QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#589127 | #8211. Enumerating Substrings | 369Pai | AC ✓ | 15ms | 9268kb | C++20 | 4.9kb | 2024-09-25 16:16:12 | 2024-09-25 16:16:12 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1e6 + 5 , MOD = 1e9 + 7 , INV2 = MOD / 2 + 1;
int n , m , k , pw[N] , ipw[N];
namespace BF
{
const int N = 10;
int s1[N] , s2[N] , cnt[N] , nxt[N] , res[N];
int Solve()
{
int ans = 0;
for(int t = 0 ; t < pw[m] ; t++)
{
memset(cnt , 0 , sizeof cnt);
bool fail = 0;
for(int i = 0 ; i < m ; i++)
{
s2[i] = t / pw[i] % k;
if(++cnt[s2[i]] > 2)fail = 1;
}
if(!fail)
{
// for(int i = 0 ; i < m ; i++)
// cerr << s2[i] << ',';
// cerr << "\n";
int border = 0;
for(int i = 1 ; i <= m / 2 ; i++)
{
bool ok = 1;
for(int j = 0 ; j < i && ok ; j++)
if(s2[j] != s2[m - i + j])ok = 0;
if(ok)border = i;
}
// cerr << "border = " << border << "\n";
for(int s = 0 ; s < pw[n] ; s++)
{
for(int i = 0 ; i < n ; i++)
s1[i] = s / pw[i] % k;
for(int i = 0 ; i <= n - m ; i++)
{
bool ok = 1;
for(int j = 0 ; j < m && ok ; j++)
if(s1[i + j] != s2[j])ok = 0;
if(ok)
{
ans++ , res[border]++;
// cerr << "\t" << i << " ";
// for(int i = 0 ; i < n ; i++)
// cerr << s1[i] << ',';
// cerr << "\n";
i += m - 1;
}
}
}
}
}
cout << ans << "\n";
// for(int i = 0 ; i <= m / 2 ; i++)
// cerr << res[i] << " \n"[i == m / 2];
return 0;
}
}
namespace NM
{
const int M = 2005;
int fac[M] , ifac[M] , ip2[M] , dk[M];
int Qpow(ll x , ll p)
{
ll res = 1;
x %= MOD , p %= MOD - 1;
if(p < 0)p += MOD - 1;
for(; p ; p >>= 1 , x = x * x % MOD)
if(p & 1)res = res * x % MOD;
return res;
}
void Init(int n)
{
ip2[0] = fac[0] = ifac[0] = 1;
for(int i = 1 ; i <= n ; i++)
fac[i] = (ll)fac[i - 1] * i % MOD;
ifac[n] = Qpow(fac[n] , MOD - 2);
for(int i = n - 1 ; i >= 1 ; i--)
ifac[i] = (ll)ifac[i + 1] * (i + 1) % MOD;
for(int i = 1 ; i <= n ; i++)
ip2[i] = (ll)ip2[i - 1] * INV2 % MOD;
}
int C(int n , int m)
{
if(n < m || m < 0)return 0;
return (ll)fac[n] * ifac[m] % MOD * ifac[n - m] % MOD;
}
int F(int k , int m)
{
int ans = 0 , s = min(m / 2 , k) , dn = 1;
for(int i = 0 ; i < m - s ; i++)dn = (ll)dn * (k - i) % MOD;
for(int j = s ; j >= max(m - k , 0) ; j--)
{
ans = (ans + ((ll)dn * ip2[j] % MOD) * ((ll)ifac[j] * ifac[m - j * 2] % MOD)) % MOD;
dn = (ll)dn * (k - m + j) % MOD;
}
ans = (ll)ans * fac[m] % MOD;
return ans;
}
int Solve()
{
Init(m);
int sum = 0 , ans = 0;
dk[0] = 1;
for(int i = 1 ; i <= min(m / 2 , k) ; i++)
dk[i] = (ll)dk[i - 1] * (k - i + 1) % MOD;
ipw[0] = 1 , ipw[1] = Qpow(k , MOD - 2);
for(int i = 2 ; i <= m ; i++)ipw[i] = (ll)ipw[i - 1] * ipw[1] % MOD;
for(int len = min(m / 2 , k) ; len >= 0 ; len--)
{
int c = (ll)dk[len] * F(k - len , m - len * 2) % MOD;
// cerr << "border len = " << len << " : " << c << "\n";
if(!len)c = (c + MOD - sum) % MOD;
else sum = (sum + c) % MOD;
int res = 0;
if(!len)res = ll(n - m + 1) * pw[n - m] % MOD;
else
{
int kni = Qpow(k , n - m) , dt = Qpow(Qpow(k , (m - len)) , MOD - 2);
