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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#320513 | #8211. Enumerating Substrings | ucup-team2112# | AC ✓ | 71ms | 22804kb | C++20 | 5.4kb | 2024-02-03 17:29:41 | 2024-02-03 17:29:42 |
Judging History
answer
#include <bits/stdc++.h>
const int mod = 1e9 + 7;
using ll = long long;
int norm(int x) {
if (x < 0) {
x += mod;
}
if (x >= mod) {
x -= mod;
}
return x;
}
template<class T>
T power(T a, int b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
struct mint {
int x;
mint(int x = 0) : x(norm(x)) {}
int val() const {
return x;
}
mint operator-() const {
return mint(norm(mod - x));
}
mint inv() const {
assert(x != 0);
return power(*this, mod - 2);
}
mint &operator*=(const mint &rhs) {
x = ll(x) * rhs.x % mod;
return *this;
}
mint &operator+=(const mint &rhs) {
x = norm(x + rhs.x);
return *this;
}
mint &operator-=(const mint &rhs) {
x = norm(x - rhs.x);
return *this;
}
mint &operator/=(const mint &rhs) {
return *this *= rhs.inv();
}
friend mint operator*(const mint &lhs, const mint &rhs) {
mint res = lhs;
res *= rhs;
return res;
}
friend mint operator+(const mint &lhs, const mint &rhs) {
mint res = lhs;
res += rhs;
return res;
}
friend mint operator-(const mint &lhs, const mint &rhs) {
mint res = lhs;
res -= rhs;
return res;
}
friend mint operator/(const mint &lhs, const mint &rhs) {
mint res = lhs;
res /= rhs;
return res;
}
friend std::istream &operator>>(std::istream &is, mint &a) {
ll v;
is >> v;
a = mint(v);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const mint &a) {
return os << a.val();
}
};
struct Comb {
int n;
std::vector<mint> _fac;
std::vector<mint> _invfac;
std::vector<mint> _inv;
Comb() : n{0}, _fac{1}, _invfac{1}, _inv{0} {}
Comb(int n) : Comb() {
init(n);
}
void init(int m) {
if (m <= n) return;
_fac.resize(m + 1);
_invfac.resize(m + 1);
_inv.resize(m + 1);
for (int i = n + 1; i <= m; i++) {
_fac[i] = _fac[i - 1] * i;
}
_invfac[m] = _fac[m].inv();
for (int i = m; i > n; i--) {
_invfac[i - 1] = _invfac[i] * i;
_inv[i] = _invfac[i] * _fac[i - 1];
}
n = m;
}
mint fac(int m) {
if (m > n) init(2 * m);
return _fac[m];
}
mint invfac(int m) {
if (m > n) init(2 * m);
return _invfac[m];
}
mint inv(int m) {
if (m > n) init(2 * m);
return _inv[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(){
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout.tie(nullptr);
int n, m, k;
std::cin >> n >> m >> k;
mint res = 0;
std::vector<mint> pw(n + 1);
pw[0] = 1;
for (int i = 1; i <= n; i += 1) {
pw[i] = pw[i - 1] * mint(k);
}
std::vector f(m + 1, std::vector<mint>(m + 1));
f[0][0] = 1;
for (int i = 1; i <= m; i += 1) {
for (int j = 0; j <= m; j += 1) {
if (j + 1 <= m) {
f[i][j + 1] += f[i - 1][j];
}
if (j + 2 <= m) {
f[i][j + 2] += f[i - 1][j] * comb.invfac(2);
}
}
}
{
mint tmp = 1;
for (int c = 0; c <= m; c += 1) {
res += f[c][m] * comb.fac(m) * tmp * mint(n - m + 1) * power(mint(k), n - m);
tmp = tmp * (k - c) * comb.inv(c + 1);
}
}
{
mint tmp = 1;
std::vector<mint> dp(m);
for (int i = 1; i <= m; i += 1) {
tmp *= k - i + 1;
if (i + i <= m) {
mint coef = 1;
for (int c = 0; c <= m - 2 * i; c += 1) {
// std::cerr << i << " " << c << " " << f[c][m - 2 * i] * comb.fac(m - 2 * i) << " " << tmp << " " << coef << "\n";
dp[i] += f[c][m - 2 * i] * comb.fac(m - 2 * i) * tmp * coef;
coef = coef * (k - i - c) * comb.inv(c + 1);
}
}
// else {
// int x = i - (m - i + 1) + 1;
// if (x + x >= i) {
// mint coef = 1;
// for (int c = 0; c <= i - 2 * x; c += 1) {
// dp[2 * m - x] += f[c][m - 2 * x] * comb.fac(m - 2 * x) * tmp;
// coef = coef * (k - x - c) * comb.inv(c + 1);
// }
// }
// }
// for (int len = 0; len <= 2 * m; len += 1) {
// res -= dp[len] * (n - len + 1) * power(mint(k), n - len);
// }
}
for (int len = 0; len < m; len += 1) {
int sign = 0;
for (int x = 2; x * m - (x - 1) * len <= n; x += 1) {
int c = x * m - (x - 1) * len;
if (sign) res += dp[len] * (n - c + 1) * pw[n - c];
else res -= dp[len] * (n - c + 1) * pw[n - c];
sign ^= 1;
}
}
}
std::cout << res << "\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: 3844kb
input:
4 2 3
output:
228
result:
ok 1 number(s): "228"
Test #2:
score: 0
Accepted
time: 71ms
memory: 22804kb
input:
999999 1999 12345678
output:
52352722
result:
ok 1 number(s): "52352722"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3588kb
