QOJ.ac
QOJ
| ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
|---|---|---|---|---|---|---|---|---|---|
| #355414 | #5105. Hand of the Free Marked | ucup-team052# | AC ✓ | 10ms | 3940kb | C++23 | 1.6kb | 2024-03-16 17:28:03 | 2024-03-16 17:28:39 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
const int N = 15;
long double val[N];
int a[N], b[N], id[N];
int k, m, n;
long double ans;
bool cmp(int i, int j) {
return val[i] > val[j];
}
void dfs1(int u, int sum) {
if (u == m + 1) {
if (sum != k) return;
long double fac = 1;
for (int i = 1; i <= k - 1; i++) fac *= i;
long double mx = 1;
int flag = 0;
for (int i = 1; i <= m; i++) {
long double now = fac * a[i] / (b[i] - a[i] + 1) / mx;
if (now >= 1) {
flag = 1;
break;
}
mx *= (1 - now);
}
if (flag) mx = 1;
else mx = 1 - mx;
long double p = 1;
int now = n;
for (int i = 1; i <= m; i++) {
for (int j = 0; j < a[i]; j++) {
p *= (long double)(b[i] - j) / (j + 1) / now;
--now;
}
}
for (int i = 1; i <= k; i++) p *= i;
// for (int i = 1; i <= m; i++) printf("%d ", a[i]);
// printf("| mx = %.6Lf, p = %.6Lf\n", mx, p);
ans += p * mx;
return;
}
for (int i = 0; i <= min(k - sum, b[u]); i++) {
a[u] = i;
dfs1(u + 1, sum + i);
}
}
int main() {
scanf("%d%d", &k, &m);
for (int i = 1; i <= m; i++) {
scanf("%d", &b[i]);
n += b[i];
}
dfs1(1, 0);
printf("%.10Lf\n", ans);
return 0;
}
/*
3 3 3 5 12
0 0 3 | mx = 0.600000, p = 0.192982
0 1 2 | mx = 0.606061, p = 0.289474
0 2 1 | mx = 1.000000, p = 0.105263
0 3 0 | mx = 1.000000, p = 0.008772
1 0 2 | mx = 0.363636, p = 0.173684
1 1 1 | mx = 1.000000, p = 0.157895
1 2 0 | mx = 1.000000, p = 0.026316
2 0 1 | mx = 1.000000, p = 0.031579
2 1 0 | mx = 1.000000, p = 0.013158
3 0 0 | mx = 1.000000, p = 0.000877
0.6982456140
*/
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 3936kb
input:
3 3 2 1 2
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #2:
score: 0
Accepted
time: 0ms
memory: 3836kb
input:
3 4 1 3 1 15
output:
0.7719298246
result:
ok answer is 0.7719298246
Test #3:
score: 0
Accepted
time: 1ms
memory: 3896kb
input:
4 1 27
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #4:
score: 0
Accepted
time: 0ms
memory: 3816kb
input:
4 3 1 2 28
output:
0.9739710790
result:
ok answer is 0.9739710790
Test #5:
score: 0
Accepted
time: 0ms
memory: 3876kb
input:
4 3 1 3 28
output:
0.9772246941
result:
ok answer is 0.9772246941
Test #6:
score: 0
Accepted
time: 1ms
memory: 3860kb
input:
5 1 130
output:
0.9523809524
result:
ok answer is 0.9523809524
Test #7:
score: 0
Accepted
time: 0ms
memory: 3812kb
input:
5 3 2 16 200
output:
0.7490392123
result:
ok answer is 0.7490392123
Test #8:
score: 0
Accepted
time: 0ms
memory: 3932kb
input:
4 10 1 2 3 4 1 2 3 4 5 100
output:
0.6954998646
result:
ok answer is 0.6954998646
Test #9:
score: 0
Accepted
time: 0ms
memory: 3872kb
input:
4 10 1 20 3 4 1 2 40 4 5 500
output:
0.2435721816
result:
ok answer is 0.2435721816
Test #10:
score: 0
Accepted
time: 0ms
memory: 3836kb
input:
3 2 152333146 373955979
output:
0.0000000228
result:
ok answer is 0.0000000228
Test #11:
score: 0
Accepted
time: 0ms
memory: 3800kb
input:
2 5 263121 2244976 14139709 57922752 200667899
output:
0.0000000363
result:
ok answer is 0.0000000363
Test #12:
score: 0
Accepted
time: 0ms
memory: 3908kb
input:
2 9 8693409 192044828 270204 207696017 4714758 43866747 54411633 159493424 1230327
output:
0.0000000268
result:
ok answer is 0.0000000268
Test #13:
score: 0
Accepted
time: 0ms
memory: 3908kb
input:
5 2 368946153 140852305
output:
0.0000004708
result:
ok answer is 0.0000004708
Test #14:
score: 0
Accepted
time: 1ms
memory: 3864kb
input:
6 7 21894756 69672 6998541 209713 14912795 3044993 4001906
