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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#447825#8526. Polygon IIMax_s_xaMAC ✓213ms6208kbC++143.4kb2024-06-18 20:44:452024-06-18 20:44:47

Judging History

你现在查看的是最新测评结果

  • [2024-06-18 20:44:47]
  • 评测
  • 测评结果:AC
  • 用时:213ms
  • 内存:6208kb
  • [2024-06-18 20:44:45]
  • 提交

answer

#include <iostream>
#include <algorithm>

typedef long long ll;
typedef double lf;

// #define DEBUG 1
struct IO
{
    #define MAXSIZE (1 << 20)
    #define isdigit(x) (x >= '0' && x <= '9')
    char buf[MAXSIZE], *p1, *p2;
    char pbuf[MAXSIZE], *pp;
    #if DEBUG
    #else
    IO() : p1(buf), p2(buf), pp(pbuf) {}
    ~IO() {fwrite(pbuf, 1, pp - pbuf, stdout);}
    #endif
    #define gc() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, MAXSIZE, stdin), p1 == p2) ? ' ' : *p1++)
    #define blank(x) (x == ' ' || x == '\n' || x == '\r' || x == '\t')

    template <typename T>
    void Read(T &x)
    {
        #if DEBUG
        std::cin >> x;
        #else
        bool sign = 0; char ch = gc(); x = 0;
        for (; !isdigit(ch); ch = gc())
            if (ch == '-') sign = 1;
        for (; isdigit(ch); ch = gc()) x = x * 10 + (ch ^ 48);
        if (sign) x = -x;
        #endif
    }
    void Read(char *s)
    {
        #if DEBUG
        std::cin >> s;
        #else
        char ch = gc();
        for (; blank(ch); ch = gc());
        for (; !blank(ch); ch = gc()) *s++ = ch;
        *s = 0;
        #endif
    }
    void Read(char &c) {for (c = gc(); blank(c); c = gc());}

    void Push(const char &c)
    {
        #if DEBUG
        putchar(c);
        #else
        if (pp - pbuf == MAXSIZE) fwrite(pbuf, 1, MAXSIZE, stdout), pp = pbuf;
        *pp++ = c;
        #endif
    }
    template <typename T>
    void Write(T x)
    {
        if (x < 0) x = -x, Push('-');
        static T sta[35];
        int top = 0;
        do sta[top++] = x % 10, x /= 10; while (x);
        while (top) Push(sta[--top] ^ 48);
    }
    template <typename T>
    void Write(T x, char lst) {Write(x), Push(lst);}
} IO;
#define Read(x) IO.Read(x)
#define Write(x, y) IO.Write(x, y)
#define Put(x) IO.Push(x)

using namespace std;

const int MAXN = 1010, mod = 1e9 + 7;

ll fac[MAXN], inv[MAXN];
inline ll C(int n, int m) {return n < m ? 0 : fac[n] * inv[m] % mod * inv[n - m] % mod;}
inline ll Qpow(ll x, int y) {ll res = 1; while (y) (y & 1) && (res = res * x % mod), x = x * x % mod, y >>= 1; return res;}

int n, a[MAXN], c[60];
ll g[MAXN], f[60][MAXN << 1];

inline ll Calc(int x) {return Qpow(x, n) * inv[n] % mod;}

int main()
{
    #if DEBUG
    #else
    ios::sync_with_stdio(0), cin.tie(0);
    #endif

    fac[0] = fac[1] = inv[0] = inv[1] = 1;
    for (int i = 2; i < MAXN; i++) fac[i] = fac[i - 1] * i % mod, inv[i] = (mod - mod / i) * inv[mod % i] % mod;
    for (int i = 2; i < MAXN; i++) inv[i] = inv[i - 1] * inv[i] % mod;

