#include <cassert> #include <cstdio> #include <iostream> #include <vector> using namespace std; class Tree { public: Tree(const vector<int>& v) : n_(RoundUp(v.size())), v_(2 * n_) { for (int i = 0; i < v.size(); ++i) v_[n_ + i] = v[i]; for (int i = n_ - 1; i >= 0; --i) v_[i] = min(v_[2 * i], v_[2 * i + 1]); } bool Absorb( const pair<int, int>& node, int* position, int* balance, long long* moves) const { const int dip = ValueAt(*position) - v_[node.first]; if (dip < *balance) { *balance -= ValueAt(*position); *position += node.second; *moves += node.second; *balance += ValueAt(*position); return true; } if (node.first >= n_) { ++*position; ++*moves; --*balance; return false; } if (!Absorb(make_pair(2 * node.first, node.second / 2), position, balance, moves)) return false; if (!Absorb(make_pair(2 * node.first + 1, node.second / 2), position, balance, moves)) return false; assert(false); } int Delta(const int left, const int right) const { return ValueAt(right) - ValueAt(left); } bool Dies(int left, int right, int* balance, long long* moves) const { // cerr << left << ' ' << right << ' ' << right - left << endl; int position = left; left += n_; right += n_; int step = 1; static vector<pair<int, int> > pre, post; pre.clear(); post.clear(); while (left < right) { // cerr << left << ' ' << right << ' ' << right - left << ' ' << step << ' ' << (right - left) * step << endl; if (left % 2) { pre.push_back(make_pair(left++, step)); // cerr << step << endl; } if (right % 2) { post.push_back(make_pair(--right, step)); // cerr << step << endl; } left /= 2; right /= 2; step *= 2; } for (int i = 0; i < pre.size(); ++i) { // cerr << position << ' ' << pre[i].second << endl; if (!Absorb(pre[i], &position, balance, moves)) return true; // cerr << position << endl; } for (int i = post.size() - 1; i >= 0; --i) { // cerr << position << ' ' << post[i].second << endl; if (!Absorb(post[i], &position, balance, moves)) return true; // cerr << position << endl; } // assert(position == right); return false; } int Dip(int left, int right) const { const int start = ValueAt(left); int dip = start; left += n_; right += n_; while (left < right) { if (left % 2) dip = min(dip, v_[left++]); if (right % 2) dip = min(dip, v_[--right]); left /= 2; right /= 2; } return start - dip; } private: static int RoundUp(int n) { int ret = 1; while (ret <= n) ret *= 2; return ret; } int ValueAt(const int i) const { return i ? v_[n_ + i - 1] : 0; } int n_; vector<int> v_; }; int Gcd(int n, int m) { while (true) { if (!n) return m; m %= n; if (!m) return n; n %= m; } } int main() { int n; scanf("%d", &n); vector<int> money(n); for (int i = 0; i < n; ++i) scanf("%d", &money[i]); int m; scanf("%d", &m); vector<bool> win(m); int total_delta = 0; for (int i = 0; i < m; ++i) { char c; do { scanf("%c", &c); } while (c != 'W' && c != 'P'); win[i] = c == 'W'; total_delta += win[i] ? 1 : -1; } // cerr << "Total delta: " << total_delta << endl; // There are this many cyclic subgames. const int gcd = Gcd(n, m); // cerr << "Subgames: " << gcd << endl; // Cycle length (single subgame). const int cycle = m / gcd; // cerr << "Cycle: " << cycle << endl; // Players per cycle. const int players = n / gcd; // cerr << "Players: " << players << endl; // Player goes this much down the win list every time they reach the machine. const int step = n % m; // cerr << "Step: " << step << endl; long long games = -1; int step_gcd = -1; for (int i = 0; i < gcd; ++i) { // cerr << "Subgame " << i << endl; int current = 0; vector<int> balance; int manual_dip = 0; for (int j = 0, k = i; j < cycle; ++j, k = (k + step) % m) { current += win[k] ? 