QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#448593 | #8526. Polygon II | GeZhiyuan | AC ✓ | 230ms | 11288kb | C++14 | 1.6kb | 2024-06-19 20:00:13 | 2024-06-19 20:00:13 |
Judging History
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