#include <bits/stdc++.h>
using namespace std;
const int MOD = 1'000'000'007;
const int INV2 = (MOD + 1) / 2;
const int N = 1'000'000;
vector <int> powInv2(2 * N + 1), fact(4 * N + 1);
void prepare() {
powInv2[0] = 1;
for (int i = 1; i <= 2 * N; i++) {
powInv2[i] = ((long long) INV2 * powInv2[i - 1]) % MOD;
}
fact[0] = 1;
for (int i = 1; i <= 4 * N; i++) {
fact[i] = ((long long) i * fact[i - 1]) % MOD;
}
}
int solveLast(int n, deque <int> &blocks) {
int nBlocks = blocks.size();
int nBlocksHalf = nBlocks / 2;
int ways = 2 * (n - nBlocksHalf);
int cnt1 = blocks.back() / 2;
ways = ((long long) cnt1 * (4 * n - 4 - 2 * nBlocksHalf) + ways) % MOD;
int prevStart = blocks.back() - 1;
if (prevStart % 2 != (nBlocks + 1) % 2) {
prevStart++;
}
int cnt2 = (2 * n - prevStart + 1) / 2 - nBlocksHalf;
ways = ((long long) cnt2 * (8 * n - 4 - 2 * nBlocks) + ways) % MOD;
ways = ((long long) (nBlocks / 2) * (4 * n - 1 - nBlocks) + ways) % MOD;
ways = ((long long) ways * powInv2[2 * n - nBlocks]) % MOD;
ways = ((long long) ways * fact[4 * n - 2 - nBlocks]) % MOD;
return ways;
}
int solveAllZero(int n) {
int ways = ((long long) (2 * n - 1) * powInv2[2 * n - 1]) % MOD;
ways = ((long long) ways * fact[4 * n - 2]) % MOD;
ways = ((long long) ways * n) % MOD;
return ways;
}
void rotateBlocks(int &numEvenBlocks, deque <int> &blocks) {
if (blocks.size() == 1) {
return ;
}
if (blocks.size() % 2) {
if (blocks.back() % 2) {
numEvenBlocks++;
} else {
numEvenBlocks--;
}
blocks.back()++;
} else {
blocks.push_back(1);
}
if (blocks.front() % 2) {
numEvenBlocks++;
} else {
numEvenBlocks--;
}
blocks.front()--;
if (!blocks.front()) {
blocks.pop_front();
numEvenBlocks--;
}
}
int solveOdd(int n, vector <int> &a) {
int aMax = *max_element(a.begin(), a.end());
if (aMax == 0) {
return solveAllZero(n);
} else if (aMax == 2) {
return 0;
}
int currBlock = 1;
deque <int> blocks;
for (int i = 2 * n - 2; i >= 0; i--) {
if (a[i] != a[i + 1]) {
blocks.push_back(currBlock);
currBlock = 0;
}
currBlock++;
}
blocks.push_back(currBlock);
int numEvenBlocks = 0;
for (int block : blocks) if (block % 2 == 0) {
numEvenBlocks++;
}
int ans = 0;
for (int p = 2 * n - 1; p >= 0; p -= 2) {
if (a[p] == 1 && numEvenBlocks == (blocks.back() % 2 == 0)) {
ans += solveLast(n, blocks);
if (ans >= MOD) {
ans -= MOD;
}
}
rotateBlocks(numEvenBlocks, blocks);
rotateBlocks(numEvenBlocks, blocks);
}
return ans;
}
int solve(int n, vector <int> &a) {
int ans = 0;
for (int r = 0; r <= 1; r++) {
for (int &ai : a) {
ai = 2 - ai;
}
ans += solveOdd(n, a);
if (ans >= MOD) {
ans -= MOD;
}
a.push_back(a[0]);
a.erase(a.begin());
}
return ans;
}
int main() {
ios_base::sync_with_stdio(false);
prepare();
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
vector <int> a(2 * n);
for (int &ai : a) {
cin >> ai;
}
