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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
#32665#2573. Two PermutationsYaoBIG#AC ✓51ms10708kbC++201.8kb2022-05-22 22:13:242022-05-22 22:13:25

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2022-05-22 22:13:25]
  • 评测
  • 测评结果:AC
  • 用时:51ms
  • 内存:10708kb
  • [2022-05-22 22:13:24]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int MOD = (int)1e9 + 7;

void mInc(int& a, int b) {
	a += b;
	if (a >= MOD) a -= MOD;
}

const int N = 100;
const int K = N * N;
int dp[2][N][K + 1];

// DP[n][m][s]: Ways to have a permutation of length n, where we ignore m positions, and have sum s
int solve(int max_n, int tar_k) {
	dp[0][0][0] = 1;
	for (int n = 0; n < max_n; ++n) {
		int c = n & 1;
		int t = c ^ 1;
		for (int m = 0; m <= n; ++m) {
			for (int s = 0; s <= n*n; ++s) {
				ll v0 = dp[c][m][s];
				if (v0 == 0) continue;
				
				// cerr << n << ' ' << m << ' ' << s << ": " << v0 << '\n';
				ll v1 = v0 * m % MOD;
				int add = n + 1;

				mInc(dp[t][m + 1][s], v0);			// n at last position, ignore last position
				mInc(dp[t][m][s + add], v0);			// n at last position, DO NOT ignore last position
				mInc(dp[t][m][s + add], v1);			// n NOT at last position, ignore last position, n hits a non-ignoring position
				if (m > 0) mInc(dp[t][m - 1][s + 2*add], v1);	// n NOT at last position, DO NOT ignore last position, n hits a non-ignoring position
				mInc(dp[t][m + 1][s], v1);			// n NOT at last position, ignore last position, n hits a ignoring position
				mInc(dp[t][m][s + add], v1);			// n NOT at last position, DO NOT ignore last position, n hits a ignoring position
			
				dp[c][m][s] = 0;
			}
		}
	}
	/*
	for (int m = 0; m <= max_n; ++m) {
		for (int s = 0; s <= max_n*max_n; ++s) {
			ll v0 = dp[max_n & 1][m][s];
			if (v0 == 0) continue;
			cerr << max_n << ' ' << m << ' ' << s - K << ": " << v0 << '\n';
		}
	}
	*/

	return dp[max_n & 1][0][tar_k];
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);

	int n, k;
	cin >> n >> k;
	
	ll res = solve(n, k);
	for (int i = 1; i <= n; ++i) res = (res * i) % MOD;
	cout << res << '\n';
}

详细

Test #1:

score: 100
Accepted
time: 4ms
memory: 5672kb

input:

2 4

output:

2

result:

ok 1 number(s): "2"

Test #2:

score: 0
Accepted
time: 1ms
memory: 5604kb

input:

3 7

output:

12

result:

ok 1 number(s): "12"

Test #3:

score: 0
Accepted
time: 0ms
memory: 7664kb

input:

4 10

output:

24

result:

ok 1 number(s): "24"

Test #4:

score: 0
Accepted
time: 3ms
memory: 5616kb

input:

4 14

output:

96

result:

ok 1 number(s): "96"

Test #5:

score: 0
Accepted
time: 1ms
memory: 5608kb

input:

5 10

output:

0

result:

ok 1 number(s): "0"

Test #6:

score: 0
Accepted
time: 3ms
memory: 5676kb

input:

5 15

output:

120

result:

ok 1 number(s): "120"

Test #7:

score: 0
Accepted
time: 3ms
memory: 5600kb

input:

5 21

output:

2400

result:

ok 1 number(s): "2400"

Test #8:

score: 0
Accepted
time: 1ms
memory: 5632kb

input:

6 21

output:

720

result:

ok 1 number(s): "720"

Test #9:

score: 0
Accepted
time: 2ms
memory: 5620kb

input:

6 30

output:

25920

result:

ok 1 number(s): "25920"

Test #10:

score: 0
Accepted
time: 2ms
memory: 5512kb

input:

6 27

output:

106560

result:

ok 1 number(s): "106560"

Test #11:

score: 0
Accepted
time: 0ms
memory: 7728kb

input:

20 300

output:

644873710

result:

ok 1 number(s): "644873710"

Test #12:

score: 0
Accepted
time: 3ms
memory: 5708kb

input:

20 139

output:

0

result:

ok 1 number(s): "0"

Test #13:

score: 0
Accepted
time: 3ms
memory: 5772kb

input:

30 470

output:

491424690

result:

ok 1 number(s): "491424690"

Test #14:

score: 0
Accepted
time: 1ms
memory: 5832kb

input:

30 500

output:

8436035

result:

ok 1 number(s): "8436035"

Test #15:

score: 0
Accepted
time: 1ms
memory: 7928kb

input:

40 1000

output:

617159088

result:

ok 1 number(s): "617159088"

Test #16:

score: 0
Accepted
time: 5ms
memory: 9720kb

input:

40 900

output:

729805907

result:

ok 1 number(s): "729805907"

Test #17:

score: 0
Accepted
time: 7ms
memory: 10152kb

input:

60 1830

output:

16340084

result:

ok 1 number(s): "16340084"

Test #18:

score: 0
Accepted
time: 11ms
memory: 9964kb

input:

60 2000

output:

832198921

result:

ok 1 number(s): "832198921"

Test #19:

score: 0
Accepted
time: 51ms
memory: 10328kb

input:

100 5050

output:

437918130

result:

ok 1 number(s): "437918130"

Test #20:

score: 0
Accepted
time: 50ms
memory: 10708kb

input:

100 700

output:

0

result:

ok 1 number(s): "0"

Test #21:

score: 0
Accepted
time: 51ms
memory: 10412kb

input:

100 10000

output:

0

result:

ok 1 number(s): "0"