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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#86602 | #4807. Melborp Lacissalc | codicon# | AC ✓ | 688ms | 38220kb | C++23 | 2.1kb | 2023-03-10 11:58:39 | 2023-03-10 11:58:41 |
Judging History
answer
//
// Created by codicon on 3/9/2023 at 6:56 PM.
//
// O(n^5/2^2)
// The idea is that there is a bijection between the n + 1prefix sums and the n values of the array
#include <bits/stdc++.h>
using namespace std;
# define add(a, b) a = ((a) + (b)) % MOD;
int n, k, t;
const int MAXN = 64, MOD = 998'244'353;
int dp[MAXN + 1][MAXN + 2][(MAXN)*(MAXN+1)/2 + 1];
long long FAC[MAXN+2], INV_FAC[MAXN+2];
long long ch[MAXN+1][MAXN+1];
long long binexp(long long b, int e) {
long long res = 1;
for (; e; b = b * b % MOD, e >>= 1) {
if (e&1) res = res * b % MOD;
}
return res;
}
long long choose(int n, int k) {
if (k > n) {
return 0;
}
return (FAC[n] * INV_FAC[k] % MOD) * INV_FAC[n-k] % MOD;
}
void set_up() {
FAC[0] = 1;
for (int i = 1; i <= MAXN+1; i++) {
FAC[i] = FAC[i-1] * i % MOD;
}
INV_FAC[MAXN+1] = binexp(FAC[MAXN+1], MOD-2);
for (int i = MAXN; i >= 0; i--) {
INV_FAC[i] = INV_FAC[i+1] * (i+1) % MOD;
}
for (int n = 0; n <= MAXN+1; n++) {
for (int k = 0; k <= MAXN+1; k++) {
ch[n][k] = choose(n, k);
}
}
}
int main() {
cin.tie(0)->sync_with_stdio(0);
cin >> n >> k >> t;
set_up();
// Base case
for (int used = 1; used <= n+1; used++) {
dp[1][used][ch[used][2]] = 1;
}
// Do dp
for (int pused = 1; pused < k; pused++) {
for (int used = 1; used <= n+1; used++) {
for (int goodness = 0; goodness <= t; goodness++) {
// Don't use prefix value
add(dp[pused + 1][used][goodness], dp[pused][used][goodness])
// Use prefix value
for (int new_used = 1;
new_used + used <= n+1 and
goodness + ch[new_used][2] <= t;
new_used++) {
add(dp[pused + 1][used + new_used][goodness + ch[new_used][2]],
dp[pused][used][goodness] * ch[used-1 + new_used][new_used] % MOD)
}
}
}
}
cout << dp[k][n+1][t];
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 2ms
memory: 3552kb
input:
2 5 1
output:
12
result:
ok 1 number(s): "12"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3756kb
input:
7 10 15
output:
2016
result:
ok 1 number(s): "2016"
Test #3:
score: 0
Accepted
time: 12ms
memory: 14404kb
input:
46 50 171
output:
645560469
result:
ok 1 number(s): "645560469"
Test #4:
score: 0
Accepted
time: 2ms
memory: 20032kb
input:
64 64 0
output:
0
result:
ok 1 number(s): "0"
Test #5:
score: 0
Accepted
time: 0ms
memory: 21304kb
input:
64 64 1
output:
326126263
result:
ok 1 number(s): "326126263"
Test #6:
score: 0
Accepted
time: 4ms
memory: 21056kb
input:
63 64 0
output:
4476118
result:
ok 1 number(s): "4476118"
Test #7:
score: 0
Accepted
time: 4ms
memory: 5672kb
input:
11 45 14
output:
963276342
result:
ok 1 number(s): "963276342"
Test #8:
score: 0
Accepted
time: 13ms
memory: 7904kb
input:
35 20 565
output:
0
result:
ok 1 number(s): "0"
Test #9:
score: 0
Accepted
time: 3ms
memory: 6424kb
input:
3 64 5
output:
0
result:
ok 1 number(s): "0"
Test #10:
score: 0
Accepted
time: 12ms
memory: 10920kb
input:
35 45 153
output:
181934997
result:
ok 1 number(s): "181934997"
Test #11:
score: 0
Accepted
time: 2ms
memory: 3880kb
input:
3 25 5
output:
0
result:
ok 1 number(s): "0"
Test #12:
score: 0
Accepted
time: 1ms
memory: 5672kb
input:
35 5 373
output:
740122840
result:
ok 1 number(s): "740122840"
Test #13:
score: 0
Accepted
time: 2ms
memory: 6224kb
input:
3 50 5
output:
0
result:
ok 1 number(s): "0"
Test #14:
score: 0
Accepted
time: 21ms
memory: 11572kb
input:
35 30 592
output:
0
result:
ok 1 number(s): "0"
Test #15:
score: 0
Accepted
time: 2ms
memory: 3556kb
input:
3 11 1
output:
540
result:
ok 1 number(s): "540"
Test #16:
score: 0
Accepted
time: 30ms
memory: 14028kb
input:
35 55 352
output:
656633208
result:
ok 1 number(s): "656633208"
Test #17:
score: 0
Accepted
time: 27ms
memory: 14628kb
input:
54 38 356
output:
215089708
result:
ok 1 number(s): "215089708"
Test #18:
score: 0
Accepted
time: 3ms
memory: 7328kb
input:
22 19 189
output:
0
result:
ok 1 number(s): "0"
Test #19:
score: 0
Accepted
time: 68ms
memory: 22828kb
input:
54 63 401
output:
987604839
result:
ok 1 number(s): "987604839"
Test #20:
score: 0
Accepted
time: 5ms
memory: 8120kb
input:
22 43 171
output:
827743481
result:
ok 1 number(s): "827743481"
Test #21:
score: 0
Accepted
time: 23ms
memory: 11868kb
input:
54 24 446
output:
551546514
result:
ok 1 number(s): "551546514"
Test #22:
score: 0
Accepted
time: 2ms
memory: 3864kb
input:
22 4 152
output:
0
result:
ok 1 number(s): "0"
Test #23:
score: 0
Accepted
time: 235ms
memory: 25352kb
input:
54 48 1306
output:
0
result:
ok 1 number(s): "0"
Test #24:
score: 0
Accepted
time: 1ms
memory: 6236kb
input:
22 29 7
output:
374430631
result:
ok 1 number(s): "374430631"
Test #25:
score: 0
Accepted
time: 39ms
memory: 7732kb
input:
54 9 1351
output:
0
result:
ok 1 number(s): "0"
Test #26:
score: 0
Accepted
time: 2ms
memory: 10180kb
input:
22 54 5
output:
267958047
result:
ok 1 number(s): "267958047"
Test #27:
score: 0
Accepted
time: 205ms
memory: 20140kb
input:
64 32 1315
output:
494251101
result:
ok 1 number(s): "494251101"
Test #28:
score: 0
Accepted
time: 8ms
memory: 5584kb
input:
33 12 332
output:
765350074
result:
ok 1 number(s): "765350074"
Test #29:
score: 0
Accepted
time: 0ms
memory: 4080kb
input:
1 57 1
output:
1
result:
ok 1 number(s): "1"
Test #30:
score: 0
Accepted
time: 12ms
memory: 10352kb
input:
33 37 363
output:
0
result:
ok 1 number(s): "0"
Test #31:
score: 0
Accepted
time: 2ms
memory: 3584kb
input:
1 17 0
output:
16
result:
ok 1 number(s): "16"
Test #32:
score: 0
Accepted
time: 17ms
memory: 14692kb
input:
33 62 148
output:
871819399
result:
ok 1 number(s): "871819399"
Test #33:
score: 0
Accepted
time: 2ms
memory: 3812kb
input:
1 42 0
output:
41
result:
ok 1 number(s): "41"
Test #34:
score: 0
Accepted
time: 9ms
memory: 7140kb
input:
33 23 179
output:
23699248
result:
ok 1 number(s): "23699248"
Test #35:
score: 0
Accepted
time: 2ms
memory: 5424kb
input:
1 3 1
output:
1
result:
ok 1 number(s): "1"
Test #36:
score: 0