cout << solve(n, a) << '\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 | #include <bits/stdc++.h> using namespace std; const int MOD = 1'000'000'007; const int INV2 = (MOD + 1) / 2; const int N = 1'000'000; vector <int> powInv2(2 * N + 1), fact(4 * N + 1); void prepare() { powInv2[0] = 1; for (int i = 1; i <= 2 * N; i++) { powInv2[i] = ((long long) INV2 * powInv2[i - 1]) % MOD; } fact[0] = 1; for (int i = 1; i <= 4 * N; i++) { fact[i] = ((long long) i * fact[i - 1]) % MOD; } } int solveLast(int n, deque <int> &blocks) { int nBlocks = blocks.size(); int nBlocksHalf = nBlocks / 2; int ways = 2 * (n - nBlocksHalf); int cnt1 = blocks.back() / 2; ways = ((long long) cnt1 * (4 * n - 4 - 2 * nBlocksHalf) + ways) % MOD; int prevStart = blocks.back() - 1; if (prevStart % 2 != (nBlocks + 1) % 2) { prevStart++; } int cnt2 = (2 * n - prevStart + 1) / 2 - nBlocksHalf; ways = ((long long) cnt2 * (8 * n - 4 - 2 * nBlocks) + ways) % MOD; ways = ((long long) (nBlocks / 2) * (4 * n - 1 - nBlocks) + ways) % MOD; ways = ((long long) ways * powInv2[2 * n - nBlocks]) % MOD; ways = ((long long) ways * fact[4 * n - 2 - nBlocks]) % MOD; return ways; } int solveAllZero(int n) { int ways = ((long long) (2 * n - 1) * powInv2[2 * n - 1]) % MOD; ways = ((long long) ways * fact[4 * n - 2]) % MOD; ways = ((long long) ways * n) % MOD; return ways; } void rotateBlocks(int &numEvenBlocks, deque <int> &blocks) { if (blocks.size() == 1) { return ; } if (blocks.size() % 2) { if (blocks.back() % 2) { numEvenBlocks++; } else { numEvenBlocks--; } blocks.back()++; } else { blocks.push_back(1); } if (blocks.front() % 2) { numEvenBlocks++; } else { numEvenBlocks--; } blocks.front()--; if (!blocks.front()) { blocks.pop_front(); numEvenBlocks--; } } int solveOdd(int n, vector <int> &a) { int aMax = *max_element(a.begin(), a.end()); if (aMax == 0) { return solveAllZero(n); } else if (aMax == 2) { return 0; } int currBlock = 1; deque <int> blocks; for (int i = 2 * n - 2; i >= 0; i--) { if (a[i] != a[i + 1]) { blocks.push_back(currBlock); currBlock = 0; } currBlock++; } blocks.push_back(currBlock); int numEvenBlocks = 0; for (int block : blocks) if (block % 2 == 0) { numEvenBlocks++; } int ans = 0; for (int p = 2 * n - 1; p >= 0; p -= 2) { if (a[p] == 1 && numEvenBlocks == (blocks.back() % 2 == 0)) { ans += solveLast(n, blocks); if (ans >= MOD) { ans -= MOD; } } rotateBlocks(numEvenBlocks, blocks); rotateBlocks(numEvenBlocks, blocks); } return ans; } int solve(int n, vector <int> &a) { int ans = 0; for (int r = 0; r <= 1; r++) { for (int &ai : a) { ai = 2 - ai; } ans += solveOdd(n, a); if (ans >= MOD) { ans -= MOD; } a.push_back(a[0]); a.erase(a.begin()); } return ans; } int main() { ios_base::sync_with_stdio(false); prepare(); int t; cin >> t; while (t--) { int n; cin >> n; vector <int> a(2 * n); for (int &ai : a) { cin >> ai; } cout << solve(n, a) << '\n'; } return 0; } |
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