#include <bits/stdc++.h>
using namespace std;
const int INPUT_SIZE = 4 * 1000010;
long long fact[INPUT_SIZE];
long long MOD_V = 1000000007;
long long MOD(long long x) {
// Assumes x >= 0
return x % MOD_V;
}
long long poww_unsafe(long long x, long long exp) {
// If x == 0, exp < 0 something went VERY wrong
if (exp == 0) {
return 1;
}
long long res = poww_unsafe(x, exp / 2);
res *= res;
res = MOD(res);
if (exp % 2 == 1) {
res *= x;
res = MOD(res);
}
return res;
}
// I should store the inverse of 2 to make this faster
long long inverse(long long x) {
return poww_unsafe(x, MOD_V - 2);
}
long long poww(long long x, long long exp) {
if (exp < 0) {
return poww_unsafe(inverse(x), -exp);
}
else {
return poww_unsafe(x, exp);
}
}
int n;
int wins[INPUT_SIZE];
int next_changepoint[INPUT_SIZE];
int segment_lengths[INPUT_SIZE];
int segment_types[INPUT_SIZE];
bool has0, has1, has2;
long long inv_2;
long long ways_to_place(int players_needing_1, int players_needing_2) {
int index = 2 * players_needing_2 + players_needing_1;
if (index < 0 || index >= INPUT_SIZE) {
// Negative numbers of players cannot be placed
return 0;
}
return MOD(fact[index] * poww(inv_2, (players_needing_2)));
}
bool is_changepoint(int pos) {
return (wins[pos] != wins[(pos + 1) % (2 * n)]);
}
long long count_ways(int swap_count) {
int tower_length = swap_count;
//cerr << "We are counting ways" << endl;
long long result = 0;
int i = 0;
if (has2 && (i % 2 == 0)) {
i++;
}
for (; i < 2 * n; i+=2) {
//cerr << "Considering placing highest number at " << i << "\n";
if (wins[i] != 1) {
// Bad head of tower placement
continue;
}
// We assume this is the place we put the tower head;
bool head_changepoint = is_changepoint(i);
// First, analyse the two types of towers that lead to the top being a changepoint
if (head_changepoint) {
//cerr << "It's a changepoint\n";
int tower_space = ((i - next_changepoint[i] + 2 * n) % (2 * n)) + 1;
// All other tower elements are always changepoints
// First do the P with loopback
// First, assume the loopback is to a tower element
long long ways_to_choose_below = tower_length / 2;
int players_needing_1_more = tower_length - 1;
int players_needing_2_more = 2 * n - players_needing_1_more - 1;
long long ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more);
long long to_add = MOD(ways_to_choose_below * ways_to_place_rest);
//cerr << to_add << " ways to add a tower with P-loopback, reuse\n";
result = MOD(result + to_add);
// Now, assume the loopback is to something else
long long ways_to_choose_loopback = tower_space / 2 - tower_length / 2; //We got back to any element of P in the tower space, but not in the tower
players_needing_1_more = tower_length + 1; // Tower + P
players_needing_2_more = 2 * n - players_needing_1_more;
ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more);
to_add = MOD(ways_to_choose_loopback * ways_to_place_rest);
//cerr << to_add << " ways to add a tower with P-loopback, no-reuse\n";
result = MOD(result + to_add);
// We are done with the first tower type. Now PP towers
// First, assume the last P goes to something repeating
long long ways_to_choose_P1 = n - tower_space / 2; // Any player with NO LOOPBACK; similar to above;
long long ways_to_choose_P2 = tower_length / 2 + 1; // Any player from the tower, or P1 (P1 has no loopback, so not in tower)
players_needing_1_more = tower_length; // +1 from P1, -1 from P2
players_needing_2_more = 2 * n - players_needing_1_more - 1;
ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more);
to_add = MOD(MOD(ways_to_choose_P1 * ways_to_choose_P2) * ways_to_place_rest);
//cerr << to_add << " ways to add a tower with PP-noloop, reuse\n";
