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#283621#7774. 基础寄术练习题December45685 806ms4268kbC++141.9kb2023-12-14 22:26:022023-12-14 22:26:02

Judging History

你现在查看的是最新测评结果

  • [2023-12-14 22:26:02]
  • 评测
  • 测评结果:85
  • 用时:806ms
  • 内存:4268kb
  • [2023-12-14 22:26:02]
  • 提交

answer

#include <cstdio>

constexpr int maxn = 100 + 5;

int n, m, p;

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

int quick_power(int x, int k) {
    int ret = 1;
    for (;;) {
        if (k & 1) {
            ret = (long long) ret * x % p;
        }
        if (!(k >>= 1)) {
            break;
        }
        x = (long long) x * x % p;
    }
    return ret;
}

int inverse(int x) {
    return quick_power(x, p - 2);
}

namespace Case1 {
    int f[maxn];

    void solve() {
        f[0] = 1;
        for (int i = 1; i <= m; i ++) {
            long long inv = inverse(i);
            for (int j = n; j; j --) {
                add(f[j], f[j - 1] * inv % p);
            }
        }
        printf("%d\n", f[n]);
    }
}

namespace Case2 {
    int f[maxn * maxn][maxn];

    void solve() {
        int ans = 0;

        for (int a1 = 1; a1 <= m; a1 ++) {
            for (int i = 0; i <= m * (m + 1) / 2; i ++) {
                for (int j = 0; j < n; j ++) {
                    f[i][j] = 0;
                }
            }
            f[0][0] = 1;

            for (int i = 1; i <= m; i ++) {
                if (a1 == i) {
                    continue;
                }

                long long inv = inverse(i);
                for (int j = i * (i + 1) / 2; j >= 0; j --) {
                    for (int k = n; k; k --) {
                        add(f[j][k], (f[j][k - 1] - (i > j ? 0 :
                            f[j - i][k - 1]) + p) * inv % p);
                    }
                }
            }

            for (int i = 0; i <= m * (m + 1) / 2; i ++) {
                add(ans, (long long) a1 * inverse(i + a1) % p * f[i][n - 1] % p);
            }
        }

        printf("%d\n", ans);
    }
}

int main() {
    int k;
    scanf("%d%d%d%d", &n, &m, &k, &p);

    if (k == 1) {
        Case1::solve();
    } else {
        Case2::solve();
    }

    return 0;
}

详细

Subtask #1:

score: 10
Accepted

Test #1:

score: 10
Accepted
time: 0ms
memory: 1616kb

input:

9 16 1 327134593

output:

162102742

result:

ok single line: '162102742'

Test #2:

score: 0
Accepted
time: 0ms
memory: 1492kb

input:

11 18 1 834359503

output:

256188485

result:

ok single line: '256188485'

Test #3:

score: 0
Accepted
time: 0ms
memory: 1580kb

input:

18 18 1 614802701

output:

552168146

result:

ok single line: '552168146'

Test #4:

score: 0
Accepted
time: 1ms
memory: 1636kb

input:

7 16 2 861918403

output:

306693876

result:

ok single line: '306693876'

Test #5:

score: 0
Accepted
time: 1ms
memory: 1624kb

input:

11 17 2 617904383

output:

393900291

result:

ok single line: '393900291'

Subtask #2:

score: 25
Accepted

Test #6:

score: 25
Accepted
time: 0ms
memory: 1636kb

input:

60 98 1 715015339

output:

690737273

result:

ok single line: '690737273'

Test #7:

score: 0
Accepted
time: 0ms
memory: 1612kb

input:

96 97 1 507892589

output:

481151247

result:

ok single line: '481151247'

Test #8:

score: 0
Accepted
time: 0ms
memory: 1612kb

input:

90 95 1 621080027

output:

255353202

result:

ok single line: '255353202'

Test #9:

score: 0
Accepted
time: 0ms
memory: 1588kb

input:

