QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#767194 | #9479. And DNA | Nelofus | AC ✓ | 1ms | 3728kb | C++20 | 2.2kb | 2024-11-20 20:07:23 | 2024-11-20 20:07:31 |
Judging History
answer
/* Code by Heratino & Nelofus */
// No I still can't seem to
// Sing more than blues when it's time for my verse
// It's true that I need you
// To turn my blues into bursting fireworks
#include <bits/stdc++.h>
using i64 = long long;
//{{{
template<typename Ta, typename Tb>
inline void chkmax(Ta &a, const Tb &b) {if (a < b) a = b;}
template<typename Ta, typename Tb>
inline void chkmin(Ta &a, const Tb &b) {if (a > b) a = b;}
//}}}
constexpr int N = 32;
constexpr int mod = 998244353;
constexpr inline int Add(const int &x, const int &y) {return x + y >= mod ? x + y - mod : x + y;}
constexpr inline int Sub(const int &x, const int &y) {return x - y < 0 ? x - y + mod : x - y;}
constexpr inline void AddTo(int &x, const int &y) {x = Add(x, y);}
constexpr inline void SubTo(int &x, const int &y) {x = Sub(x, y);}
struct matrix {
int a[3][3];
matrix() {memset(a, 0, sizeof(a));}
constexpr int* operator [] (const int &x) {return a[x];}
friend matrix operator * (matrix &A, matrix &B) {
matrix C;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
for (int k = 0; k < 3; k++)
AddTo(C[i][j], 1ll * A[i][k] * B[k][j] % mod);
return C;
}
};
int f[N][2];
inline matrix fpow(matrix x, int k) {
matrix res;
for (int i = 0; i < 3; i++)
res[i][i] = 1;
for (; k; k >>= 1, x = x * x)
if (k & 1)
res = res * x;
return res;
}
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int n, m;
std::cin >> n >> m;
if (m == 0) {
std::cout << 1 << '\n';
return 0;
}
matrix trans;
trans[0][0] = 0, trans[0][1] = 1, trans[0][2] = 0;
trans[1][0] = 0, trans[1][1] = 0, trans[1][2] = 1;
trans[2][0] = 1, trans[2][1] = 1, trans[2][2] = 0;
matrix t = fpow(trans, n - 3);
int w = (2ll * t[2][1] + 3ll * t[2][2]) % mod;
int k = std::__lg(m) + 1;
f[0][0] = 1;
for (int i = 0; i < k; i++) {
// 为 0 的转移
if (m >> i & 1)
AddTo(f[i + 1][0], 1ll * w * f[i][0] % mod);
else
AddTo(f[i + 1][1], f[i][0]), AddTo(f[i + 1][0], f[i][0]);
// 为 1 的转移
if (m >> i & 1)
AddTo(f[i + 1][0], f[i][1]), AddTo(f[i + 1][1], f[i][1]);
else
AddTo(f[i + 1][1], 1ll * w * f[i][1] % mod);
}
std::cout << f[k][0] << '\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3652kb
input:
3 2
output:
4
result:
ok "4"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3648kb
input:
3 0
output:
1
result:
ok "1"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3652kb
input:
100 100
output:
343406454
result:
ok "343406454"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3668kb
input:
686579306 119540831
output:
260602195
result:
ok "260602195"
Test #5:
score: 0
Accepted
time: 0ms
memory: 3724kb
input:
26855095 796233790
output:
492736984
result:
ok "492736984"
Test #6:
score: 0
Accepted
time: 0ms
memory: 3720kb
input:
295310488 262950628
output:
503008241
result:
ok "503008241"
Test #7:
score: 0
Accepted
time: 0ms
memory: 3640kb
input:
239670714 149827706
output:
994702969
result:
ok "994702969"
Test #8:
score: 0
Accepted
time: 0ms
memory: 3588kb
input:
790779949 110053353
output:
898252188
result:
ok "898252188"
Test #9:
score: 0
Accepted
time: 0ms
memory: 3644kb
input:
726600542 795285932
output:
183726777
result:
ok "183726777"
Test #10:
score: 0
Accepted
time: 0ms
memory: 3656kb
input:
957970519 585582861
output:
298814018
result:
ok "298814018"
Test #11:
score: 0
Accepted
time: 0ms
memory: 3712kb
input:
93349859 634036506
output:
110693443
result:
ok "110693443"
Test #12:
score: 0
Accepted
time: 0ms
memory: 3656kb
input:
453035113 34126396
output:
306244220
result:
ok "306244220"
Test #13:
score: 0
Accepted
time: 0ms
memory: 3652kb
input:
31994526 100604502
output:
930620701
result:
ok "930620701"
Test #14:
score: 0
Accepted
time: 0ms
memory: 3656kb
input:
234760741 249817734
output:
440195858
result:
ok "440195858"
Test #15:
score: 0
Accepted
time: 0ms
memory: 3716kb
input:
542621111 646412689
output:
207377992
result:
ok "207377992"
Test #16:
score: 0
Accepted
time: 0ms
memory: 3648kb
input:
28492783 602632297
output:
65234506
result:
ok "65234506"
Test #17:
score: 0
Accepted
time: 0ms
memory: 3592kb
input:
213500301 768820204
output:
540205113
result:
ok "540205113"
Test #18:
score: 0
Accepted
time: 0ms
memory: 3728kb
input:
697808101 753041955
output:
93561295
result:
ok "93561295"
Test #19:
score: 0
Accepted
time: 0ms
memory: 3668kb
input:
585126464 450455977
output:
91109717
result:
ok "91109717"
Test #20:
score: 0
Accepted
time: 0ms
memory: 3652kb
input:
236696315 482334538
output:
925575199
result:
ok "925575199"
Test #21:
score: 0
Accepted
time: 0ms
memory: 3592kb
input:
632719214 298704996
output:
358926097
result:
ok "358926097"
Test #22:
score: 0
Accepted
time: 1ms
memory: 3672kb
input:
869119333 933404114
output:
318501108
result:
ok "318501108"
Test #23:
score: 0
Accepted
time: 0ms
memory: 3592kb
input:
6977994 814763202
output:
585332987
result:
ok "585332987"
Test #24:
score: 0
Accepted
time: 0ms
memory: 3716kb
input:
3 1
output:
3
result:
ok "3"
Test #25:
score: 0
Accepted
time: 0ms
memory: 3604kb
input:
3 1000000000
output:
279679226
result:
ok "279679226"
Test #26:
score: 0
Accepted
time: 0ms
memory: 3592kb
input:
4 0
output:
1
result:
ok "1"
Test #27:
score: 0
Accepted
time: 0ms
memory: 3656kb
input:
4 1
output:
2
result:
ok "2"
Test #28:
score: 0
Accepted
time: 0ms
memory: 3716kb
input:
4 1000000000
output:
1755648
result:
ok "1755648"
Test #29:
score: 0
Accepted
time: 0ms
memory: 3656kb
input:
1000000000 0
output:
1
result:
ok "1"
Test #30:
score: 0
Accepted
time: 0ms
memory: 3668kb
input:
1000000000 1
output:
696798313
result:
ok "696798313"
Test #31:
score: 0
Accepted
time: 0ms
memory: 3596kb
input:
1000000000 1000000000
output:
703786301
result:
ok "703786301"
Extra Test:
score: 0
Extra Test Passed