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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#448593#8526. Polygon IIGeZhiyuanAC ✓230ms11288kbC++141.6kb2024-06-19 20:00:132024-06-19 20:00:13

Judging History

你现在查看的是最新测评结果

  • [2024-06-19 20:00:13]
  • 评测
  • 测评结果:AC
  • 用时:230ms
  • 内存:11288kb
  • [2024-06-19 20:00:13]
  • 提交

answer

#include<bits/stdc++.h>

using namespace std;
typedef long long ll;

const ll N = 1000 + 5, M = 50 + 5, Mod = 1e9 + 7;

inline ll power(ll x, ll y){
	ll ret = 1;
	while(y){
		if(y & 1) ret = ret * x % Mod;
		x = x * x % Mod, y >>= 1;
	}
	return ret;
}

inline ll inv(ll x){
	return power(x, Mod - 2);
}

ll n = 0, m = 0, c[M] = {}, binom[N][N] = {}, h[N] = {}, f[M] = {}, g[M][N] = {}, ans = 0;

inline ll calc(ll k){
	ll r = 0;
	for(ll i = 0 ; i <= n ; i ++) if(i <= k){
		ll z = binom[n][i] * power(k - i, n) % Mod;
		if(i & 1) r = (r + Mod - z) % Mod; else r = (r + z) % Mod;
	}
	for(ll i = 1 ; i <= n ; i ++) r = r * inv(i) % Mod;
	return r;
}

int main(){
	scanf("%lld", &n);
	for(ll i = 1, x = 0 ; i <= n ; i ++){
		scanf("%lld", &x), x ++;
		c[x] ++, m = max(m, x);
	}
	for(ll i = 0 ; i <= n ; i ++){
		binom[i][0] = 1;
		for(ll j = 1 ; j <= i ; j ++) binom[i][j] = (binom[i - 1][j - 1] + binom[i - 1][j]) % Mod;
	}
	
	h[0] = 1;
	for(ll i = 1 ; i <= n ; i ++) h[i] = h[i - 1] * inv(2) % Mod;
	f[m] = 1;
	for(ll x = m, k = 0 ; x >= 1 ; x --){
		f[x - 1] = (f[x - 1] + f[x] * h[k]) % Mod, g[x - 1][1] = (g[x - 1][1] + f[x - 1] * c[x]) % Mod;
		for(ll i = 1 ; i <= n ; i ++) for(ll j = 0 ; j <= k ; j ++) if(j < 2 * i){
			ll w = binom[k][j] * h[k] % Mod;
			if(2 * i - j <= n) g[x - 1][2 * i - j] = (g[x - 1][2 * i - j] + g[x][i] * w) % Mod;
			else ans = (ans + g[x][i] * w) % Mod;
		}
		k += c[x];
	}
	for(ll i = 1 ; i <= n ; i ++) ans = (ans + g[0][i] * calc(i)) % Mod;
	ans = (Mod + 1 - ans) % Mod;
	printf("%lld", ans);
	return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 3904kb

input:

3
0 2 0

output:

166666668

result:

ok 1 number(s): "166666668"

Test #2:

score: 0
Accepted
time: 1ms
memory: 3900kb

input:

3
0 0 0

output:

500000004

result:

ok 1 number(s): "500000004"

Test #3:

score: 0
Accepted
time: 0ms
memory: 4012kb

input:

3
5 6 7

output:

208333335

result:

ok 1 number(s): "208333335"

Test #4:

score: 0
Accepted
time: 1ms
memory: 3920kb

input:

3
0 25 50

output:

889268532

result:

ok 1 number(s): "889268532"

Test #5:

score: 0
Accepted
time: 1ms
memory: 4136kb

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: 4276kb

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: 3ms
memory: 4456kb

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: 143ms
memory: 10960kb

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: 195ms
memory: 11284kb

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: 177ms
memory: 11204kb

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: 176ms
memory: 11000kb

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: 5ms
memory: 4840kb

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: 180ms
memory: 11200kb

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: 185ms
memory: 11288kb

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: 177ms
memory: 11284kb

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: 226ms
memory: 11276kb

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: 226ms
memory: 11052kb

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: 230ms
memory: 11204kb

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: 4084kb

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: 121ms
memory: 10804kb

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: 3940kb

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