85 94 1 297115421

output:

122254364

result:

ok single line: '122254364'

Test #10:

score: 0
Accepted
time: 0ms
memory: 1488kb

input:

81 91 1 460412027

output:

148037986

result:

ok single line: '148037986'

Subtask #3:

score: 15
Accepted

Test #11:

score: 15
Accepted
time: 13ms
memory: 1812kb

input:

29 29 2 545875273

output:

171843225

result:

ok single line: '171843225'

Test #12:

score: 0
Accepted
time: 13ms
memory: 1720kb

input:

29 29 2 342070607

output:

291380196

result:

ok single line: '291380196'

Test #13:

score: 0
Accepted
time: 16ms
memory: 1764kb

input:

30 30 2 293965439

output:

148471965

result:

ok single line: '148471965'

Test #14:

score: 0
Accepted
time: 16ms
memory: 1804kb

input:

30 30 2 528219961

output:

203632962

result:

ok single line: '203632962'

Test #15:

score: 0
Accepted
time: 0ms
memory: 1608kb

input:

30 30 1 202836509

output:

158493990

result:

ok single line: '158493990'

Subtask #4:

score: 10
Accepted

Test #16:

score: 10
Accepted
time: 14ms
memory: 1780kb

input:

27 30 2 360712453

output:

80987914

result:

ok single line: '80987914'

Test #17:

score: 0
Accepted
time: 12ms
memory: 1808kb

input:

26 29 2 377615957

output:

278812897

result:

ok single line: '278812897'

Test #18:

score: 0
Accepted
time: 12ms
memory: 1792kb

input:

22 30 2 163686233

output:

19517828

result:

ok single line: '19517828'

Test #19:

score: 0
Accepted
time: 10ms
memory: 1768kb

input:

20 29 2 785657729

output:

713061509

result:

ok single line: '713061509'

Test #20:

score: 0
Accepted
time: 0ms
memory: 1640kb

input:

24 29 1 374090597

output:

312615700

result:

ok single line: '312615700'

Subtask #5:

score: 15
Accepted

Test #21:

score: 15
Accepted
time: 37ms
memory: 1852kb

input:

29 38 2 909155077

output:

745973305

result:

ok single line: '745973305'

Test #22:

score: 0
Accepted
time: 60ms
memory: 1952kb

input:

40 40 2 1067474879

output:

995503334

result:

ok single line: '995503334'

Test #23:

score: 0
Accepted
time: 33ms
memory: 3800kb

input:

32 37 2 751116719

output:

699924081

result:

ok single line: '699924081'

Test #24:

score: 0
Accepted
time: 34ms
memory: 1924kb

input:

33 37 2 496100951

output:

21741458

result:

ok single line: '21741458'

Test #25:

score: 0
Accepted
time: 0ms
memory: 1616kb

input:

34 38 1 499914887

output:

386116226

result:

ok single line: '386116226'

Subtask #6:

score: 10
Accepted

Test #26:

score: 10
Accepted
time: 565ms
memory: 4268kb

input:

57 66 2 767174999

output:

315351738

result:

ok single line: '315351738'

Test #27:

score: 0
Accepted
time: 621ms
memory: 2532kb

input:

52 69 2 399947623

output:

237685494

result:

ok single line: '237685494'

Test #28:

score: 0
Accepted
time: 555ms
memory: 2460kb

input:

63 64 2 903693961

output:

520250635

result:

ok single line: '520250635'

Test #29:

score: 0
Accepted
time: 806ms
memory: 2628kb

input:

65 70 2 268454909

output:

255864893

result:

ok single line: '255864893'

Test #30:

score: 0
Accepted
time: 0ms
memory: 1612kb

input:

58 68 1 562105223

output:

175445185

result:

ok single line: '175445185'

Subtask #7:

score: 0
Time Limit Exceeded

Test #31:

score: 0
Time Limit Exceeded

input:

96 96 2 453296971

output:


result: