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#480217#8529. Balance of Permutationucup-team1766AC ✓1149ms32436kbC++173.4kb2024-07-16 10:31:112024-07-16 10:31:12

Judging History

你现在查看的是最新测评结果

  • [2024-07-16 10:31:12]
  • 评测
  • 测评结果:AC
  • 用时:1149ms
  • 内存:32436kb
  • [2024-07-16 10:31:11]
  • 提交

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