QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#284026#7774. 基础寄术练习题zzzYheng100 ✓1497ms36168kbC++172.1kb2023-12-15 20:58:052023-12-15 20:58:06

Judging History

你现在查看的是最新测评结果

  • [2023-12-15 20:58:06]
  • 评测
  • 测评结果:100
  • 用时:1497ms
  • 内存:36168kb
  • [2023-12-15 20:58:05]
  • 提交

answer

#include <bits/stdc++.h>

#define int long long

using namespace std;

const int kMaxN = 105;

int n, m, k, p;

int getPow(int x, int y) {
	int res = 1;
	while (y) {
		if (y & 1) res = res * x % p;
		x = x * x % p;
		y >>= 1;
	}
	return res;
}

void add(int &x, int y) {
	x += y;
	if (x >= p) x -= p;
	if (x < 0) x += p;
}

namespace Task1 {

int inv[kMaxN];

int f[kMaxN][kMaxN];

int ans;

void main() {
	for (int i = 1; i <= m; ++i) {
		inv[i] = getPow(i, p - 2);
	}
	f[0][0] = 1;
	for (int i = 1; i <= n; ++i) {
		for (int j = 1; j <= m; ++j) {
			for (int k = 0; k < j; ++k) {
				add(f[i][j], f[i - 1][k] * inv[j] % p);
			}
		}
	}
	for (int i = 1; i <= m; ++i) add(ans, f[n][i]);
	cout << ans << '\n';
}

}

namespace Task2 {

const int kMaxN = 105;

int a1;

int inv[kMaxN * kMaxN];

int f[2][kMaxN][kMaxN * kMaxN][2];

int ans;

void work() {
	f[0][0][0][0] = 1;
	for (int i = 1; i <= m; ++i) {
		for (int j = 0; j < n; ++j) {
			for (int k = 0; k < n * m; ++k) {
				for (int t = 0; t < 2; ++t) {
					f[i & 1][j][k][t] = 0;
				}
			}
		}
		for (int j = 0; j < n; ++j) {
			for (int k = 0; k <= n * m; ++k) {
				for (int t = 0; t < 2; ++t) {
					// 没有取到 T 中
					add(f[i & 1][j][k][t], f[i - 1 & 1][j][k][t]);

					// 取到 T 中但没取到 S 中
					if (j)
						add(f[i & 1][j][k][t], f[i - 1 & 1][j - 1][k][t] * inv[i] % p);
					// 取到 T 中并且取到 S 中
					if (j && k >= i) 
						add(f[i & 1][j][k][t], -f[i - 1 & 1][j - 1][k - i][t] * inv[i] % p);
					// 取 i 作为 a1
					if (t && k >= i) {
						add(f[i & 1][j][k][t], f[i - 1 & 1][j][k - i][0] * i % p);
					}
				}
			}
		}
	}
	for (int s = 1; s <= n * m; ++s) {
		add(ans, f[m & 1][n - 1][s][1] * inv[s] % p);
	}
}

void main() {
	for (int i = 1; i <= n * m; ++i) inv[i] = getPow(i, p - 2);
	work();
	cout << ans << '\n';
}

}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0), cout.tie(0);
	
	cin >> n >> m >> k >> p;
	if (k == 1) Task1::main();
	else Task2::main();
	
	return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Subtask #1:

score: 10
Accepted

Test #1:

score: 10
Accepted
time: 1ms
memory: 3460kb

input:

9 16 1 327134593

output:

162102742

result:

ok single line: '162102742'

Test #2:

score: 0
Accepted
time: 0ms
memory: 3400kb

input:

11 18 1 834359503

output:

256188485

result:

ok single line: '256188485'

Test #3:

score: 0
Accepted
time: 0ms
memory: 3364kb

input:

18 18 1 614802701

output:

552168146

result:

ok single line: '552168146'

Test #4:

score: 0
Accepted
time: 1ms
memory: 7572kb

input:

7 16 2 861918403

output:

306693876

result:

ok single line: '306693876'

Test #5:

score: 0
Accepted
time: 2ms
memory: 7792kb

input:

11 17 2 617904383

output:

393900291

result:

ok single line: '393900291'

Subtask #2:

score: 25
Accepted

Test #6:

score: 25
Accepted
time: 2ms
memory: 3448kb

input:

60 98 1 715015339

output:

690737273

result:

ok single line: '690737273'

Test #7:

score: 0
Accepted
time: 3ms
memory: 3704kb

input:

96 97 1 507892589

output:

481151247

result:

ok single line: '481151247'

Test #8:

score: 0
Accepted
time: 2ms
memory: 3536kb

input:

90 95 1 621080027

output:

255353202

result:

ok single line: '255353202'

