 0, memo, memo_a, memo_b);
}
vector<PII> build_sub_runs(const vector<PII>& runs, int l, int a, int r, int b) {
vector<PII> out;
if (l == r) {
out.PB({runs[l].st, b});
return out;
}
out.PB({runs[l].st, a});
FOR(i, l + 1, r - 1) {
out.PB(runs[i]);
}
out.PB({runs[r].st, b});
return out;
}
int32_t main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
EncodedWord s = read_encoded_word();
EncodedWord t = read_encoded_word();
if (use_unrolled_solver(s, t)) {
cout << solve_unrolled(s, t) << '\n';
return 0;
}
const int target = -s.total;
const vector<PII>& rt = t.runs;
vector<int> pref(SZ(rt) + 1, 0);
REP(i, SZ(rt)) {
pref[i + 1] = pref[i] + (rt[i].st == '(' ? rt[i].nd : -rt[i].nd);
}
int answer = 0;
REP(i, SZ(rt)) {
int sign = (rt[i].st == '(' ? 1 : -1);
int len = sign * target;
if (1 <= len && len <= rt[i].nd) {
vector<PII> sub = {{rt[i].st, len}};
if (need_merge(s.runs, sub) == 0) {
answer += rt[i].nd - len + 1;
}
}
}
REP(l, SZ(rt)) {
FOR(r, l + 1, SZ(rt) - 1) {
int middle_sum = pref[r] - pref[l + 1];
int sl = (rt[l].st == '(' ? 1 : -1);
int sr = (rt[r].st == '(' ? 1 : -1);
int c = (target - middle_sum) / sr;
int k = -sl / sr;
int lo = 1;
int hi = rt[l].nd;
if (k == 1) {
lo = max(lo, 1 - c);
hi = min(hi, rt[r].nd - c);
} else {
lo = max(lo, c - rt[r].nd);
hi = min(hi, c - 1);
}
if (lo > hi) {
continue;
}
map<int, int> cache;
auto eval = [&](int a) -> int {
auto it = cache.find(a);
if (it != cache.end()) {
return it->nd;
}
int b = c + k * a;
vector<PII> sub = build_sub_runs(rt, l, a, r, b);
int val = need_merge(s.runs, sub);
cache[a] = val;
return val;
};
int L = lo;
int R = hi;
while (L < R) {
int mid = (L + R) / 2;
if (eval(mid) <= eval(mid + 1)) {
R = mid;
} else {
L = mid + 1;
}
}
int best = L;
if (eval(best) != 0) {
continue;
}
int left = lo;
int right = best;
while (left < right) {
int mid = (left + right) / 2;
if (eval(mid) == 0) {
right = mid;
} else {
left = mid + 1;
}
}
int first = left;
left = best;
right = hi;
while (left < right) {
int mid = (left + right + 1) / 2;
if (eval(mid) == 0) {
left = mid;
} else {
right = mid - 1;
}
}
int last = left;
answer += last - first + 1;
}
}
cout << answer << '\n';
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 | #pragma GCC optimize("O3,unroll-loops") #include <bits/stdc++.h> using namespace std; #define PB push_back #define LL long long #define int LL #define FOR(i,a,b) for (int i = (a); i <= (b); i++) #define FORD(i,a,b) for (int i = (a); i >= (b); i--) #define REP(i,n) FOR(i,0,(int)(n)-1) #define st first #define nd second #define ALL(x) (x).begin(), (x).end() #define SZ(x) ((int)(x).size()) #define VI vector<int> #define PII pair<int,int> #define LD long double struct EncodedWord { vector<PII> runs; int total = 0; int length = 0; }; EncodedWord read_encoded_word() { int blocks = 0; char first = 0; cin >> blocks >> first; EncodedWord word; char current = first; REP(i, blocks) { int repetitions = 0; cin >> repetitions; word.runs.PB({current, repetitions}); word.total += (current == '(' ? repetitions : -repetitions); word.length += repetitions; current = (current == '(' ? ')' : '('); } return word; } string expand_word(const EncodedWord& word) { string out; out.reserve(SZ(word.runs) ? (size_t)word.length : 0); for (auto [c, len] : word.runs) { out.append((size_t)len, c); } return out; } int bracket_value(char c) { return c == '(' ? 