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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 |
---|---|---|---|---|---|---|---|---|---|
#480217 | #8529. Balance of Permutation | ucup-team1766 | AC ✓ | 1149ms | 32436kb | C++17 | 3.4kb | 2024-07-16 10:31:11 | 2024-07-16 10:31:12 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 31;
// dp[i][j][k] = # partial permutations of 1...i with j unpaired elements in 1...i
// and sum of right indices k.
__uint128_t dp[2 * MAXN][MAXN][MAXN * MAXN];
__uint128_t string_to_uint128(string x) {
__uint128_t res = 0;
for (int i = 0; i < x.size(); i++) {
res *= 10;
res += (x[i] - '0');
}
return res;
}
// Ways to finish the partial permutation described by filled with balance b.
__uint128_t cnt_ways_finish(int n, int b, vector<int> filled) {
vector<int> paired(2 * n);
for (int i = 0; i < filled.size(); i++) {
paired[i * 2] = 1;
paired[filled[i] * 2 + 1] = 2;
if (filled[i] < i) {
paired[i * 2] = 2;
paired[filled[i] * 2 + 1] = 1;
}
}
for (int i = 0; i <= 2 * n; i++) {
for (int j = 0; j <= n; j++) {
for (int k = 0; k < n * n; k++) {
dp[i][j][k] = 0;
}
}
}
dp[0][0][0] = 1;
int cnt_ind = 0;
int cnt_val = 0;
for (int i = 0; i < 2 * n; i++) {
for (int j = 0; j <= n; j++) {
for (int k = 0; k < n * n; k++) {
if (dp[i][j][k] == 0) {
continue;
}
if (!paired[i]) {
if (j > 0) {
// ind_ops + val_ops = j
// ind_ops + cnt_ind = val_ops + cnt_val + (i % 2)
// ind_ops + cnt_ind = j - ind_ops + cnt_val + (i % 2)
int ind_ops = (j + cnt_val - cnt_ind + (i % 2)) / 2;
int val_ops = j - ind_ops;
if (i % 2 == 0) {
// considering an index
dp[i + 1][j - 1][k + i / 2] += dp[i][j][k] * val_ops;
} else {
// condidering a value
dp[i + 1][j - 1][k + i / 2] += dp[i][j][k] * ind_ops;
}
}
if (j < n) {
dp[i + 1][j + 1][k] += dp[i][j][k];
}
} else if (paired[i] == 1) {
dp[i + 1][j][k] += dp[i][j][k];
} else {
dp[i + 1][j][k + i / 2] += dp[i][j][k];
}
}
}
if (paired[i] && i % 2 == 0) {
cnt_ind++;
} else if (paired[i]) {
cnt_val++;
}
}
for (int i = 0; i < n * n; i++) {
int balance = i - (n * (n - 1) - i);
if (balance == b) {
return dp[2 * n][0][i];
}
}
assert(0);
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int n, b;
string strk;
cin >> n >> b >> strk;
__uint128_t k = string_to_uint128(strk);
vector<int> p;
vector<bool> left(n, 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (left[j]) {
p.push_back(j);
__uint128_t cnt = cnt_ways_finish(n, b, p);
if (cnt >= k) {
left[j] = 0;
break;
}
k -= cnt;
p.pop_back();
}
}
}
for (int pi : p) {
cout << pi + 1 << " ";
}
cout << "\n";
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 9792kb
input:
6 6 6
output:
1 2 6 3 4 5
result:
ok 6 numbers
Test #2:
score: 0
Accepted
time: 609ms
memory: 31884kb
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: 0ms
memory: 3496kb
input:
1 0 1
output:
1
result:
ok 1 number(s): "1"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3892kb
input:
2 0 1
output:
1 2
result:
ok 2 number(s): "1 2"
Test #5:
score: 0
Accepted
time: 1ms
memory: 5620kb
input:
2 2 1
output:
2 1
result:
ok 2 number(s): "2 1"
Test #6:
score: 0
Accepted
time: 1ms
memory: 7752kb
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: 1ms
memory: 10112kb
input:
7 20 100
output:
3 6 7 4 1 5 2
result:
ok 7 numbers
Test #8:
score: 0
Accepted
time: 1ms
memory: 11908kb
input:
7 2 6
output:
2 1 3 4 5 6 7
result:
ok 7 numbers
Test #9:
score: 0
Accepted
time: 1ms
memory: 9864kb
input:
7 24 1
output:
4 5 6 7 1 2 3
result:
ok 7 numbers
Test #10:
score: 0
Accepted
time: 1ms
memory: 9872kb
input:
7 22 360
output:
7 6 4 3 5 2 1
result:
ok 7 numbers
Test #11:
score: 0
Accepted
time: 2ms
memory: 11780kb
input:
7 20 358
output:
5 7 2 4 6 3 1
result:
ok 7 numbers
Test #12:
score: 0
Accepted
time: 0ms
memory: 13908kb
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: 2ms
memory: 13888kb
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: 219ms
memory: 27356kb
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: 403ms
memory: 28832kb
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: 370ms
memory: 29272kb
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: 398ms
memory: 30748kb
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: 470ms
memory: 31016kb
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: 580ms
memory: 31464kb
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: 820ms
memory: 32232kb
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: 722ms
memory: 32436kb
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: 334ms
memory: 31940kb
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: 333ms
memory: 32004kb
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: 818ms
memory: 32020kb
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: 748ms
memory: 32000kb
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: 855ms
memory: 32016kb
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: 72ms
memory: 32004kb
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: 637ms
memory: 31940kb
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: 1149ms
memory: 32204kb
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: 947ms
memory: 31956kb
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: 806ms
memory: 31984kb
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: 566ms
memory: 32012kb
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: 1005ms
memory: 31884kb
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: 92ms
memory: 31984kb
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: 77ms
memory: 32020kb
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