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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 |
---|---|---|---|---|---|---|---|---|---|
#284026 | #7774. 基础寄术练习题 | zzzYheng | 100 ✓ | 1497ms | 36168kb | C++17 | 2.1kb | 2023-12-15 20:58:05 | 2023-12-15 20:58:06 |
Judging History
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;
}
详细
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'