QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#588914 | #8211. Enumerating Substrings | hcywoi | AC ✓ | 167ms | 30556kb | C++14 | 5.9kb | 2024-09-25 15:12:01 | 2024-09-25 15:12:02 |
Judging History
answer
#include <bits/stdc++.h>
using i64 = long long;
template<class T>
T qmi(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
i64 mul(i64 a, i64 b, i64 p) {
i64 res = a * b - i64(1.L * a * b / p) * p;
res %= p;
if (res < 0) {
res += p;
}
return res;
}
template<int P>
struct modint {
int x;
constexpr modint() : x{} {}
constexpr modint(i64 x) : x{norm(x % getmod())} {}
static int mod;
constexpr static int getmod() {
if (P > 0) {
return P;
} else {
return mod;
}
}
constexpr static void setmod(int m) {
mod = m;
}
constexpr int norm(int x) const {
if (x < 0) {
x += getmod();
}
if (x >= getmod()) {
x -= getmod();
}
return x;
}
constexpr int val() const {
return x;
}
explicit constexpr operator int() const {
return x;
}
constexpr modint operator-() const {
modint res;
res.x = norm(getmod() - x);
return res;
}
constexpr modint inv() const {
assert(x != 0);
return qmi(*this, getmod() - 2);
}
constexpr modint &operator*= (modint v) & {
x = 1LL * x * v.x % getmod();
return *this;
}
constexpr modint &operator+= (modint v) & {
x = norm(x + v.x);
return *this;
}
constexpr modint &operator-= (modint v) & {
x = norm(x - v.x);
return *this;
}
constexpr modint &operator/= (modint v) & {
return *this *= v.inv();
}
friend constexpr modint operator- (modint a, modint b) {
modint res = a;
res -= b;
return res;
}
friend constexpr modint operator+ (modint a, modint b) {
modint res = a;
res += b;
return res;
}
friend constexpr modint operator* (modint a, modint b) {
modint res = a;
res *= b;
return res;
}
friend constexpr modint operator/ (modint a, modint b) {
modint res = a;
res /= b;
return res;
}
friend constexpr std::istream &operator>> (std::istream& is, modint& a) {
i64 v;
is >> v;
a = modint(v);
return is;
}
friend constexpr std::ostream &operator<< (std::ostream& os, const modint& a) {
return os << a.val();
}
friend constexpr bool operator== (modint a, modint b) {
return a.val() == b.val();
}
friend constexpr bool operator!= (modint a, modint b) {
return a.val() != b.val();
}
};
constexpr int P = 1e9 + 7;
using mint = modint<P>;
struct Comb {
int n;
std::vector<mint> fact;
std::vector<mint> invefact;
std::vector<mint> inve;
Comb() : n{0}, fact{1}, invefact{1}, inve{0} {}
Comb(int n) : Comb() {
init(n);
}
void init(int m) {
if (m <= n) return;
fact.resize(m + 1);
invefact.resize(m + 1);
inve.resize(m + 1);
for (int i = n + 1; i <= m; i ++ ) {
fact[i] = fact[i - 1] * i;
}
invefact[m] = fact[m].inv();
for (int i = m; i > n; i -- ) {
invefact[i - 1] = invefact[i] * i;
inve[i] = invefact[i] * fact[i - 1];
}
n = m;
}
mint fac(int m) {
if (m > n) init(2 * m);
return fact[m];
}
mint invfac(int m) {
if (m > n) init(2 * m);
return invefact[m];
}
mint inv(int m) {
if (m > n) init(2 * m);
return inve[m];
}
mint binom(int n, int m) {
if (n < m || m < 0) return 0;
return fac(n) * invfac(m) * invfac(n - m);
}
} comb;
int main() {
// freopen("lake.in", "r", stdin);