output:
0.0000985677
result:
ok answer is 0.0000985677
Test #15:
score: 0
Accepted
time: 0ms
memory: 3872kb
input:
7 8 10393835 5758 42813 141353298 4827 7467584 30955 5450
output:
0.0002531002
result:
ok answer is 0.0002531002
Test #16:
score: 0
Accepted
time: 0ms
memory: 3908kb
input:
9 2 510542963 107597808
output:
0.0011741015
result:
ok answer is 0.0011741015
Test #17:
score: 0
Accepted
time: 1ms
memory: 3924kb
input:
9 4 61285845 5006573 857873 164342879
output:
0.0062702500
result:
ok answer is 0.0062702500
Test #18:
score: 0
Accepted
time: 2ms
memory: 3856kb
input:
8 9 150817030 1785608 1799504 185570 765031 91189422 826565 162065 31840039
output:
0.0012989187
result:
ok answer is 0.0012989187
Test #19:
score: 0
Accepted
time: 0ms
memory: 3892kb
input:
3 3 303536168 13837393 495002513
output:
0.0000000222
result:
ok answer is 0.0000000222
Test #20:
score: 0
Accepted
time: 0ms
memory: 3868kb
input:
3 6 53418609 234629667 123823068 34111351 5030364 122184307
output:
0.0000000628
result:
ok answer is 0.0000000628
Test #21:
score: 0
Accepted
time: 0ms
memory: 3900kb
input:
2 8 367991 173352184 277736038 8490 1609033 14778992 46849 7751
output:
0.0000000342
result:
ok answer is 0.0000000342
Test #22:
score: 0
Accepted
time: 0ms
memory: 3836kb
input:
7 2 267723891 27011243
output:
0.0000342002
result:
ok answer is 0.0000342002
Test #23:
score: 0
Accepted
time: 0ms
memory: 3896kb
input:
7 4 142414601 5258379 6663526 395635619
output:
0.0000366564
result:
ok answer is 0.0000366564
Test #24:
score: 0
Accepted
time: 1ms
memory: 3936kb
input:
6 10 74360718 12028354 85290 298827 991561 26513484 13713894 241157 664292 69531
output:
0.0000558282
result:
ok answer is 0.0000558282
Test #25:
score: 0
Accepted
time: 0ms
memory: 3924kb
input:
8 2 248584022 141021009
output:
0.0002069789
result:
ok answer is 0.0002069789
Test #26:
score: 0
Accepted
time: 1ms
memory: 3892kb
input:
8 5 21702603 142314177 4721812 36026710 10702024
output:
0.0009356407
result:
ok answer is 0.0009356407
Test #27:
score: 0
Accepted
time: 3ms
memory: 3900kb
input:
8 10 167779 219592785 89060 377095564 169349 75686 382454 10537801 86060 487630
output:
0.0006624125
result:
ok answer is 0.0006624125
Test #28:
score: 0
Accepted
time: 0ms
memory: 3916kb
input:
2 1 2
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #29:
score: 0
Accepted
time: 0ms
memory: 3820kb
input:
2 1 1000000000
output:
0.0000000020
result:
ok answer is 0.0000000020
Test #30:
score: 0
Accepted
time: 1ms
memory: 3940kb
input:
2 2 1 1
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #31:
score: 0
Accepted
time: 0ms
memory: 3900kb
input:
2 2 1 999999999
output:
0.0000000040
result:
ok answer is 0.0000000040
Test #32:
score: 0
Accepted
time: 0ms
memory: 3900kb
input:
2 2 999999999 1
output:
0.0000000040
result:
ok answer is 0.0000000040
Test #33:
score: 0
Accepted
time: 0ms
memory: 3924kb
input:
2 2 500000000 500000000
output:
0.0000000040
result:
ok answer is 0.0000000040
Test #34:
score: 0
Accepted
time: 0ms
memory: 3860kb
input:
2 3 1 1 1
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #35:
score: 0
Accepted
time: 0ms
memory: 3892kb
input:
2 3 1 3 2
output:
0.9333333333
result:
ok answer is 0.9333333333
Test #36:
score: 0
Accepted
time: 0ms
memory: 3900kb
input:
2 3 1 999999997 2
output:
0.0000000060
result:
ok answer is 0.0000000060
Test #37:
score: 0
Accepted
time: 0ms
memory: 3856kb
input:
2 10 1 1 1 1 1 1 1 1 1 1
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #38:
score: 0
Accepted
time: 0ms
memory: 3908kb
input:
2 10 1 2 1 2 1 2 1 2 1 2
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #39:
score: 0