result = MOD(result + to_add);
// Now, assume second P is a new player
ways_to_choose_P1 = n - tower_space / 2;//Any player with NO LOOPBACK, as above
ways_to_choose_P2 = n - tower_length / 2 - 1; // We can choose anyone not from tower or P1
players_needing_1_more = tower_length + 2; // Tower, P1, P2
players_needing_2_more = 2 * n - players_needing_1_more;
ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more);
to_add = MOD(MOD(ways_to_choose_P1 * ways_to_choose_P2) * ways_to_place_rest);
//cerr << to_add << " ways to add a tower with PP-noloop, no-reuse\n";
result = MOD(result + to_add);
}
else {
//cerr << "It's not a changepoint\n";
// Here we count the second type of towers -- ones with the dreadful changepoint foundation, where child processes get killed by daemons
// First, the horrific PA tower, with loops for horns
// The P is set to the changepoint, meaning we need not worry for its threat
int P_pos = next_changepoint[i];
int tower_plus_P_space = ((i - P_pos + 2 * n) % (2 * n)) + 1;
// Assume A goes to a tower element
long long ways_to_place_A = tower_length / 2;
int players_needing_1_more = tower_length; // Tower + P1 - A
int players_needing_2_more = 2*n - players_needing_1_more - 1; // A needs 0
long long ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more);
long long to_add = MOD(ways_to_place_A * ways_to_place_rest);
//cerr << to_add << " ways to add a tower with PA-loopback, reuse\n";
result = MOD(result + to_add);
// Now assume A loops back to a new element
ways_to_place_A = (tower_plus_P_space - 1) / 2 - tower_length / 2; //Go to any A-element in the tower+P-space (has odd length) that is not in the tower
players_needing_1_more = tower_length + 2; // Tower + P1 + A
players_needing_2_more = 2 * n - players_needing_1_more;
ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more);
to_add = MOD(ways_to_place_A * ways_to_place_rest);
//cerr << to_add << " ways to add a tower with PA-loopback, no-reuse\n";
result = MOD(result + to_add);
// Now, the terrible PAA tower, which we assume have no loops for horns to prevent double counting
// P is again a changepoint, so it is fixed
// Assume the second A goes to an already appearing element
long long ways_to_place_A1 = (2 * n - tower_plus_P_space + 1) / 2; //Ways to place without loopback -- any element not in the tower+P-space, +1 since this segment is odd with both endp in A
long long ways_to_place_A2 = tower_length / 2 + 1; // Anything from tower or A1
players_needing_1_more = tower_length + 1; // +P1, +A1, -A2
players_needing_2_more = 2 * n - players_needing_1_more - 1;
ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more);
to_add = MOD(MOD(ways_to_place_A1 * ways_to_place_A2) * ways_to_place_rest);
//cerr << "A1: " << ways_to_place_A1 << "\nA2: " << ways_to_place_A2 << "\nRest: " << ways_to_place_rest << "\n";
//cerr << to_add << " ways to add a tower with PAA, reuse\n";
result = MOD(result + to_add);
// Now finally, assume A goes to something new
ways_to_place_A1 = (2 * n - tower_plus_P_space + 1) / 2;//Ways to place without loopback
ways_to_place_A2 = n - (tower_length / 2) - 1; // Anything but tower or A1
players_needing_1_more = tower_length + 3; // P, A1, A2
players_needing_2_more = 2 * n - players_needing_1_more;
ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more);
//cerr << "A1: " << ways_to_place_A1 << "\nA2: " << ways_to_place_A2 << "\nRest: " << ways_to_place_rest << "\n";
to_add = MOD(MOD(ways_to_place_A1 * ways_to_place_A2) * ways_to_place_rest);
//cerr << to_add << " ways to add a tower with PAA, no-reuse\n";
result = MOD(result + to_add);