Test #9:

score: 0
Accepted
time: 0ms
memory: 3524kb

input:

85 94 1 297115421

output:

122254364

result:

ok single line: '122254364'

Test #10:

score: 0
Accepted
time: 2ms
memory: 3524kb

input:

81 91 1 460412027

output:

148037986

result:

ok single line: '148037986'

Subtask #3:

score: 15
Accepted

Test #11:

score: 15
Accepted
time: 15ms
memory: 12148kb

input:

29 29 2 545875273

output:

171843225

result:

ok single line: '171843225'

Test #12:

score: 0
Accepted
time: 9ms
memory: 12148kb

input:

29 29 2 342070607

output:

291380196

result:

ok single line: '291380196'

Test #13:

score: 0
Accepted
time: 15ms
memory: 10260kb

input:

30 30 2 293965439

output:

148471965

result:

ok single line: '148471965'

Test #14:

score: 0
Accepted
time: 16ms
memory: 12316kb

input:

30 30 2 528219961

output:

203632962

result:

ok single line: '203632962'

Test #15:

score: 0
Accepted
time: 1ms
memory: 3596kb

input:

30 30 1 202836509

output:

158493990

result:

ok single line: '158493990'

Subtask #4:

score: 10
Accepted

Test #16:

score: 10
Accepted
time: 6ms
memory: 10156kb

input:

27 30 2 360712453

output:

80987914

result:

ok single line: '80987914'

Test #17:

score: 0
Accepted
time: 11ms
memory: 10060kb

input:

26 29 2 377615957

output:

278812897

result:

ok single line: '278812897'

Test #18:

score: 0
Accepted
time: 9ms
memory: 10084kb

input:

22 30 2 163686233

output:

19517828

result:

ok single line: '19517828'

Test #19:

score: 0
Accepted
time: 4ms
memory: 9852kb

input:

20 29 2 785657729

output:

713061509

result:

ok single line: '713061509'

Test #20:

score: 0
Accepted
time: 0ms
memory: 3476kb

input:

24 29 1 374090597

output:

312615700

result:

ok single line: '312615700'

Subtask #5:

score: 15
Accepted

Test #21:

score: 15
Accepted
time: 19ms
memory: 10112kb

input:

29 38 2 909155077

output:

745973305

result:

ok single line: '745973305'

Test #22:

score: 0
Accepted
time: 41ms
memory: 12940kb

input:

40 40 2 1067474879

output:

995503334

result:

ok single line: '995503334'

Test #23:

score: 0
Accepted
time: 26ms
memory: 12368kb

input:

32 37 2 751116719

output:

699924081

result:

ok single line: '699924081'

Test #24:

score: 0
Accepted
time: 28ms
memory: 12456kb

input:

33 37 2 496100951

output:

21741458

result:

ok single line: '21741458'

Test #25:

score: 0
Accepted
time: 1ms
memory: 3484kb

input:

34 38 1 499914887

output:

386116226

result:

ok single line: '386116226'

Subtask #6:

score: 10
Accepted

Test #26:

score: 10
Accepted
time: 247ms
memory: 19464kb

input:

57 66 2 767174999

output:

315351738

result:

ok single line: '315351738'

Test #27:

score: 0
Accepted
time: 234ms
memory: 16840kb

input:

52 69 2 399947623

output:

237685494

result:

ok single line: '237685494'

Test #28:

score: 0
Accepted
time: 278ms
memory: 19980kb

input:

63 64 2 903693961

output:

520250635

result:

ok single line: '520250635'

Test #29:

score: 0
Accepted
time: 354ms
memory: 22636kb

input:

65 70 2 268454909

output:

255864893

result:

ok single line: '255864893'

Test #30:

score: 0
Accepted
time: 1ms
memory: 3504kb

input:

58 68 1 562105223

output:

175445185

result:

ok single line: '175445185'

Subtask #7:

score: 15
Accepted

Test #31:

score: 15
Accepted
time: 1497ms
memory: 36168kb

input:

96 96 2 453296971

output:

222864385

result:

ok single line: '222864385'

Test #32:

score: 0
Accepted
time: 1211ms
memory: 31076kb

input:

85 96 2 859572601

output:

457416092

result:

ok single line: '457416092'

Test #33:

score: 0
Accepted
time: 1243ms
memory: 33936kb

input:

89 94 2 753918677

output:

366789523

result:

ok single line: '366789523'

Test #34:

score: 0
Accepted
time: 1238ms
memory: 34204kb

input:

91 92 2 202806031

output:

64270709

result:

ok single line: '64270709'

Test #35:

score: 0
Accepted
time: 3ms
memory: 3660kb

input:

100 100 1 493945957

output:

109570004

result:

ok single line: '109570004'