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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#297556 | #4903. 细菌 | luyiming123 | 15 | 106ms | 21460kb | C++14 | 4.8kb | 2024-01-04 18:47:58 | 2024-01-04 18:48:00 |
Judging History
answer
# include <bits/stdc++.h>
using namespace std;
using i64 = long long;
using ui64 = unsigned long long;
const int N = 2.4e5 + 5;
const i64 mod = 998244353, ivg = (mod + 1) / 3;
void Add(i64 &x, i64 y) {x = (x + y) % mod; if(x < 0) x += mod; return; }
int d, lim[3], pos[3], r[N], L;
i64 Poly[3][N], sumC[N], fac[N], ifac[N];
i64 qpow(i64 x, i64 p = mod - 2ll)
{
i64 ans = 1ll;
while(p)
{
if(p & 1) ans = ans * x % mod;
x = x * x % mod, p >>= 1;
}
return ans;
}
void NTT(i64 *a, bool type) {
static ui64 f[N], w[N];
for(int i = 0; i < L; i++) f[i] = a[r[i] = (r[i >> 1] >> 1) | (i & 1 ? L >> 1 : 0)];
for(int d = 1; d < L; d <<= 1) {
int wd = qpow(type ? 3 : ivg, (mod - 1) / (d + d));
for(int j = w[0] = 1; j < d; j++) w[j] = 1ll * w[j - 1] * wd % mod;
for(int i = 0; i < L; i += d << 1) {
for(int j = 0; j < d; j++) {
int y = w[j] * f[i | j | d] % mod;
f[i | j | d] = f[i | j] + mod - y, f[i | j] += y;
}
}
if(d == (1 << 16)) for(int p = 0; p < L; p++) f[p] %= mod;
}
i64 inv = qpow(L, mod - 2);
for(int i = 0; i < L; i++) a[i] = f[i] % mod * (type ? 1 : inv) % mod;
}
void Init(int n = N - 5)
{
fac[0] = ifac[0] = 1ll;
for(int i = 1; i <= n; i++) fac[i] = fac[i - 1] * 1ll * i % mod;
ifac[n] = qpow(fac[n]);
for(int i = n - 1; i >= 1; i--) ifac[i] = ifac[i + 1] * 1ll * (i + 1) % mod;
return;
}
i64 C(int n, int m)
{
if(n < m) return 0;
return fac[n] * ifac[m] % mod * ifac[n - m] % mod;
}
void solve(int o, int d)
{
// bool deb = (o == 0 && d == 1);
bool deb = 1;
// printf("solve : %d, %d\n", o, d);
int lim = ::lim[o], pos = ::pos[o];
// Line : y = 0, y = lim + 1
// Line : y = lim + 1 最后被触碰
i64 Ans = 0;
// int lf = 0, rg = lim + 1;
int mx = min(d, (lim - pos + d) / 2), mn = (d + 1) / 2;
// printf("mx = %d, mn = %d\n", mx, mn);
Add(Ans, sumC[mx] - (mn > 0 ? sumC[mn - 1] : 0));
//[lf, pos - 1]
if(pos > 1)
{
mx = (d - 1) / 2, mn = max(0, (2 - pos + d) / 2);
// printf("2 : mx = %d, mn = %d\n", mx, mn);
Add(Ans, sumC[mx] - (mn > 0 ? sumC[mn - 1] : 0));
}
// if(deb) printf("Answer = %lld\n", Ans);
for(int i = 1; i * (lim + 1) + 1 <= pos + d; i++)
{
int lf = i * (lim + 1) + 1, rg = min((i + 1) * (lim + 1) - 1, pos + d);
int mx = (rg - pos + d) / 2, mn = (lf - pos + d + 1) / 2;
Add(Ans, ((i & 1) ? -1 : 1) * (sumC[mx] - (mn > 0 ? sumC[mn - 1] : 0)));
}
// Line : y = 0 最后被触碰 pos reverse
pos = lim - pos + 1;
for(int i = 1; i * (lim + 1) + 1 <= pos + d; i++)
{
int lf = i * (lim + 1) + 1, rg = min((i + 1) * (lim + 1) - 1, pos + d);
int mx = (rg - pos + d) / 2, mn = (lf - pos + d + 1) / 2;
// printf("fuck : mx = %d, mn = %d\n", mx, mn);