}
/*
// First count ways when below-tower is repeating a placement
long long ways_to_place_below_head = tower_length / 2;
int players_needing_1_more = tower_length - 1;
int players_needing_2_more = 2 * n - players_needing_1_more - 1;
long long add0 = MOD(MOD(ways_to_place_head * ways_to_place_below_head) * ways_to_place_rest);
result = MOD(result + add0);
// Now count ways when below-tower is a new player
// Invalid if tower_length = 2n, but then we mult by 0
ways_to_place_below_head = (n - tower_length / 2);
players_needing_1_more = tower_length + 1;
players_needing_2_more = 2 * n - players_needing_1_more;
ways_to_place_rest = fact[2 * players_needing_2_more + players_needing_1_more] * poww(2, - players_needing_2_more);
long long add1 = MOD(MOD(ways_to_place_head * ways_to_place_below_head) * ways_to_place_rest);
result = MOD(result + add1);*/
}
return result;
}
int main() {
std::ios_base::sync_with_stdio(false);
cin.tie(nullptr);
fact[0] = 1;
for (int i = 1; i < INPUT_SIZE; i++) {
fact[i] = MOD(i * fact[i - 1]);
}
inv_2 = inverse(2);
int t;
cin >> t;
for (int r = 0; r < t; r++) {
cin >> n;
has0 = false;
has1 = false;
has2 = false;
for (int i = 0; i < 2 * n; i++) {
cin >> wins[i];
has0 |= wins[i] == 0;
has1 |= wins[i] == 1;
has2 |= wins[i] == 2;
}
if (has0 && has2) {
cout << 0 << "\n";
continue;
}
if (has0 xor has1 xor has2) {
if (has0 || has2) {
long long one_player_tops = MOD(n * 1 * ways_to_place(0, 2 * n - 1));
long long two_players_top = MOD(MOD(n * (n-1)) * ways_to_place(2, 2 * n - 2));
cout << MOD(one_player_tops + two_players_top) << "\n";
}
// There is only one kind of number, do some mess
if (has1) {
// Top is APP or PAA; assume PAA and mult by 2
long long ways_to_choose_P = n;
long long ways_to_choose_A1 = n;
//long long ways_to_repeat_A1 = 1;
long long ways_for_new_A2 = (n-1);
long long repeat_A = MOD(MOD(ways_to_choose_P * ways_to_choose_A1) * ways_to_place(1, 2 * n - 2));
long long new_A = MOD(ways_to_choose_P * MOD(ways_to_choose_A1 * MOD(ways_for_new_A2 * ways_to_place(3, 2 * n - 3))));
cout << MOD(2 * (repeat_A + new_A)) << "\n";
}
continue;
}
// We know there are exactly 2 kinds of numbers, we do analysis
int start = 0;
while (!is_changepoint(start)) {
start++;
}
start++;
// Check if changepoints have right parity
if (wins[start] == 1) {
if (wins[(start - 1 + 2 * n) % (2 * n)] == 0) {
// Changepoint made it better for A
// A P should be sitting here
if (start % 2 != 0) {
cout << 0 << "\n";
continue;
}
}
if (wins[(start - 1 + 2 * n) % (2 * n)] == 2) {
// Changepoint made it better for P
// An A should be sitting here
if (start % 2 == 0) {
cout << 0 << "\n";
continue;
}
}
}
if (wins[start] == 2) {
// Changepoint made it better for A
// A P should be sitting here
if (start % 2 != 0) {
cout << 0 << "\n";
continue;
}
}
if (wins[start] == 0) {
// Changepoint made it better for P
// An A should be sitting here
if (start % 2 == 0) {
cout << 0 << "\n";
continue;
}
}
bool all_odd_lengths = true;
int last_number = wins[start];
int length = 1;
int segment_count = 0;
for (int i = 1; i < 2 * n; i++) {
int w;
w = wins[(start + i) % (2 * n)];
if (w == last_number) {
length++;
}
else {
segment_lengths[segment_count] = length;
segment_types[segment_count] = last_number;
segment_count++;
if (length % 2 == 0) {
all_odd_lengths = false;
}
length = 1;
}
last_number = w;
}
segment_lengths[segment_count] = length;
segment_types[segment_count] = last_number;
segment_count++;
if (!all_odd_lengths) {
cout << 0 << "\n";
continue;
}
assert(segment_count % 2 == 0);
// We know that there are a bunch of segments, all with odd lengths. How many diff assignments there are?