1 : -1; balance.push_back(current); if (current < manual_dip) manual_dip = current; if (i == 0 && k == gcd) { // cerr << "Seems that " << j << " * " << step << " == " << gcd << " mod " << m << endl; step_gcd = j; } } // cerr << "Step to GCD is " << step_gcd << endl; // cerr << "Manual delta is " << current << endl; // cerr << "Manual dip is " << manual_dip << endl; Tree t(balance); for (int j = 0, k = i; k < n; k += gcd, j = (j + step_gcd) % cycle) { /* { // Sanity check. Is player k starting at jth spot in the cycle? long long ll = j; ll *= step; ll += i; ll %= m; if (k % m != ll) cerr << j << ' ' << k % m << ' ' << ll << endl; } cerr << "Player "<< j << " at " << k << endl; */ long long moves = 0; int balance = money[k]; /* cerr << "Start " << moves << " " << balance << endl; // Slow sanity check. { int balance_sanity = balance; for (int l = j; l < cycle; ++l) { long long ll = l; ll *= step; ll += i; ll %= m; if (l == j) cerr << "First game at " << ll << endl; balance_sanity += win[ll] ? 1 : -1; assert(balance_sanity > 0); } cerr << "Next round should be " << moves + cycle - (j % cycle) << ' ' << balance_sanity << endl; } */ // Do we live to the beginning of a round? if (!t.Dies(j % cycle, cycle, &balance, &moves)) { // cerr << "Next round " << moves << " " << balance << endl; const int delta = t.Delta(0, cycle); // cerr << "Delta " << delta << endl; if (delta < 0) { // Advance time, so that our fate is decided in the next round. const int dip = t.Dip(0, cycle); // cerr << "Dip " << dip << endl; if (balance > dip) { long long rounds = 1 + ((balance - dip - 1) / -delta); moves += rounds * cycle; balance += rounds * delta; } // cerr << "Pre death " << moves << ' ' << balance << endl; } /* // Slow sanity check - comment out once we find the bug. { int balance_sanity = balance; for (int l = 0, ll = i; l < cycle; ++l, ll = (ll + step) % m) { balance_sanity += win[ll] ? 1 : -1; if (balance_sanity == 0) { cerr << "Sanity death at " << l << ' ' << ll << endl; cerr << "Moves should be " << moves + l + 1 << endl; break; } } } */ // Can we play forever? if (!t.Dies(0, cycle, &balance, &moves)) continue; } // cerr << "Death " << moves << " " << balance << endl; // Convert per-player moves to global move counter. --moves; moves *= n; moves += k; ++moves; // cerr << "Converted moves " << moves << endl; // Update the max. if (games == -1 || moves < games) games = moves; } } printf("%lld\n", games); 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 | #include <cassert> #include <cstdio> #include <iostream> #include <vector> using namespace std; class Tree { public: Tree(const vector<int>& v) : n_(RoundUp(v.size())), v_(2 * n_) { for (int i = 0; i < v.size(); ++i) v_[n_ + i] = v[i]; for (int i = n_ - 1; i >= 0; --i) v_[i] = min(v_[2 * i], v_[2 * i + 1]); } bool Absorb( const pair<int, int>& node, int* position, int* balance, long long* moves) const { const int dip = ValueAt(*position) - v_[node.first]; if (dip < *balance) { *balance -= ValueAt(*position); *position += node.second; *moves += node.second; *balance += ValueAt(*position); return true; } if (node.first >= n_) { ++*position; ++*moves; --*balance; return false; } if (!Absorb(make_pair(2 * node.first, node.second / 2), position, balance, moves)) return false; if (!Absorb(make_pair(2 * node.first + 1, node.second / 2), position, balance, moves)) return false; assert(false); } int Delta(const int left, const int right) const { return ValueAt(right) - ValueAt(left); } bool Dies(int left, int right, int* balance, long long* moves) const { // cerr << left << ' ' << right << ' ' << right - left << endl; int position = left; left += n_; right += n_; int step = 1; static vector<pair<int, int> > pre, post; pre.clear(); post.clear(); while (left < right) { // cerr << left << ' ' << right << ' ' << right - left << ' ' << step << ' ' << (right - left) * step << endl; if (left % 2) { pre.push_back(make_pair(left++, step)); // cerr << step << endl; } if (right % 2) { post.push_back(make_pair(--right, step)); // cerr << step << endl; } left /= 2; right /= 2; step *= 2; } for (int i = 0; i < pre.size(); ++i) { // cerr << position << ' ' << pre[i].second << endl; if (!Absorb(pre[i], &position, balance, moves)) return true; // cerr << position << endl; } for (int i = post.size() - 1; i >= 0; --i) { // cerr << position << ' ' << post[i].second << endl; if (!Absorb(post[i], &position, balance, moves)) return true; // cerr << position << endl; } // assert(position == right); return false; } int Dip(int left, int right) const { const int start = ValueAt(left); int dip = start; left += n_; right += n_; while (left < right) { if (left % 2) dip = min(dip, v_[left++]); if (right % 2) dip = min(dip, v_[--right]); left /= 2; right /= 2; } return start - dip; } private: static int RoundUp(int n) { int ret = 1; while (ret <= n) ret *= 2; return ret; } int ValueAt(const int i) const { return i ? v_[n_ + i - 1] : 0; } int n_; vector<int> v_; }; int Gcd(int n, int m) { while (true) { if (!n) return m; m %= n; if (!m) return n; n %= m; } } int main() { int n; scanf("%d", &n); vector<int> money(n); for (int i = 0; i < n; ++i) scanf("%d", &money[i]); int m; scanf("%d", &m); vector<bool> win(m); int total_delta = 0; for (int i = 0; i < m; ++i) { char c; do { scanf("%c", &c); } while (c != 'W' && c != 'P'); win[i] = c == 'W'; total_delta += win[i] ? 1 : -1; } // cerr << "Total delta: " << total_delta << endl; // There are this many cyclic subgames. const int gcd = Gcd(n, m); // cerr << "Subgames: " << gcd << endl; // Cycle length (single subgame). const int cycle = m / gcd; // cerr << "Cycle: " << cycle << endl; // Players per cycle. const int players = n / gcd; // cerr << "Players: " << players << endl; // Player goes this much down the win list every time they reach the machine. const int step = n % m; // cerr << "Step: " << step << endl; long long games = -1; int step_gcd = -1; for (int i = 0; i < gcd; ++i) { // cerr << "Subgame " << i << endl; int current = 0; vector<int> balance; int manual_dip = 0; for (int j = 0, k = i; j < cycle; ++j, k = (k + step) % m) { current += win[k] ? 1 : -1; balance.push_back(current); if (current < manual_dip) manual_dip = current; if (i == 0 && k == gcd) { // cerr << "Seems that " << j << " * " << step << " == " << gcd << " mod " << m << endl; step_gcd = j; } } // cerr << "Step to GCD is " << step_gcd << endl; // cerr << "Manual delta is " << current << endl; // cerr << "Manual dip is " << manual_dip << endl; Tree t(balance); for (int j = 0, k = i; k < n; k += gcd, j = (j + step_gcd) % cycle) { /* { // Sanity check. Is player k starting at jth spot in the cycle? long long ll = j; ll *= step; ll += i; ll %= m; if (k % m != ll) cerr << j << ' ' << k % m << ' ' << ll << endl; } cerr << "Player "<< j << " at " << k << endl; */ long long moves = 0; int balance = money[k]; /* cerr << "Start " << moves << " " << balance << endl; // Slow sanity check. { int balance_sanity = balance; for (int l = j; l < cycle; ++l) { long long ll = l; ll *= step; ll += i; ll %= m; if (l == j) cerr << "First game at " << ll << endl; balance_sanity += win[ll] ? 1 : -1; assert(balance_sanity > 0); } cerr << "Next round should be " << moves + cycle - (j % cycle) << ' ' << balance_sanity << endl; } */ // Do we live to the beginning of a round? if (!t.Dies(j % cycle, cycle, &balance, &moves)) { // cerr << "Next round " << moves << " " << balance << endl; const int delta = t.Delta(0, cycle); // cerr << "Delta " << delta << endl; if (delta < 0) { // Advance time, so that our fate is decided in the next round. const int dip = t.Dip(0, cycle); // cerr << "Dip " << dip << endl; if (balance > dip) { long long rounds = 1 + ((balance - dip - 1) / -delta); moves += rounds * cycle; balance += rounds * delta; } // cerr << "Pre death " << moves << ' ' << balance << endl; } /* // Slow sanity check - comment out once we find the bug. { int balance_sanity = balance; for (int l = 0, ll = i; l < cycle; ++l, ll = (ll + step) % m) { balance_sanity += win[ll] ? 1 : -1; if (balance_sanity == 0) { cerr << "Sanity death at " << l << ' ' << ll << endl; cerr << "Moves should be " << moves + l + 1 << endl; break; } } } */ // Can we play forever? if (!t.Dies(0, cycle, &balance, &moves)) continue; } // cerr << "Death " << moves << " " << balance << endl; // Convert per-player moves to global move counter. --moves; moves *= n; moves += k; ++moves; // cerr << "Converted moves " << moves << endl; // Update the max. if (games == -1 || moves < games) games = moves; } } printf("%lld\n", games); return 0; } |