    Read(n);
    for (int i = 1; i <= n; i++) Read(a[i]), c[a[i]]++;

    for (int i = 0; i <= n; i++)
        for (int j = 0; j <= i; j++)
            g[i] = (g[i] + (j & 1 ? -1 : 1) * C(n, j) * Calc(i - j)) % mod;
    g[n + 1] = 1;
    for (int i = 0; i <= n; i++) f[0][i] = (g[i + 1] - g[i] + mod) % mod;
    for (int i = 49; i >= 0; i--) c[i] += c[i + 1];
    for (int i = 0; i <= 50; i++)
    {
        for (int j = 0; j <= n; j++)
            if (f[i][j])
            {
                for (int k = 0; k <= c[i + 1]; k++)
                    f[i + 1][j + k >> 1] = (f[i + 1][j + k >> 1] + f[i][j] * C(c[i + 1], k)) % mod;
            }
    }
    ll ans = 0, sum = 0;
    for (int i = 1; i <= n; i++) ans = (ans + f[a[i]][0]) % mod, sum += a[i];
    ans = (1 - ans * Qpow(inv[2], sum) % mod + mod) % mod;
    cout << ans << '\n';
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3812kb

input:

3
0 2 0

output:

166666668

result:

ok 1 number(s): "166666668"

Test #2:

score: 0
Accepted
time: 0ms
memory: 5820kb

input:

3
0 0 0

output:

500000004

result:

ok 1 number(s): "500000004"

Test #3:

score: 0
Accepted
time: 0ms
memory: 5932kb

input:

3
5 6 7

output:

208333335

result:

ok 1 number(s): "208333335"

Test #4:

score: 0
Accepted
time: 1ms
memory: 5876kb

input:

3
0 25 50

output:

889268532

result:

ok 1 number(s): "889268532"

Test #5:

score: 0
Accepted
time: 0ms
memory: 3792kb

input:

10
39 11 25 1 12 44 10 46 27 15

output:

913863330

result:

ok 1 number(s): "913863330"

Test #6:

score: 0
Accepted
time: 1ms
memory: 3972kb

input:

57
43 22 3 16 7 5 24 32 25 16 41 28 24 30 28 10 32 48 41 43 34 37 48 34 3 9 21 41 49 25 2 0 36 45 34 33 45 9 42 29 43 9 38 34 44 33 44 6 46 39 22 36 40 37 19 34 3

output:

400729664

result:

ok 1 number(s): "400729664"

Test #7:

score: 0
Accepted
time: 0ms
memory: 5792kb

input:

100
44 32 6 6 6 44 12 32 6 9 23 12 14 23 12 14 23 49 6 14 32 23 49 9 32 24 23 6 32 6 49 23 12 44 24 9 14 6 24 44 24 23 44 44 49 32 49 12 49 49 24 49 12 23 3 14 6 3 3 6 12 3 49 24 49 24 24 32 23 32 49 14 3 24 49 3 32 14 44 24 49 3 32 23 49 44 44 9 23 14 49 9 3 6 44 24 3 3 12 44

output:

32585394

result:

ok 1 number(s): "32585394"

Test #8:

score: 0
Accepted
time: 30ms
memory: 3932kb

input:

1000
2 27 0 0 27 0 2 0 27 0 27 27 0 0 0 0 0 2 0 27 0 2 2 0 27 27 0 0 0 27 2 2 2 27 0 2 27 2 0 2 27 0 0 27 0 27 0 0 27 2 27 2 2 27 2 27 0 0 27 0 27 0 2 27 2 2 0 27 27 27 27 0 27 0 27 0 2 2 0 2 2 27 0 0 27 0 0 27 0 2 27 27 2 27 2 0 0 2 27 27 27 27 27 27 2 2 0 2 2 0 2 2 0 27 0 27 2 2 0 27 27 0 0 27 2 2...

output:

94588769

result:

ok 1 number(s): "94588769"

Test #9:

score: 0
Accepted
time: 108ms
memory: 6208kb

input:

1000
40 14 47 3 32 18 3 49 22 23 32 18 23 24 18 32 23 39 32 27 49 49 22 50 50 22 23 47 14 47 50 32 22 24 49 49 18 22 18 22 50 3 32 47 40 3 39 22 24 47 32 49 49 22 32 39 14 49 39 3 32 22 24 18 39 49 24 18 40 23 23 49 39 39 18 39 27 49 14 27 27 14 18 24 39 22 40 50 18 18 18 39 39 18 23 23 22 3 49 47 2...

output:

626481946

result:

ok 1 number(s): "626481946"

Test #10:

score: 0
Accepted
time: 80ms
memory: 6052kb

input:

1000
28 32 35 9 21 11 43 23 45 15 23 2 8 3 39 41 31 9 45 35 27 14 40 28 31 9 31 9 9 40 8 6 27 43 3 27 23 49 27 6 28 25 11 9 15 27 38 27 12 28 25 2 15 27 45 6 27 1 21 38 1 25 27 21 49 31 31 14 39 39 8 39 40 28 15 31 21 14 43 38 11 8 8 23 9 11 15 2 11 39 32 14 28 15 40 49 27 9 23 9 9 6 21 2 2 1 14 11 ...

output:

644443122

result:

ok 1 number(s): "644443122"

Test #11:

score: 0
Accepted
time: 84ms
memory: 4040kb

input:

972
39 15 23 0 40 29 43 47 6 9 30 9 2 8 19 9 45 25 26 38 33 18 6 33 44 48 24 8 4 16 33 42 33 31 36 33 13 16 3 12 21 19 1 30 24 23 43 35 0 33 31 32 23 31 36 12 26 0 29 48 28 33 28 28 3 49 9 5 29 8 29 28 49 41 33 49 5 49 6 9 50 25 39 11 1 36 6 44 10 34 32 31 25 31 36 36 3 9 50 35 47 43 25 46 30 18 5 2...

output:

684920840

result:

ok 1 number(s): "684920840"

Test #12:

score: 0
Accepted
time: 3ms
memory: 5836kb

input:

147
34 47 42 23 46 3 41 9 15 42 21 32 24 1 19 46 29 35 38 20 2 43 36 47 19 23 20 9 6 28 48 46 45 21 19 41 31 36 50 7 11 25 0 43 38 46 21 2 26 40 32 14 45 35 47 21 13 26 26 30 3 36 35 45 36 21 21 25 2 40 35 50 23 3 16 44 40 42 6 37 36 19 20 14 30 47 13 49 47 45 26 12 15 21 42 30 19 5 21 9 28 8 3 34 4...

output:

972735235

result:

ok 1 number(s): "972735235"

Test #13:

score: 0
Accepted
time: 86ms
memory: 5844kb

input:

1000
36 15 9 5 35 37 17 30 24 13 18 32 14 35 36 26 23 7 21 15 43 15 21 11 33 33 9 16 5 26 1 45 48 27 20 20 20 48 42 27 22 7 39 35 11 38 33 47 22 34 43 4 32 0 47 35 48 8 9 3 40 3 27 22 20 43 12 37 30 18 2 37 37 35 44 3 42 14 20 24 44 5 17 38 46 41 28 23 21 7 13 15 35 38 21 14 6 37 37 6 13 34 32 13 23...

output:

179933029

result:

ok 1 number(s): "179933029"

Test #14:

score: 0
Accepted
time: 88ms
memory: 4064kb

input:

1000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7...

output:

540327646

result:

ok 1 number(s): "540327646"

Test #15:

score: 0
Accepted
time: 87ms
memory: 6092kb

input:

1000
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 46 46 46 46 46 46 46 46 46 46 46 46 46 4...

output:

169647494

result:

ok 1 number(s): "169647494"

Test #16:

score: 0
Accepted
time: 204ms
memory: 6184kb

input:

1000
11 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 40 50 50 50 50 50 21 50 12 50 50 50 50 50 0 50 50 50 38 50 50 50 50 50 50 25 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 50 50 50 50 50 50 50 50 ...

output:

862643524

result:

ok 1 number(s): "862643524"

Test #17:

score: 0
Accepted
time: 213ms
memory: 4316kb

input:

1000
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 5...

output:

819612372

result:

ok 1 number(s): "819612372"

Test #18:

score: 0
Accepted
time: 205ms
memory: 5896kb

input:

1000
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 5...

output:

18215579

result:

ok 1 number(s): "18215579"

Test #19:

score: 0
Accepted
time: 1ms
memory: 5820kb

input:

16
0 2 24 1 23 9 14 17 28 29 25 27 15 19 11 20

output:

115090079

result:

ok 1 number(s): "115090079"

Test #20:

score: 0
Accepted
time: 14ms
memory: 5764kb

input:

1000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0...

output:

819612372

result:

ok 1 number(s): "819612372"

Test #21:

score: 0
Accepted
time: 1ms
memory: 3912kb

input:

18
9 4 21 5 22 6 9 16 3 14 11 2 0 12 6 3 7 21

output:

0

result:

ok 1 number(s): "0"

Extra Test:

score: 0
Extra Test Passed