input:
7 4 2
output:
182
result:
ok 1 number(s): "182"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3880kb
input:
4 3 4
output:
480
result:
ok 1 number(s): "480"
Test #5:
score: 0
Accepted
time: 0ms
memory: 3876kb
input:
3 1 1
output:
3
result:
ok 1 number(s): "3"
Test #6:
score: 0
Accepted
time: 0ms
memory: 3632kb
input:
5 5 1
output:
0
result:
ok 1 number(s): "0"
Test #7:
score: 0
Accepted
time: 0ms
memory: 3580kb
input:
7 4 3
output:
5784
result:
ok 1 number(s): "5784"
Test #8:
score: 0
Accepted
time: 0ms
memory: 3684kb
input:
5 2 4
output:
3932
result:
ok 1 number(s): "3932"
Test #9:
score: 0
Accepted
time: 0ms
memory: 3648kb
input:
8 2 2
output:
1522
result:
ok 1 number(s): "1522"
Test #10:
score: 0
Accepted
time: 0ms
memory: 3608kb
input:
8 1 2
output:
2048
result:
ok 1 number(s): "2048"
Test #11:
score: 0
Accepted
time: 0ms
memory: 3876kb
input:
7 5 3
output:
2430
result:
ok 1 number(s): "2430"
Test #12:
score: 0
Accepted
time: 0ms
memory: 3648kb
input:
10 4 3
output:
272004
result:
ok 1 number(s): "272004"
Test #13:
score: 0
Accepted
time: 27ms
memory: 7376kb
input:
675978 614 2
output:
0
result:
ok 1 number(s): "0"
Test #14:
score: 0
Accepted
time: 6ms
memory: 4148kb
input:
244613 38 1
output:
0
result:
ok 1 number(s): "0"
Test #15:
score: 0
Accepted
time: 24ms
memory: 12332kb
input:
186293 1462 1
output:
0
result:
ok 1 number(s): "0"
Test #16:
score: 0
Accepted
time: 7ms
memory: 6388kb
input:
24867 886 1
output:
0
result:
ok 1 number(s): "0"
Test #17:
score: 0
Accepted
time: 41ms
memory: 10904kb
input:
976164 1014 2
output:
0
result:
ok 1 number(s): "0"
Test #18:
score: 0
Accepted
time: 0ms
memory: 3920kb
input:
179356 2 716844809
output:
577866092
result:
ok 1 number(s): "577866092"
Test #19:
score: 0
Accepted
time: 19ms
memory: 5716kb
input:
621001 130 310625363
output:
892869197
result:
ok 1 number(s): "892869197"
Test #20:
score: 0
Accepted
time: 28ms
memory: 8748kb
input:
678862 850 754662812
output:
582264789
result:
ok 1 number(s): "582264789"
Test #21:
score: 0
Accepted
time: 30ms
memory: 9424kb
input:
650845 978 348443366
output:
825425732
result:
ok 1 number(s): "825425732"
Test #22:
score: 0
Accepted
time: 26ms
memory: 6500kb
input:
669914 402 87448112
output:
318098088
result:
ok 1 number(s): "318098088"
Test #23:
score: 0
Accepted
time: 39ms
memory: 8320kb
input:
998593 530 681228665
output:
408255654
result:
ok 1 number(s): "408255654"
Test #24:
score: 0
Accepted
time: 42ms
memory: 19680kb
input:
369361 1954 125266115
output:
509912384
result:
ok 1 number(s): "509912384"
Test #25:
score: 0
Accepted
time: 48ms
memory: 14172kb
input:
900226 1378 424079373
output:
406320917
result:
ok 1 number(s): "406320917"
Test #26:
score: 0
Accepted
time: 28ms
memory: 13344kb
input:
334887 1506 17859926
output:
503264679
result:
ok 1 number(s): "503264679"
Test #27:
score: 0
Accepted
time: 37ms
memory: 8152kb
input:
936048 544 53978328
output:
548647866
result:
ok 1 number(s): "548647866"
Test #28:
score: 0
Accepted
time: 15ms
memory: 10176kb
input:
152789 1264 792983073
output:
839541707
result:
ok 1 number(s): "839541707"
Test #29:
score: 0
Accepted
time: 41ms
memory: 13588kb
input:
714493 1392 91796331
output:
721071046
result:
ok 1 number(s): "721071046"
Test #30:
score: 0
Accepted
time: 11ms
memory: 6848kb
input:
269571 816 830801077
output:
330064211
result:
ok 1 number(s): "330064211"
Test #31:
score: 0
Accepted
time: 41ms
memory: 9856kb
input:
845120 944 424581630
output:
348960190
result:
ok 1 number(s): "348960190"
Test #32:
score: 0
Accepted
time: 20ms
memory: 5844kb
input:
533990 368 163586376
output:
522092095
result:
ok 1 number(s): "522092095"
Test #33:
score: 0
Accepted
time: 29ms
memory: 16668kb
input:
181707 1792 462399634
output:
373795106
result:
ok 1 number(s): "373795106"
Test #34:
score: 0
Accepted
time: 44ms
memory: 19156kb
input:
417349 1920 761212891
output:
587051329
result:
ok 1 number(s): "587051329"
Test #35:
score: 0
Accepted
time: 32ms
memory: 12456kb
input:
526583 1344 500217637
output:
108767800
result:
ok 1 number(s): "108767800"
Test #36:
score: 0
Accepted
time: 34ms
memory: 8828kb
input:
867054 769 93998191
output:
239123369
result:
ok 1 number(s): "239123369"
Extra Test:
score: 0
Extra Test Passed