start = 1;
while(!is_changepoint(start)) {
start++;
}
int next = start;
start--;
for (int i = 0; i < 2 * n; i++) {
int index = (start - i + 2 * n) % (2 * n);
next_changepoint[index] = next;
if (is_changepoint(index)) {
next = index;
}
}
cout << count_ways(segment_count) << "\n";
}
}
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 | #include <bits/stdc++.h> using namespace std; const int INPUT_SIZE = 4 * 1000010; long long fact[INPUT_SIZE]; long long MOD_V = 1000000007; long long MOD(long long x) { // Assumes x >= 0 return x % MOD_V; } long long poww_unsafe(long long x, long long exp) { // If x == 0, exp < 0 something went VERY wrong if (exp == 0) { return 1; } long long res = poww_unsafe(x, exp / 2); res *= res; res = MOD(res); if (exp % 2 == 1) { res *= x; res = MOD(res); } return res; } // I should store the inverse of 2 to make this faster long long inverse(long long x) { return poww_unsafe(x, MOD_V - 2); } long long poww(long long x, long long exp) { if (exp < 0) { return poww_unsafe(inverse(x), -exp); } else { return poww_unsafe(x, exp); } } int n; int wins[INPUT_SIZE]; int next_changepoint[INPUT_SIZE]; int segment_lengths[INPUT_SIZE]; int segment_types[INPUT_SIZE]; bool has0, has1, has2; long long inv_2; long long ways_to_place(int players_needing_1, int players_needing_2) { int index = 2 * players_needing_2 + players_needing_1; if (index < 0 || index >= INPUT_SIZE) { // Negative numbers of players cannot be placed return 0; } return MOD(fact[index] * poww(inv_2, (players_needing_2))); } bool is_changepoint(int pos) { return (wins[pos] != wins[(pos + 1) % (2 * n)]); } long long count_ways(int swap_count) { int tower_length = swap_count; //cerr << "We are counting ways" << endl; long long result = 0; int i = 0; if (has2 && (i % 2 == 0)) { i++; } for (; i < 2 * n; i+=2) { //cerr << "Considering placing highest number at " << i << "\n"; if (wins[i] != 1) { // Bad head of tower placement continue; } // We assume this is the place we put the tower head; bool head_changepoint = is_changepoint(i); // First, analyse the two types of towers that lead to the top being a changepoint if (head_changepoint) { //cerr << "It's a changepoint\n"; int tower_space = ((i - next_changepoint[i] + 2 * n) % (2 * n)) + 1; // All other tower elements are always changepoints // First do the P with loopback // First, assume the loopback is to a tower element long long ways_to_choose_below = tower_length / 2; int players_needing_1_more = tower_length - 1; int players_needing_2_more = 2 * n - players_needing_1_more - 1; long long ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more); long long to_add = MOD(ways_to_choose_below * ways_to_place_rest); //cerr << to_add << " ways to add a tower with P-loopback, reuse\n"; result = MOD(result + to_add); // Now, assume the loopback is to something else long long ways_to_choose_loopback = tower_space / 2 - tower_length / 2; //We got back to any element of P in the tower space, but not in the tower players_needing_1_more = tower_length + 1; // Tower + P players_needing_2_more = 2 * n - players_needing_1_more; ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more); to_add = MOD(ways_to_choose_loopback * ways_to_place_rest); //cerr << to_add << " ways to add a tower with P-loopback, no-reuse\n"; result = MOD(result + to_add); // We are done with the first tower type. Now PP towers // First, assume the last P goes to something repeating long long ways_to_choose_P1 = n - tower_space / 2; // Any player with NO LOOPBACK; similar to above; long long ways_to_choose_P2 = tower_length / 2 + 1; // Any player from the tower, or P1 (P1 has no loopback, so not in tower) players_needing_1_more = tower_length; // +1 from P1, -1 from P2 players_needing_2_more = 2 * n - players_needing_1_more - 1; ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more); to_add = MOD(MOD(ways_to_choose_P1 * ways_to_choose_P2) * ways_to_place_rest); //cerr << to_add << " ways to add a tower with PP-noloop, reuse\n"; result = MOD(result + to_add); // Now, assume second P is a new player ways_to_choose_P1 = n - tower_space / 2;//Any player with NO LOOPBACK, as above ways_to_choose_P2 = n - tower_length / 2 - 1; // We can choose anyone not from tower or P1 players_needing_1_more = tower_length + 2; // Tower, P1, P2 players_needing_2_more = 2 * n - players_needing_1_more; ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more); to_add = MOD(MOD(ways_to_choose_P1 * ways_to_choose_P2) * ways_to_place_rest); //cerr << to_add << " ways to add a tower with PP-noloop, no-reuse\n"; result = MOD(result + to_add); } else { //cerr << "It's not a changepoint\n"; // Here we count the second type of towers -- ones with the dreadful changepoint foundation, where child processes get killed by daemons // First, the horrific PA tower, with loops for horns // The P is set to the changepoint, meaning we need not worry for its threat int P_pos = next_changepoint[i]; int tower_plus_P_space = ((i - P_pos + 2 * n) % (2 * n)) + 1; // Assume A goes to a tower element long long ways_to_place_A = tower_length / 2; int players_needing_1_more = tower_length; // Tower + P1 - A int players_needing_2_more = 2*n - players_needing_1_more - 1; // A needs 0 long long ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more); long long to_add = MOD(ways_to_place_A * ways_to_place_rest); //cerr << to_add << " ways to add a tower with PA-loopback, reuse\n"; result = MOD(result + to_add); // Now assume A loops back to a new element ways_to_place_A = (tower_plus_P_space - 1) / 2 - tower_length / 2; //Go to any A-element in the tower+P-space (has odd length) that is not in the tower players_needing_1_more = tower_length + 2; // Tower + P1 + A players_needing_2_more = 2 * n - players_needing_1_more; ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more); to_add = MOD(ways_to_place_A * ways_to_place_rest); //cerr << to_add << " ways to add a tower with PA-loopback, no-reuse\n"; result = MOD(result + to_add); // Now, the terrible PAA tower, which we assume have no loops for horns to prevent double counting // P is again a changepoint, so it is fixed // Assume the second A goes to an already appearing element long long ways_to_place_A1 = (2 * n - tower_plus_P_space + 1) / 2; //Ways to place without loopback -- any element not in the tower+P-space, +1 since this segment is odd with both endp in A long long ways_to_place_A2 = tower_length / 2 + 1; // Anything from tower or A1 players_needing_1_more = tower_length + 1; // +P1, +A1, -A2 players_needing_2_more = 2 * n - players_needing_1_more - 1; ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more); to_add = MOD(MOD(ways_to_place_A1 * ways_to_place_A2) * ways_to_place_rest); //cerr << "A1: " << ways_to_place_A1 << "\nA2: " << ways_to_place_A2 << "\nRest: " << ways_to_place_rest << "\n"; //cerr << to_add << " ways to add a tower with PAA, reuse\n"; result = MOD(result + to_add); // Now finally, assume A goes to something new ways_to_place_A1 = (2 * n - tower_plus_P_space + 1) / 2;//Ways to place without loopback ways_to_place_A2 = n - (tower_length / 2) - 1; // Anything but tower or A1 players_needing_1_more = tower_length + 3; // P, A1, A2 players_needing_2_more = 2 * n - players_needing_1_more; ways_to_place_rest = ways_to_place(players_needing_1_more, players_needing_2_more); //cerr << "A1: " << ways_to_place_A1 << "\nA2: " << ways_to_place_A2 << "\nRest: " << ways_to_place_rest << "\n"; to_add = MOD(MOD(ways_to_place_A1 * ways_to_place_A2) * ways_to_place_rest); //cerr << to_add << " ways to add a tower with PAA, no-reuse\n"; result = MOD(result + to_add); } /* // First count ways when below-tower is repeating a placement long long ways_to_place_below_head = tower_length / 2; int players_needing_1_more = tower_length - 1; int players_needing_2_more = 2 * n - players_needing_1_more - 1; long long add0 = MOD(MOD(ways_to_place_head * ways_to_place_below_head) * ways_to_place_rest); result = MOD(result + add0); // Now count ways when below-tower is a new player // Invalid if tower_length = 2n, but then we mult by 0 ways_to_place_below_head = (n - tower_length / 2); players_needing_1_more = tower_length + 1; players_needing_2_more = 2 * n - players_needing_1_more; ways_to_place_rest = fact[2 * players_needing_2_more + players_needing_1_more] * poww(2, - players_needing_2_more); long long add1 = MOD(MOD(ways_to_place_head * ways_to_place_below_head) * ways_to_place_rest); result = MOD(result + add1);*/ } return result; } int main() { std::ios_base::sync_with_stdio(false); cin.tie(nullptr); fact[0] = 1; for (int i = 1; i < INPUT_SIZE; i++) { fact[i] = MOD(i * fact[i - 1]); } inv_2 = inverse(2); int t; cin >> t; for (int r = 0; r < t; r++) { cin >> n; has0 = false; has1 = false; has2 = false; for (int i = 0; i < 2 * n; i++) { cin >> wins[i]; has0 |= wins[i] == 0; has1 |= wins[i] == 1; has2 |= wins[i] == 2; } if (has0 && has2) { cout << 0 << "\n"; continue; } if (has0 xor has1 xor has2) { if (has0 || has2) { long long one_player_tops = MOD(n * 1 * ways_to_place(0, 2 * n - 1)); long long two_players_top = MOD(MOD(n * (n-1)) * ways_to_place(2, 2 * n - 2)); cout << MOD(one_player_tops + two_players_top) << "\n"; } // There is only one kind of number, do some mess if (has1) { // Top is APP or PAA; assume PAA and mult by 2 long long ways_to_choose_P = n; long long ways_to_choose_A1 = n; //long long ways_to_repeat_A1 = 1; long long ways_for_new_A2 = (n-1); long long repeat_A = MOD(MOD(ways_to_choose_P * ways_to_choose_A1) * ways_to_place(1, 2 * n - 2)); long long new_A = MOD(ways_to_choose_P * MOD(ways_to_choose_A1 * MOD(ways_for_new_A2 * ways_to_place(3, 2 * n - 3)))); cout << MOD(2 * (repeat_A + new_A)) << "\n"; } continue; } // We know there are exactly 2 kinds of numbers, we do analysis int start = 0; while (!is_changepoint(start)) { start++; } start++; // Check if changepoints have right parity if (wins[start] == 1) { if (wins[(start - 1 + 2 * n) % (2 * n)] == 0) { // Changepoint made it better for A // A P should be sitting here if (start % 2 != 0) { cout << 0 << "\n"; continue; } } if (wins[(start - 1 + 2 * n) % (2 * n)] == 2) { // Changepoint made it better for P // An A should be sitting here if (start % 2 == 0) { cout << 0 << "\n"; continue; } } } if (wins[start] == 2) { // Changepoint made it better for A // A P should be sitting here if (start % 2 != 0) { cout << 0 << "\n"; continue; } } if (wins[start] == 0) { // Changepoint made it better for P // An A should be sitting here if (start % 2 == 0) { cout << 0 << "\n"; continue; } } bool all_odd_lengths = true; int last_number = wins[start]; int length = 1; int segment_count = 0; for (int i = 1; i < 2 * n; i++) { int w; w = wins[(start + i) % (2 * n)]; if (w == last_number) { length++; } else { segment_lengths[segment_count] = length; segment_types[segment_count] = last_number; segment_count++; if (length % 2 == 0) { all_odd_lengths = false; } length = 1; } last_number = w; } segment_lengths[segment_count] = length; segment_types[segment_count] = last_number; segment_count++; if (!all_odd_lengths) { cout << 0 << "\n"; continue; } assert(segment_count % 2 == 0); // We know that there are a bunch of segments, all with odd lengths. How many diff assignments there are? start = 1; while(!is_changepoint(start)) { start++; } int next = start; start--; for (int i = 0; i < 2 * n; i++) { int index = (start - i + 2 * n) % (2 * n); next_changepoint[index] = next; if (is_changepoint(index)) { next = index; } } cout << count_ways(segment_count) << "\n"; } } |
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