for(int i = m , l = 2 ; i <= n ; i += m - len , l++ , kni = (ll)kni * dt % MOD)
{
int t = 0 , tt = 0 , r = m - len;
int p = ll(pw[r] - 1) * ipw[r] % MOD;
// for(int j = 1 ; j <= n - i + 1 ; j++)
// {
// auto W = [&](int l)
// {
// if(l >= r)return (ll)p * pw[l] % MOD;
// return (ll)pw[l];
// // return (ll)(pw[min(r , l)] - (l >= r)) * pw[max(l - r , 0)] % MOD;
// };
// tt = (tt + (ll)W(j - 1) * W(n - i - j + 1)) % MOD;
// }
if(n - i + 1 >= 2 * r)
{
int p2 = (ll)p * p % MOD;
t = (ll(n - i + 1 - r * 2) * p2 % MOD + ll(2 * r) * p % MOD) % MOD;
}
else
{
int L = max(0 , n - i - r + 1);
int R = min(n - i + 2 , r + 1);
t = (ll(R - L - 1) + ll(L + n - i + 2 - R) * p) % MOD;
// cerr << "\t" << t << "\n";
}
t = (ll)t * kni % MOD;
// cerr << t << ' ' << tt << " ; " << kni << " = " << Qpow(k , n - i) << " ; " << r << ';' << n - i + 1 << "\n";
// if(i < n)
// {
// if(i < n - 1)t = (t + (n - i - 1) * ((ll)(k - 1) * (k - 1) % MOD) % MOD * pw[n - i - 2]) % MOD;
// t = (t + 2ll * (k - 1) % MOD * pw[n - i - 1]) % MOD;
// }
// else t = 1;
res = (res + (ll)(l >> 1) * t) % MOD;
}
}
// cerr << len << ":" << c << " * " << res << "\n";
ans = (ans + (ll)res * c) % MOD;
}
cout << ans << "\n";
return 0;
}
}
signed main()
{
ios::sync_with_stdio(0);
cin.tie(0) , cout.tie(0);
cin >> n >> m >> k;
pw[0] = 1;
for(int i = 1 ; i <= n ; i++)
pw[i] = (ll)k * pw[i - 1] % MOD;
// if(n <= 5 && m <= 5 && k <= 3)
// BF::Solve();
NM::Solve();
return 0;
}
这程序好像有点Bug,我给组数据试试?
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 5740kb
input:
4 2 3
output:
228
result:
ok 1 number(s): "228"
Test #2:
score: 0
Accepted
time: 15ms
memory: 8612kb
input:
999999 1999 12345678
output:
52352722
result:
ok 1 number(s): "52352722"
Test #3:
score: 0
Accepted
time: 0ms
memory: 5740kb
input:
7 4 2
output:
182
result:
ok 1 number(s): "182"
Test #4:
score: 0
Accepted
time: 0ms
memory: 5788kb
input:
4 3 4
output:
480
result:
ok 1 number(s): "480"
Test #5:
score: 0
Accepted
time: 1ms
memory: 5668kb
input:
3 1 1
output:
3
result:
ok 1 number(s): "3"
Test #6:
score: 0
Accepted
time: 1ms
memory: 5716kb
input:
5 5 1
output:
0
result:
ok 1 number(s): "0"
Test #7:
score: 0
Accepted
time: 0ms
memory: 5744kb
input:
7 4 3
output:
5784
result:
ok 1 number(s): "5784"
Test #8:
score: 0
Accepted
time: 0ms
memory: 5736kb
input:
5 2 4
output:
3932
result:
ok 1 number(s): "3932"
Test #9:
score: 0
Accepted
time: 1ms
memory: 5788kb
input:
8 2 2
output:
1522
result:
ok 1 number(s): "1522"
Test #10:
score: 0
Accepted
time: 0ms
memory: 5788kb
input:
8 1 2
output:
2048
result:
ok 1 number(s): "2048"
Test #11:
score: 0
Accepted
time: 1ms
memory: 5672kb
input:
7 5 3
output:
2430
result:
ok 1 number(s): "2430"
Test #12:
score: 0
Accepted
time: 0ms
memory: 5672kb
input:
10 4 3
output:
272004
result:
ok 1 number(s): "272004"
Test #13:
score: 0
Accepted
time: 4ms
memory: 7840kb
input:
675978 614 2
output:
0
result:
ok 1 number(s): "0"
Test #14:
score: 0
Accepted
time: 2ms
memory: 5796kb
input:
244613 38 1
output:
0
result:
ok 1 number(s): "0"
Test #15:
score: 0
Accepted
time: 1ms
memory: 5744kb
input:
186293 1462 1
output:
0
result:
ok 1 number(s): "0"
Test #16:
score: 0
Accepted
time: 1ms
memory: 5660kb
input:
24867 886 1
output:
0
result:
ok 1 number(s): "0"
Test #17:
score: 0
Accepted
time: 5ms
memory: 7804kb
input:
976164 1014 2
output:
0
result:
ok 1 number(s): "0"
Test #18:
score: 0
Accepted
time: 3ms
memory: 7784kb
input:
179356 2 716844809
output:
577866092
result:
ok 1 number(s): "577866092"
Test #19:
score: 0
Accepted
time: 6ms
memory: 7696kb
input:
621001 130 310625363
output:
892869197
result:
ok 1 number(s): "892869197"
Test #20:
score: 0
Accepted
time: 8ms
memory: 7776kb
input:
678862 850 754662812
output:
582264789
result:
ok 1 number(s): "582264789"
Test #21:
score: 0
Accepted
time: 8ms
memory: 7732kb
input:
650845 978 348443366
output:
825425732
result:
ok 1 number(s): "825425732"
Test #22:
score: 0
Accepted
time: 7ms
memory: 7840kb
input:
669914 402 87448112
output:
318098088
result:
ok 1 number(s): "318098088"
Test #23:
score: 0
Accepted
time: 7ms
memory: 9232kb
input:
998593 530 681228665
output:
408255654
result:
ok 1 number(s): "408255654"
Test #24:
score: 0
Accepted
time: 9ms
memory: 5812kb
input:
369361 1954 125266115
output:
509912384
result:
ok 1 number(s): "509912384"
Test #25:
score: 0
Accepted
time: 12ms
memory: 9268kb
input:
900226 1378 424079373
output:
406320917
result:
ok 1 number(s): "406320917"
Test #26:
score: 0
Accepted
time: 3ms
memory: 5748kb
input:
334887 1506 17859926
output:
503264679
result:
ok 1 number(s): "503264679"
Test #27:
score: 0
Accepted
time: 10ms
memory: 8868kb
input:
936048 544 53978328
output:
548647866
result:
ok 1 number(s): "548647866"
Test #28:
score: 0
Accepted
time: 4ms
memory: 5732kb
input:
152789 1264 792983073
output:
839541707
result:
ok 1 number(s): "839541707"
Test #29:
score: 0
Accepted
time: 7ms
memory: 7856kb
input:
714493 1392 91796331
output:
721071046
result:
ok 1 number(s): "721071046"
Test #30:
score: 0
Accepted
time: 4ms
memory: 7832kb
input:
269571 816 830801077
output:
330064211
result:
ok 1 number(s): "330064211"
Test #31:
score: 0
Accepted
time: 10ms
memory: 9020kb
input:
845120 944 424581630
output:
348960190
result:
ok 1 number(s): "348960190"
Test #32:
score: 0
Accepted
time: 6ms
memory: 7788kb
input:
533990 368 163586376
output:
522092095
result:
ok 1 number(s): "522092095"
Test #33:
score: 0
Accepted
time: 7ms
memory: 5808kb
input:
181707 1792 462399634
output:
373795106
result:
ok 1 number(s): "373795106"
Test #34:
score: 0
Accepted
time: 9ms
memory: 7800kb
input:
417349 1920 761212891
output:
587051329
result:
ok 1 number(s): "587051329"
Test #35:
score: 0
Accepted
time: 8ms
memory: 7736kb
input:
526583 1344 500217637
output:
108767800
result:
ok 1 number(s): "108767800"
Test #36:
score: 0
Accepted
time: 9ms
memory: 7812kb
input:
867054 769 93998191
output:
239123369
result:
ok 1 number(s): "239123369"
Extra Test:
score: 0
Extra Test Passed