// freopen("lake.out", "w", stdout);
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int n, m, k;
std::cin >> n >> m >> k;
std::vector<mint> pw2(n + 1), inv2(n + 1), pwk(n + 1);
pw2[0] = pwk[0] = inv2[0] = 1;
for (int i = 0; i < n; i ++ ) {
pw2[i + 1] = pw2[i] * 2;
pwk[i + 1] = pwk[i] * k;
inv2[i + 1] = inv2[i] * qmi(mint(2), P - 2);
}
std::vector<std::vector<mint>> f(m + 1, std::vector<mint>(m + 1));
for (int i = 0; i <= m; i ++ ) {
f[i][0] = 1;
for (int j = 0; j < m; j ++ ) {
f[i][j + 1] = f[i][j] * (k - i - j);
}
}
auto C = [&](int n, int m) -> mint {
if (n < m || m < 0) {
return 0;
}
return f[k - n][m] * comb.invfac(m);
};
std::vector<mint> g(m + 1);
for (int len = 0; len <= m; len ++ ) {
// for (int i = 0; i <= (m - 2 * len) / 2; i ++ ) {
// g[len] += comb.binom(k, len) * comb.fac(len) * comb.binom(k - len, i) * comb.binom(k - len - i, m - 2 * len - 2 * i) * comb.fac(m - 2 * len) * qmi(pw2[i], P - 2);
// }
// std::cerr << len << " " << g[len] << "\n";
for (int i = 0; i <= (m - 2 * len) / 2; i ++ ) {
g[len] += C(k - len, i) * C(k - len - i, m - 2 * i - 2 * len) * comb.fac(m - 2 * len) * inv2[i];
}
g[len] *= f[0][len];
// std::cerr << len << " " << g[len] << "\n";
}
// for (int i = m - 1; i >= 0; i -- ) {
// g[i] -= g[i + 1];
// }
for (int i = 1; i <= m; i ++ ) {
g[0] -= g[i];
}
mint ans = pwk[n - m] * (n - m + 1) * g[0];
for (int len = 1; len <= m / 2; len ++ ) {
mint sum = 0;
for (int k = 1; len + k * (m - len) <= n; k ++ ) {
int x = len + k * (m - len);
sum += (k % 2 ? 1 : -1) * (n - x + 1) * pwk[n - x];
}
ans += sum * g[len];
}
std::cout << ans << "\n";
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: 0ms
memory: 3564kb
input:
4 2 3
output:
228
result:
ok 1 number(s): "228"
Test #2:
score: 0
Accepted
time: 167ms
memory: 30556kb
input:
999999 1999 12345678
output:
52352722
result:
ok 1 number(s): "52352722"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3628kb
input:
7 4 2
output:
182
result:
ok 1 number(s): "182"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3600kb
input:
4 3 4
output:
480
result:
ok 1 number(s): "480"
Test #5:
score: 0
Accepted
time: 0ms
memory: 3564kb
input:
3 1 1
output:
3
result:
ok 1 number(s): "3"
Test #6:
score: 0
Accepted
time: 0ms
memory: 3516kb
input:
5 5 1
output:
0
result:
ok 1 number(s): "0"
Test #7:
score: 0
Accepted
time: 0ms
memory: 3604kb
input:
7 4 3
output:
5784
result:
ok 1 number(s): "5784"
Test #8:
score: 0
Accepted
time: 0ms
memory: 3628kb
input:
5 2 4
output:
3932
result:
ok 1 number(s): "3932"
Test #9:
score: 0
Accepted
time: 0ms
memory: 3604kb
input:
8 2 2
output:
1522
result:
ok 1 number(s): "1522"
Test #10:
score: 0
Accepted
time: 0ms
memory: 3636kb
input:
8 1 2
output:
2048
result:
ok 1 number(s): "2048"
Test #11:
score: 0
Accepted
time: 0ms
memory: 3544kb
input:
7 5 3
output:
2430
result:
ok 1 number(s): "2430"
Test #12:
score: 0
Accepted
time: 0ms
memory: 3564kb
input:
10 4 3
output:
272004
result:
ok 1 number(s): "272004"
Test #13:
score: 0
Accepted
time: 96ms
memory: 12436kb
input:
675978 614 2
output:
0
result:
ok 1 number(s): "0"
Test #14:
score: 0
Accepted
time: 31ms
memory: 6044kb
input:
244613 38 1
output:
0
result:
ok 1 number(s): "0"
Test #15:
score: 0
Accepted
time: 42ms
memory: 13880kb
input:
186293 1462 1
output:
0
result:
ok 1 number(s): "0"
Test #16:
score: 0
Accepted
time: 9ms
memory: 6576kb
input:
24867 886 1
output:
0
result:
ok 1 number(s): "0"
Test #17:
score: 0
Accepted
time: 139ms
memory: 18712kb
input:
976164 1014 2
output:
0
result:
ok 1 number(s): "0"
Test #18:
score: 0
Accepted
time: 26ms
memory: 5316kb
input:
179356 2 716844809
output:
577866092
result:
ok 1 number(s): "577866092"
Test #19:
score: 0
Accepted
time: 89ms
memory: 10464kb
input:
621001 130 310625363
output:
892869197
result:
ok 1 number(s): "892869197"
Test #20:
score: 0
Accepted
time: 100ms
memory: 14056kb
input:
678862 850 754662812
output:
582264789
result:
ok 1 number(s): "582264789"
Test #21:
score: 0
Accepted
time: 93ms
memory: 14600kb
input:
650845 978 348443366
output:
825425732
result:
ok 1 number(s): "825425732"
Test #22:
score: 0
Accepted
time: 94ms
memory: 11700kb
input:
669914 402 87448112
output:
318098088
result:
ok 1 number(s): "318098088"
Test #23:
score: 0
Accepted
time: 146ms
memory: 16048kb
input:
998593 530 681228665
output:
408255654
result:
ok 1 number(s): "408255654"
Test #24:
score: 0
Accepted
time: 75ms
memory: 22576kb
input:
369361 1954 125266115
output:
509912384
result:
ok 1 number(s): "509912384"
Test #25:
score: 0
Accepted
time: 137ms
memory: 21160kb
input:
900226 1378 424079373
output:
406320917
result:
ok 1 number(s): "406320917"
Test #26:
score: 0
Accepted
time: 62ms
memory: 16148kb
input:
334887 1506 17859926
output:
503264679
result:
ok 1 number(s): "503264679"
Test #27:
score: 0
Accepted
time: 128ms
memory: 15412kb
input:
936048 544 53978328
output:
548647866
result:
ok 1 number(s): "548647866"
Test #28:
score: 0
Accepted
time: 30ms
memory: 11192kb
input:
152789 1264 792983073
output:
839541707
result:
ok 1 number(s): "839541707"
Test #29:
score: 0
Accepted
time: 111ms
memory: 19240kb
input:
714493 1392 91796331
output:
721071046
result:
ok 1 number(s): "721071046"
Test #30:
score: 0
Accepted
time: 44ms
memory: 8992kb
input:
269571 816 830801077
output:
330064211
result:
ok 1 number(s): "330064211"
Test #31:
score: 0
Accepted
time: 129ms
memory: 16448kb
input:
845120 944 424581630
output:
348960190
result:
ok 1 number(s): "348960190"
Test #32:
score: 0
Accepted
time: 74ms
memory: 9904kb
input:
533990 368 163586376
output:
522092095
result:
ok 1 number(s): "522092095"
Test #33:
score: 0
Accepted
time: 43ms
memory: 18012kb
input:
181707 1792 462399634
output:
373795106
result:
ok 1 number(s): "373795106"
Test #34:
score: 0
Accepted
time: 81ms
memory: 22720kb
input:
417349 1920 761212891
output:
587051329
result:
ok 1 number(s): "587051329"
Test #35:
score: 0
Accepted
time: 90ms
memory: 16668kb
input:
526583 1344 500217637
output:
108767800
result:
ok 1 number(s): "108767800"
Test #36:
score: 0
Accepted
time: 129ms
memory: 15748kb
input:
867054 769 93998191
output:
239123369
result:
ok 1 number(s): "239123369"
Extra Test:
score: 0
Extra Test Passed