QOJ.ac
QOJ
| ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
|---|---|---|---|---|---|---|---|---|---|
| #451497 | #8529. Balance of Permutation | HKOI0# | AC ✓ | 5147ms | 31540kb | C++20 | 6.5kb | 2024-06-23 15:14:49 | 2024-06-23 15:14:49 |
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_a + rem_b <= n - len; 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_a + rem_b <= n - len; 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];
}
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 (true) {
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;
}
详细
Test #1:
score: 100
Accepted
time: 2ms
memory: 10032kb
input:
6 6 6
output:
1 2 6 3 4 5
result:
ok 6 numbers
Test #2:
score: 0
Accepted
time: 2368ms
memory: 31176kb
input:
30 300 3030303030303030303030
output:
1 2 3 4 9 23 20 28 24 16 21 17 27 29 8 26 25 30 19 18 22 12 7 13 6 10 5 15 14 11
result:
ok 30 numbers
Test #3:
score: 0
Accepted
time: 1ms
memory: 5832kb
input:
1 0 1
output:
1
result:
ok 1 number(s): "1"
Test #4:
score: 0
Accepted
time: 1ms
memory: 7964kb
input:
2 0 1
output:
1 2
result:
ok 2 number(s): "1 2"
Test #5:
score: 0
Accepted
time: 1ms
memory: 9700kb
input:
2 2 1
output:
2 1
result:
ok 2 number(s): "2 1"
Test #6:
score: 0
Accepted
time: 1ms
memory: 9812kb
input:
5 8 3
output:
1 5 4 2 3
result:
ok 5 number(s): "1 5 4 2 3"
Test #7:
score: 0
Accepted
time: 2ms
memory: 11864kb
input:
7 20 100
output:
3 6 7 4 1 5 2
result:
ok 7 numbers
Test #8:
score: 0
Accepted
time: 2ms
memory: 11968kb
input:
7 2 6
output:
2 1 3 4 5 6 7
result:
ok 7 numbers
Test #9:
score: 0
Accepted
time: 0ms
memory: 10076kb
input:
7 24 1
output:
4 5 6 7 1 2 3
result:
ok 7 numbers
Test #10:
score: 0
Accepted
time: 2ms
memory: 9720kb
input:
7 22 360
output:
7 6 4 3 5 2 1
result:
ok 7 numbers
Test #11:
score: 0
Accepted
time: 2ms
memory: 13792kb
input:
7 20 358
output:
5 7 2 4 6 3 1
result:
ok 7 numbers
Test #12:
score: 0
Accepted
time: 3ms
memory: 14256kb
input:
10 48 10001
output:
7 5 8 9 6 10 3 4 1 2
result:
ok 10 numbers
Test #13:
score: 0
Accepted
time: 4ms
memory: 14208kb
input:
10 42 10101
output:
3 9 6 8 10 5 7 2 1 4
result:
ok 10 numbers
Test #14:
score: 0
Accepted
time: 1136ms
memory: 27340kb
input:
25 300 1
output:
7 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 8 9 10 11 12 13
result:
ok 25 numbers
Test #15:
score: 0
Accepted
time: 1746ms
memory: 26888kb
input:
25 300 283788388040048639877
output:
25 24 23 22 21 20 19 18 17 16 11 12 13 14 15 10 9 8 7 5 6 4 2 1 3
result:
ok 25 numbers
Test #16:
score: 0
Accepted
time: 1860ms
memory: 30892kb
input:
26 302 105773752969551707419545
output:
19 22 25 13 17 18 23 20 10 26 16 6 5 11 14 12 24 4 3 21 1 15 7 8 2 9
result:
ok 26 numbers
Test #17:
score: 0
Accepted
time: 2081ms
memory: 30624kb
input:
27 308 8781128321749037280676555
output:
16 18 17 21 25 6 20 24 22 15 27 5 7 8 2 9 26 13 1 3 14 10 23 19 4 11 12
result:
ok 27 numbers
Test #18:
score: 0
Accepted
time: 2330ms
memory: 30348kb
input:
28 304 806517199954337651602356955
output:
12 17 5 16 23 26 25 15 20 2 19 7 22 24 6 13 11 10 28 8 1 21 18 14 27 3 4 9
result:
ok 28 numbers
Test #19:
score: 0
Accepted
time: 3016ms
memory: 30696kb
input:
29 322 40281026669581503094652149519
output:
16 21 10 25 17 29 9 28 2 8 26 27 22 4 3 5 18 14 19 1 23 20 15 11 13 7 6 12 24
result:
ok 29 numbers
Test #20:
score: 0
Accepted
time: 4240ms
memory: 31540kb
input:
30 400 46479902466857426153849991132
output:
25 19 30 29 9 20 26 21 14 27 28 10 22 11 24 2 7 4 18 17 5 13 12 6 8 1 15 23 16 3
result:
ok 30 numbers
Test #21:
score: 0
Accepted
time: 3799ms
memory: 31472kb
input:
30 450 1140008168482799670544355
output:
26 16 17 18 19 20 21 22 23 24 25 27 28 29 30 1 2 3 5 9 4 8 14 10 6 11 12 15 7 13
result:
ok 30 numbers
Test #22:
score: 0
Accepted
time: 1577ms
memory: 31348kb
input:
30 150 480087379811286955791425915
output:
7 4 8 5 16 3 1 12 13 11 9 10 15 25 18 17 20 30 28 2 6 14 23 21 24 26 27 22 19 29
result:
ok 30 numbers
Test #23:
score: 0
Accepted
time: 1581ms
memory: 31268kb
input:
30 150 480087379811286955791439470
output:
7 4 8 5 16 3 1 12 13 11 9 10 15 25 18 17 20 30 28 2 19 6 22 24 21 23 26 14 29 27
result:
ok 30 numbers
Test #24:
score: 0
Accepted
time: 4248ms
memory: 31272kb
input:
30 440 41509275104334759322587324
output:
22 23 20 24 18 30 19 26 21 28 4 29 17 25 27 16 3 1 2 5 8 13 10 15 7 12 9 14 11 6
result:
ok 30 numbers
Test #25:
score: 0
Accepted
time: 3819ms
memory: 31240kb
input:
30 450 1140008168482800727111311
output:
26 16 17 18 19 20 21 22 23 24 25 27 28 29 30 1 2 5 7 14 4 15 8 11 3 13 10 9 6 12
result:
ok 30 numbers
Test #26:
score: 0
Accepted
time: 4324ms
memory: 31228kb
input:
30 400 52289890275214604423031772929
output:
26 27 29 21 28 16 18 11 2 25 24 23 6 30 20 13 17 10 15 4 9 12 8 22 19 1 5 7 3 14
result:
ok 30 numbers
Test #27:
score: 0
Accepted
time: 317ms
memory: 31380kb
input:
30 0 1
output:
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
result:
ok 30 numbers
Test #28:
score: 0
Accepted
time: 3527ms
memory: 31196kb
input:
30 450 1
output:
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
result:
ok 30 numbers
Test #29:
score: 0
Accepted
time: 5147ms
memory: 31232kb
input:
30 450 1710012252724199424000000
output:
30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
result:
ok 30 numbers
Test #30:
score: 0
Accepted
time: 4769ms
memory: 31244kb
input:
30 450 1692383260428073656742269
output:
30 27 26 28 18 29 21 19 25 17 20 16 24 22 23 7 13 4 6 3 5 12 1 15 14 9 11 8 2 10
result:
ok 30 numbers
Test #31:
score: 0
Accepted
time: 4333ms
memory: 31300kb
input:
30 302 5918364042599361729860937331200
output:
30 29 28 27 26 25 14 8 9 10 11 12 13 7 15 16 17 18 19 20 21 22 23 24 6 5 4 3 2 1
result:
ok 30 numbers
Test #32:
score: 0
Accepted
time: 2653ms
memory: 31228kb
input:
30 254 2256781660157136563723839089600
output:
25 2 3 12 7 16 19 8 22 6 11 17 27 26 10 24 15 21 20 18 28 9 30 23 14 13 5 29 4 1
result:
ok 30 numbers
Test #33:
score: 0
Accepted
time: 4585ms
memory: 31288kb
input:
30 448 3131906441000512625049600
output:
23 20 28 18 26 30 19 29 27 22 17 24 21 25 2 13 16 15 14 12 11 10 9 8 7 6 5 4 3 1
result:
ok 30 numbers
Test #34:
score: 0
Accepted
time: 322ms
memory: 31536kb
input:
30 2 20
output:
1 2 3 4 5 6 7 8 9 11 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
result:
ok 30 numbers
Test #35:
score: 0
Accepted
time: 342ms
memory: 31200kb
input:
30 2 29
output:
2 1 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
result:
ok 30 numbers
Extra Test:
score: 0
Extra Test Passed