1 : -1; } pair<VI, vector<char>> build_prefix_info(const string& s) { VI pref(SZ(s) + 1, 0); vector<char> reachable_empty(SZ(s) + 1, false); reachable_empty[0] = true; FOR(i, 1, SZ(s)) { pref[i] = pref[i - 1] + bracket_value(s[i - 1]); reachable_empty[i] = reachable_empty[i - 1] && (pref[i] >= 0); } return {pref, reachable_empty}; } int solve_unrolled(const EncodedWord& s_enc, const EncodedWord& t_enc) { const string s = expand_word(s_enc); const string t = expand_word(t_enc); auto [pref_s, reachable_empty] = build_prefix_info(s); vector<char> prev(SZ(s) + 1, false), cur(SZ(s) + 1, false); int answer = 0; REP(left, SZ(t)) { prev = reachable_empty; int fragment_balance = 0; FOR(right, left, SZ(t) - 1) { fragment_balance += bracket_value(t[right]); cur[0] = prev[0] && (fragment_balance >= 0); FOR(i, 1, SZ(s)) { cur[i] = (pref_s[i] + fragment_balance >= 0) && (prev[i] || cur[i - 1]); } swap(prev, cur); if (pref_s[SZ(s)] + fragment_balance == 0 && prev[SZ(s)]) { ++answer; } } } return answer; } bool use_unrolled_solver(const EncodedWord& s, const EncodedWord& t) { if (s.length + t.length > 3000) return false; return true; } int single_need(const vector<PII>& runs, int idx, VI& memo) { if (idx >= SZ(runs)) { return 0; } if (memo[idx] != -1) { return memo[idx]; } if (runs[idx].st == '(') { memo[idx] = max(0LL, single_need(runs, idx + 1, memo) - runs[idx].nd); return memo[idx]; } return memo[idx] = runs[idx].nd + single_need(runs, idx + 1, memo); } int pair_need(const vector<PII>& a, const vector<PII>& b, int ia, int ib, vector<VI>& memo, VI& memo_a, VI& memo_b) { if (ia >= SZ(a)) { return single_need(b, ib, memo_b); } if (ib >= SZ(b)) { return single_need(a, ia, memo_a); } int& ans = memo[ia][ib]; if (ans != -1) { return ans; } if (a[ia].st == '(' || b[ib].st == '(') { int gain = 0; int na = ia, nb = ib; if (a[ia].st == '(') { gain += a[na++].nd; } if (b[ib].st == '(') { gain += b[nb++].nd; } return ans = max(0LL, pair_need(a, b, na, nb, memo, memo_a, memo_b) - gain); } return ans = min(a[ia].nd + pair_need(a, b, ia + 1, ib, memo, memo_a, memo_b), b[ib].nd + pair_need(a, b, ia, ib + 1, memo, memo_a, memo_b)); } int need_merge(const vector<PII>& a, const vector<PII>& b) { vector<VI> memo(SZ(a), VI(SZ(b), -1)); VI memo_a(SZ(a), -1), memo_b(SZ(b), -1); return pair_need(a, b, 0, 0, memo, memo_a, memo_b); } vector<PII> build_sub_runs(const vector<PII>& runs, int l, int a, int r, int b) { vector<PII> out; if (l == r) { out.PB({runs[l].st, b}); return out; } out.PB({runs[l].st, a}); FOR(i, l + 1, r - 1) { out.PB(runs[i]); } out.PB({runs[r].st, b}); return out; } int32_t main() { ios::sync_with_stdio(false); cin.tie(nullptr); EncodedWord s = read_encoded_word(); EncodedWord t = read_encoded_word(); if (use_unrolled_solver(s, t)) { cout << solve_unrolled(s, t) << '\n'; return 0; } const int target = -s.total; const vector<PII>& rt = t.runs; vector<int> pref(SZ(rt) + 1, 0); REP(i, SZ(rt)) { pref[i + 1] = pref[i] + (rt[i].st == '(' ? rt[i].nd : -rt[i].nd); } int answer = 0; REP(i, SZ(rt)) { int sign = (rt[i].st == '(' ? 1 : -1); int len = sign * target; if (1 <= len && len <= rt[i].nd) { vector<PII> sub = {{rt[i].st, len}}; if (need_merge(s.runs, sub) == 0) { answer += rt[i].nd - len + 1; } } } REP(l, SZ(rt)) { FOR(r, l + 1, SZ(rt) - 1) { int middle_sum = pref[r] - pref[l + 1]; int sl = (rt[l].st == '(' ? 1 : -1); int sr = (rt[r].st == '(' ? 1 : -1); int c = (target - middle_sum) / sr; int k = -sl / sr; int lo = 1; int hi = rt[l].nd; if (k == 1) { lo = max(lo, 1 - c); hi = min(hi, rt[r].nd - c); } else { lo = max(lo, c - rt[r].nd); hi = min(hi, c - 1); } if (lo > hi) { continue; } map<int, int> cache; auto eval = [&](int a) -> int { auto it = cache.find(a); if (it != cache.end()) { return it->nd; } int b = c + k * a; vector<PII> sub = build_sub_runs(rt, l, a, r, b); int val = need_merge(s.runs, sub); cache[a] = val; return val; }; int L = lo; int R = hi; while (L < R) { int mid = (L + R) / 2; if (eval(mid) <= eval(mid + 1)) { R = mid; } else { L = mid + 1; } } int best = L; if (eval(best) != 0) { continue; } int left = lo; int right = best; while (left < right) { int mid = (left + right) / 2; if (eval(mid) == 0) { right = mid; } else { left = mid + 1; } } int first = left; left = best; right = hi; while (left < right) { int mid = (left + right + 1) / 2; if (eval(mid) == 0) { left = mid; } else { right = mid - 1; } } int last = left; answer += last - first + 1; } } cout << answer << '\n'; return 0; } |
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