Accepted
time: 0ms
memory: 3876kb
input:
2 10 1 2 3 4 5 6 7 8 9 10
output:
0.3629629630
result:
ok answer is 0.3629629630
Test #40:
score: 0
Accepted
time: 0ms
memory: 3816kb
input:
2 10 1 1 1 1 1 999999980 2 2 2 2
output:
0.0000000200
result:
ok answer is 0.0000000200
Test #41:
score: 0
Accepted
time: 0ms
memory: 3892kb
input:
3 1 3
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #42:
score: 0
Accepted
time: 0ms
memory: 3832kb
input:
3 1 500000000
output:
0.0000000120
result:
ok answer is 0.0000000120
Test #43:
score: 0
Accepted
time: 1ms
memory: 3904kb
input:
3 2 1 2
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #44:
score: 0
Accepted
time: 0ms
memory: 3832kb
input:
3 2 999999998 1
output:
0.0000000090
result:
ok answer is 0.0000000090
Test #45:
score: 0
Accepted
time: 0ms
memory: 3900kb
input:
3 3 3 3 3
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #46:
score: 0
Accepted
time: 0ms
memory: 3896kb
input:
3 3 5 12 1
output:
0.7965686275
result:
ok answer is 0.7965686275
Test #47:
score: 0
Accepted
time: 1ms
memory: 3896kb
input:
3 10 99999990 99999991 99999992 99999993 99999994 99999995 99999996 99999997 99999998 99999999
output:
0.0000000600
result:
ok answer is 0.0000000600
Test #48:
score: 0
Accepted
time: 1ms
memory: 3868kb
input:
10 1 10
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #49:
score: 0
Accepted
time: 0ms
memory: 3860kb
input:
10 1 500000000
output:
0.0072576001
result:
ok answer is 0.0072576001
Test #50:
score: 0
Accepted
time: 1ms
memory: 3832kb
input:
10 1 1000000000
output:
0.0036288000
result:
ok answer is 0.0036288000
Test #51:
score: 0
Accepted
time: 0ms
memory: 3920kb
input:
10 2 5 5
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #52:
score: 0
Accepted
time: 0ms
memory: 3868kb
input:
10 2 10 5
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #53:
score: 0
Accepted
time: 0ms
memory: 3932kb
input:
10 2 999999999 1
output:
0.0036288100
result:
ok answer is 0.0036288100
Test #54:
score: 0
Accepted
time: 1ms
memory: 3900kb
input:
10 2 500000000 500000000
output:
0.0072576001
result:
ok answer is 0.0072576001
Test #55:
score: 0
Accepted
time: 0ms
memory: 3896kb
input:
10 2 499999999 500000001
output:
0.0072576001
result:
ok answer is 0.0072576001
Test #56:
score: 0
Accepted
time: 0ms
memory: 3916kb
input:
10 3 10 10 10
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #57:
score: 0
Accepted
time: 0ms
memory: 3816kb
input:
10 3 11 10 10
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #58:
score: 0
Accepted
time: 1ms
memory: 3924kb
input:
10 3 11 999999970 10
output:
0.0036290094
result:
ok answer is 0.0036290094
Test #59:
score: 0
Accepted
time: 0ms
memory: 3816kb
input:
10 3 499999990 2 499999999
output:
0.0072576200
result:
ok answer is 0.0072576200
Test #60:
score: 0
Accepted
time: 1ms
memory: 3872kb
input:
10 3 333333333 333333333 333333333
output:
0.0108864001
result:
ok answer is 0.0108864001
Test #61:
score: 0
Accepted
time: 0ms
memory: 3864kb
input:
10 10 1 1 1 1 1 1 1 1 1 1
output:
1.0000000000
result:
ok answer is 1.0000000000
Test #62:
score: 0
Accepted
time: 10ms
memory: 3864kb
input:
10 10 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000
output:
0.0362880003
result:
ok answer is 0.0362880003
Test #63:
score: 0
Accepted
time: 7ms
memory: 3776kb
input:
10 10 99999999 99999998 99999997 99999996 99999995 99999994 99999993 99999992 99999991 99999990
output:
0.0362880023
result:
ok answer is 0.0362880023
Test #64:
score: 0
Accepted
time: 1ms
memory: 3864kb
input:
10 10 1 2 1 2 1 2 1 2 999999980 3
output:
0.0036289496
result:
ok answer is 0.0036289496
Extra Test:
score: 0
Extra Test Passed