Accepted
time: 16ms
memory: 12544kb
input:
33 47 211
output:
267909794
result:
ok 1 number(s): "267909794"
Test #37:
score: 0
Accepted
time: 1ms
memory: 6524kb
input:
11 26 32
output:
0
result:
ok 1 number(s): "0"
Test #38:
score: 0
Accepted
time: 9ms
memory: 4972kb
input:
43 6 579
output:
280289125
result:
ok 1 number(s): "280289125"
Test #39:
score: 0
Accepted
time: 4ms
memory: 5864kb
input:
11 50 5
output:
865381083
result:
ok 1 number(s): "865381083"
Test #40:
score: 0
Accepted
time: 50ms
memory: 12812kb
input:
43 31 750
output:
0
result:
ok 1 number(s): "0"
Test #41:
score: 0
Accepted
time: 0ms
memory: 6064kb
input:
11 11 12
output:
753565341
result:
ok 1 number(s): "753565341"
Test #42:
score: 0
Accepted
time: 35ms
memory: 16036kb
input:
43 56 290
output:
575236094
result:
ok 1 number(s): "575236094"
Test #43:
score: 0
Accepted
time: 4ms
memory: 5200kb
input:
11 36 52
output:
0
result:
ok 1 number(s): "0"
Test #44:
score: 0
Accepted
time: 1ms
memory: 7760kb
input:
44 16 0
output:
0
result:
ok 1 number(s): "0"
Test #45:
score: 0
Accepted
time: 1ms
memory: 6852kb
input:
12 61 31
output:
682427534
result:
ok 1 number(s): "682427534"
Test #46:
score: 0
Accepted
time: 21ms
memory: 14968kb
input:
44 41 365
output:
759457870
result:
ok 1 number(s): "759457870"
Test #47:
score: 0
Accepted
time: 0ms
memory: 7124kb
input:
22 19 70
output:
247296498
result:
ok 1 number(s): "247296498"
Test #48:
score: 0
Accepted
time: 84ms
memory: 23516kb
input:
54 64 444
output:
418216086
result:
ok 1 number(s): "418216086"
Test #49:
score: 0
Accepted
time: 1ms
memory: 7632kb
input:
22 44 52
output:
779702126
result:
ok 1 number(s): "779702126"
Test #50:
score: 0
Accepted
time: 118ms
memory: 14880kb
input:
54 25 1303
output:
0
result:
ok 1 number(s): "0"
Test #51:
score: 0
Accepted
time: 3ms
memory: 5848kb
input:
22 5 49
output:
219556981
result:
ok 1 number(s): "219556981"
Test #52:
score: 0
Accepted
time: 221ms
memory: 25644kb
input:
54 49 1269
output:
0
result:
ok 1 number(s): "0"
Test #53:
score: 0
Accepted
time: 2ms
memory: 6240kb
input:
22 30 14
output:
719775605
result:
ok 1 number(s): "719775605"
Test #54:
score: 0
Accepted
time: 48ms
memory: 7884kb
input:
54 10 1314
output:
0
result:
ok 1 number(s): "0"
Test #55:
score: 0
Accepted
time: 7ms
memory: 10236kb
input:
22 54 12
output:
325137058
result:
ok 1 number(s): "325137058"
Test #56:
score: 0
Accepted
time: 163ms
memory: 19288kb
input:
54 35 1359
output:
0
result:
ok 1 number(s): "0"
Test #57:
score: 0
Accepted
time: 0ms
memory: 5720kb
input:
33 13 335
output:
202725820
result:
ok 1 number(s): "202725820"
Test #58:
score: 0
Accepted
time: 688ms
memory: 38220kb
input:
64 64 2080
output:
1
result:
ok 1 number(s): "1"
Test #59:
score: 0
Accepted
time: 2ms
memory: 3392kb
input:
1 1 0
output:
0
result:
ok 1 number(s): "0"
Test #60:
score: 0
Accepted
time: 2ms
memory: 3436kb
input:
1 1 1
output:
1
result:
ok 1 number(s): "1"
Test #61:
score: 0
Accepted
time: 621ms
memory: 36184kb
input:
63 63 2016
output:
1
result:
ok 1 number(s): "1"