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QOJ
| ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
|---|---|---|---|---|---|---|---|---|---|
| #451490 | #8529. Balance of Permutation | HKOI0# | WA | 0ms | 12200kb | C++20 | 11.2kb | 2024-06-23 15:03:15 | 2024-06-23 15:03:18 |
Judging History
answer
#include <bits/stdc++.h>
#define sz(v) (int)v.size()
#define all(v) v.begin(), v.end()
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
// #define int __int128_t
using i128 = __int128;
istream& operator>> (istream& in, __int128_t& x){
string s; in >> s;
x = 0; for (auto c : s) x = x * 10 + c - '0';
return in;
}
ostream& operator<< (ostream& out, __int128_t x){
string s; while (x) s.push_back('0' + x % 10), x /= 10; if (s.empty()) s = "0";
reverse(all(s)); return out << s;
}
template<typename T> void chadd(T& x, T y){ x += y; }
const int B = 450 + 11;
i128 dp[31][31][B * 2];
i128 dp2[31][31][B * 2];
bool ok_a[31], ok_b[31];
i128 countPerm(int n, vector<int>& p, int len, int b){
fill(ok_a + 1, ok_a + 31, true); fill(ok_b, ok_b + 31, true);
fill(ok_a + 1, ok_a + 1 + len, false); for (int i = 0; i < len; i++) ok_b[p[i]] = false;
// for (int i = 1; i <= n; i++) {
// cout << ok_a[i] << ' ';
// }
// cout << endl;
// for (int i = 1; i <= n; i++) {
// cout << ok_b[i] << ' ';
// }
// cout << endl;
for (int r = 0; r <= 0; r++) {
for (int b = 0; b < B * 2; b++) {
dp[r][0][b] = dp[0][r][b] = 0;
}
}
dp[0][0][B] = 1;
int bl = B, br = B;
for (int i = 0; i < n; i++) {
for (int r = 0; r <= i + 1; r++) {
for (int b = 0; b < B * 2; b++) {
dp[r][i + 1][b] = dp[i + 1][r][b] = 0;
}
}
auto copy_and_clear = [&] () {
for (int rem_a = 0; rem_a <= i + 1; rem_a++) {
for (int rem_b = 0; rem_b <= i + 1; rem_b++) {
for (int balance = bl; balance <= br; balance++) {
dp2[rem_a][rem_b][balance] = dp[rem_a][rem_b][balance];
dp[rem_a][rem_b][balance] = 0;
}
}
}
};
auto valid_balance = [&] (int x) {
return 0 <= x && x < B * 2;
};
// top row
if (ok_a[i + 1]) {
copy_and_clear();
for (int rem_a = 0; rem_a <= i; rem_a++) {
for (int rem_b = 0; rem_b <= i; rem_b++) {
for (int balance = bl; balance <= br; balance++) {
i128 old_val = dp2[rem_a][rem_b][balance];
if (!old_val) continue;
// match backwards
if (rem_b && valid_balance(balance + (i + 1))) {
chadd(dp[rem_a][rem_b - 1][balance + (i + 1)], old_val * rem_b);
}
// match forwards
if (valid_balance(balance - (i - 1))) {
chadd(dp[rem_a + 1][rem_b][balance - (i + 1)], old_val);
}
}
}
}
bl -= (i + 1); br += (i + 1);
bl = max(0, bl);
br = min(B * 2 - 1, br);
}
// printf("Half\n");
// for (int r = 0; r <= i + 1; r++) {
// for (int s = 0; s <= i + 1; s++) {
// for (int b = 0; b < B * 2; b++) {
// if (dp[r][s][b]) {
// printf("dp[%lld][%lld][%lld][%lld] = %lld\n", (int64_t) (i + 1), (int64_t) r, (int64_t) s, (int64_t) b, (int64_t) dp[r][s][b]);
// }
// }
// }
// }
// bottom row
if (ok_b[i + 1]) {
copy_and_clear();
for (int rem_a = 0; rem_a <= i; rem_a++) {
for (int rem_b = 0; rem_b <= i; rem_b++) {
for (int balance = bl; balance <= br; balance++) {
i128 old_val = dp2[rem_a][rem_b][balance];
if (!old_val) continue;
// if (old_val) cout << rem_a << ' ' << rem_b << ' ' << balance << endl;
// match backwards
if (rem_a && valid_balance(balance + (i + 1))) {
chadd(dp[rem_a - 1][rem_b][balance + (i + 1)], old_val * rem_a);
}
// match forwards
if (valid_balance(balance - (i - 1))) {
chadd(dp[rem_a][rem_b + 1][balance - (i + 1)], old_val);
}
}
}
}
bl -= (i + 1); br += (i + 1);
bl = max(0, bl);
br = min(B * 2 - 1, br);
}
// printf("End\n");
// for (int r = 0; r <= i + 1; r++) {
// for (int s = 0; s <= i + 1; s++) {
// for (int b = 0; b < B * 2; b++) {
// if (dp[r][s][b]) {
// printf("dp[%lld][%lld][%lld][%lld] = %lld\n", (int64_t) (i + 1), (int64_t) r, (int64_t) s, (int64_t) b, (int64_t) dp[r][s][b]);
// }
// }
// }
// }
}
// for (int i = B - b; i <= B + b; i++) {
// cout << dp[n][0][0][i] << ' ';
// }
// cout << endl;
// cout << "RESULT " << dp[n][0][0][B + b] << endl;
return dp[0][0][B + b];
}
int64_t dp_64[31][31][B * 2];
int64_t dp2_64[31][31][B * 2];
i128 countPerm_64(int n, vector<int>& p, int len, int b){