Add(Ans, ((i & 1) ? -1 : 1) * (sumC[mx] - (mn > 0 ? sumC[mn - 1] : 0)));
}
Poly[o][d] = Ans;
// printf("fkkkk!\n");
return;
}
void solve2(int o)
{
int lim = ::lim[o], pos = ::pos[o];
static i64 dp[2][N];
int lf = 1 - pos + d, rg = lim - pos + d;
for(int i = 0; i <= (d << 1); i++) dp[0][i] = dp[1][i] = 0;
dp[0][d] = 1;
Poly[o][0] = 1;
for(int i = 1; i <= d; i++)
{
int op = (i & 1);
for(int j = 0; j <= (d << 1); j++) dp[op][j] = 0;
for(int j = lf; j <= rg; j++)
{
if(j < rg) Add(dp[op][j + 1], dp[op ^ 1][j]);
if(j > lf) Add(dp[op][j - 1], dp[op ^ 1][j]);
}
Poly[o][i] = 0;
for(int j = lf; j <= rg; j++) Add(Poly[o][i], dp[op][j]);
}
return;
}
int main(void)
{
Init();
scanf("%d", &d);
for(int i = 0; i < 3; i++) scanf("%d", &lim[i]);
for(int i = 0; i < 3; i++) scanf("%d", &pos[i]);
//init sumC[i] (means C(d, 1) + ... + C(d, i))
// printf("YES1\n");
for(int o = 0; o < 3; o++)
{
if(1ll * d < 1ll * lim[o] * lim[o])
{
Poly[o][0] = 1;
for(int i = 0; i <= d; i++) sumC[i] = 0;
sumC[0] = 1;
for(int d0 = 1; d0 <= d; d0++)
{
for(int i = 0; i < d0; i++)
{
sumC[i] = sumC[i] * 2ll % mod - C(d0 - 1, i);
}
sumC[d0] = sumC[d0 - 1] + 1;
solve(o, d0);
}
}
else solve2(o);
// for(int i = 0; i <= d; i++) printf("Poly[%d][%d] = %lld\n", o, i, Poly[o][i]);
// printf("Yes : o = %d\n", o);
}
for(int o = 0; o < 3; o++)
{
for(int i = 0; i <= d; i++) Poly[o][i] = Poly[o][i] * ifac[i] % mod;
}
L = 1;
while(L <= (d << 1)) L <<= 1;
for(int o = 0; o < 3; o++) NTT(Poly[o], 1);
for(int i = 0; i < L; i++) Poly[0][i] = Poly[0][i] * Poly[1][i] % mod * Poly[2][i] % mod;
NTT(Poly[0], 0);
printf("%lld\n", Poly[0][d] * fac[d] % mod);
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Subtask #1:
score: 5
Accepted
Test #1:
score: 5
Accepted
time: 0ms
memory: 21400kb
input:
50 41 46 42 8 20 21
output:
791406134
result:
ok 1 number(s): "791406134"
Test #2:
score: 0
Accepted
time: 0ms
memory: 20420kb
input:
50 49 44 48 49 15 25
output:
544847893
result:
ok 1 number(s): "544847893"
Subtask #2:
score: 10
Accepted
Dependency #1:
100%
Accepted
Test #3:
score: 10
Accepted
time: 101ms
memory: 20660kb
input:
5000 4994 4990 4990 976 2257 2505
output:
836390717
result:
ok 1 number(s): "836390717"
Test #4:
score: 0
Accepted
time: 106ms
memory: 21460kb
input:
5000 4994 4997 4994 4399 1826 1332
output:
65414465
result:
ok 1 number(s): "65414465"
Subtask #3:
score: 0
Time Limit Exceeded
Test #5:
score: 0
Time Limit Exceeded
input:
120000 300 1 1 141 1 1
output:
result:
Subtask #4:
score: 0
Time Limit Exceeded
Test #8:
score: 0
Time Limit Exceeded
input:
119000 119991 119991 1 23819 52139 1
output:
result:
Subtask #5:
score: 0
Skipped
Dependency #4:
0%
Subtask #6:
score: 0
Skipped
Dependency #3:
0%
Subtask #7:
score: 0
Skipped
Dependency #1:
100%
Accepted
Dependency #2:
100%
Accepted
Dependency #3:
0%