fill(ok_a + 1, ok_a + 31, true); fill(ok_b, ok_b + 31, true);
fill(ok_a + 1, ok_a + 1 + len, false); for (int i = 0; i < len; i++) ok_b[p[i]] = false;
// for (int i = 1; i <= n; i++) {
// cout << ok_a[i] << ' ';
// }
// cout << endl;
// for (int i = 1; i <= n; i++) {
// cout << ok_b[i] << ' ';
// }
// cout << endl;
for (int r = 0; r <= 0; r++) {
for (int b = 0; b < B * 2; b++) {
dp_64[r][0][b] = dp_64[0][r][b] = 0;
}
}
dp_64[0][0][B] = 1;
int bl = B, br = B;
for (int i = 0; i < n; i++) {
for (int r = 0; r <= i + 1; r++) {
for (int b = bl; b <= br; b++) {
dp_64[r][i + 1][b] = dp_64[i + 1][r][b] = 0;
}
}
auto copy_and_clear = [&] () {
for (int rem_a = 0; rem_a <= i + 1; rem_a++) {
for (int rem_b = 0; rem_b <= i + 1; rem_b++) {
for (int balance = bl; balance <= br; balance++) {
dp2_64[rem_a][rem_b][balance] = dp_64[rem_a][rem_b][balance];
dp_64[rem_a][rem_b][balance] = 0;
}
}
}
};
auto valid_balance = [&] (int x) {
return 0 <= x && x < B * 2;
};
// top row
if (ok_a[i + 1]) {
copy_and_clear();
for (int rem_a = 0; rem_a <= i; rem_a++) {
for (int rem_b = 0; rem_b <= i; rem_b++) {
for (int balance = bl; balance <= br; balance++) {
int64_t old_val = dp2_64[rem_a][rem_b][balance];
if (!old_val) continue;
// match backwards
if (rem_b && valid_balance(balance + (i + 1))) {
chadd(dp_64[rem_a][rem_b - 1][balance + (i + 1)], old_val * rem_b);
}
// match forwards
if (valid_balance(balance - (i - 1))) {
chadd(dp_64[rem_a + 1][rem_b][balance - (i + 1)], old_val);
}
}
}
}
bl -= (i + 1); br += (i + 1);
bl = max(0, bl);
br = min(B * 2 - 1, br);
}
// printf("Half\n");
// for (int r = 0; r <= i + 1; r++) {
// for (int s = 0; s <= i + 1; s++) {
// for (int b = 0; b < B * 2; b++) {
// if (dp_64[r][s][b]) {
// printf("dp_64[%lld][%lld][%lld][%lld] = %lld\n", (int64_t) (i + 1), (int64_t) r, (int64_t) s, (int64_t) b, (int64_t) dp_64[r][s][b]);
// }
// }
// }
// }
// bottom row
if (ok_b[i + 1]) {
copy_and_clear();
for (int rem_a = 0; rem_a <= i; rem_a++) {
for (int rem_b = 0; rem_b <= i; rem_b++) {
for (int balance = bl; balance <= br; balance++) {
int64_t old_val = dp2_64[rem_a][rem_b][balance];
if (!old_val) continue;
// if (old_val) cout << rem_a << ' ' << rem_b << ' ' << balance << endl;
// match backwards
if (rem_a && valid_balance(balance + (i + 1))) {
chadd(dp_64[rem_a - 1][rem_b][balance + (i + 1)], old_val * rem_a);
}
// match forwards
if (valid_balance(balance - (i - 1))) {
chadd(dp_64[rem_a][rem_b + 1][balance - (i + 1)], old_val);
}
}
}
}
bl -= (i + 1); br += (i + 1);
bl = max(0, bl);
br = min(B * 2 - 1, br);
}
// printf("End\n");
// for (int r = 0; r <= i + 1; r++) {
// for (int s = 0; s <= i + 1; s++) {
// for (int b = 0; b < B * 2; b++) {
// if (dp_64[r][s][b]) {
// printf("dp_64[%lld][%lld][%lld][%lld] = %lld\n", (int64_t) (i + 1), (int64_t) r, (int64_t) s, (int64_t) b, (int64_t) dp_64[r][s][b]);
// }
// }
// }
// }
}
// for (int i = B - b; i <= B + b; i++) {
// cout << dp_64[n][0][0][i] << ' ';
// }
// cout << endl;
// cout << "RESULT " << dp_64[n][0][0][B + b] << endl;
return dp_64[0][0][B + b];
}
void solve() {
int n, b;
i128 k;
cin >> n >> b >> k;
vector<int> p(n);
vector<bool> rem(n + 1, true);
for (int i = 0; i < n; i++) {
for (int j = 1; j <= n; j++) {
if (!rem[j]) continue;
// cout << "POSITION " << i << " VALUE " << j << " => K " << k << endl;
p[i] = j;
vector<int> x(p.begin(), p.begin() + i + 1);
vector<int> y;
i128 cp;
if (n - i > 16) {
cp = countPerm(n, p, i + 1, b - ((i + 1) - j < 0 ? j - (i + 1) : (i + 1) - j));
} else {
cp = countPerm_64(n, p, i + 1, b - ((i + 1) - j < 0 ? j - (i + 1) : (i + 1) - j));
}
if (k <= cp) {
rem[j] = false;
b -= ((i + 1) - j < 0 ? j - (i + 1) : (i + 1) - j);
break;
} else {
k -= cp;
}
}
}
for (int i = 0; i < n; i++) {
cout << p[i] << ' ';
}
cout << '\n';
}
signed main() {
#ifndef LOCAL
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
int T = 1;
// cin >> T;
while (T--) solve();
return 0;
}
Details
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Test #1:
score: 0
Wrong Answer
time: 0ms
memory: 12200kb
input:
6 6 6
output:
1 2 3 4 6 6
result:
wrong answer 3rd numbers differ - expected: '6', found: '3'