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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#333533 | #8211. Enumerating Substrings | nhuang685 | RE | 108ms | 34460kb | C++20 | 5.9kb | 2024-02-20 06:42:59 | 2024-02-20 06:42:59 |
Judging History
answer
/**
* @file qoj8211-1.cpp
* @author n685
* @brief
* @date 2024-02-19
*
*
*/
#include <bits/stdc++.h>
#ifdef LOCAL
#include "dd/debug.h"
#else
#define dbg(...) 42
#define dbgR(...) 4242
#define dbgP(...) 420
#define dbgRP(...) 420420
void nline() {}
#endif
template <class T> constexpr std::pair<T, T> exEucl(T a, T b) {
if (a < b) {
// auto [x, y] = exEucl(b, a);
T x, y;
std::tie(x, y) = exEucl(b, a);
return {y, x};
}
if (b == 0) {
assert(a == 1);
return {1, 0};
}
// auto [x, y] = exEucl(b, a % b);
T x, y;
std::tie(x, y) = exEucl(b, a % b);
return {y, x - (a / b) * y};
}
template <
class T, class U,
typename std::enable_if<std::is_integral<U>::value, bool>::type = true>
constexpr T binpow(T a, U b) {
// 0^0 = 1
T res = 1;
while (b > 0) {
if (b % 2 == 1) {
res *= a;
}
a *= a;
b /= 2;
}
return res;
}
template <class Md, class V = int64_t> struct Mod {
using T = typename std::decay<decltype(Md::value)>::type;
T val = 0;
template <class U> static constexpr T normalize(U val) {
if (val <= -Md::value || Md::value <= val) {
val %= Md::value;
}
if (val < 0) {
val += Md::value;
}
return static_cast<T>(val);
}
constexpr Mod() : val(0) {}
template <class U, typename std::enable_if<std::is_integral<U>::value,
bool>::type = true>
constexpr Mod(U _val) {
val = normalize(_val);
}
// addition
constexpr Mod &operator+=(Mod b) {
val += b.val;
if (val >= Md::value) {
val -= Md::value;
}
return *this;
}
friend constexpr Mod operator+(Mod a, Mod b) { return (a += b); }
constexpr Mod &operator++() { return (*this += 1); }
constexpr Mod operator++(int) {
Mod res = *this;
++(*this);
return res;
}
// subtraction
constexpr Mod &operator-=(Mod b) {
val -= b.val;
if (val < 0) {
val += Md::value;
}
return *this;
}
friend constexpr Mod operator-(Mod a, Mod b) { return (a -= b); }
constexpr Mod &operator--() { return (*this -= 1); }
constexpr Mod operator--(int) {
Mod res = *this;
--(*this);
return res;
}
// multiplication
constexpr Mod &operator*=(Mod b) {
val = static_cast<T>(static_cast<V>(val) * b.val % Md::value);
return *this;
}
friend constexpr Mod operator*(Mod a, Mod b) { return (a *= b); }
template <class U> constexpr Mod binpow(U b) const {
return ::binpow(*this, b);
}
constexpr Mod inv() const {
return Mod(exEucl(static_cast<V>(val), static_cast<V>(Md::value)).first);
// return binpow(Md::value - 2);
}
// comparison
constexpr bool operator==(Mod b) const { return (val == b.val); }
// constexpr auto operator<=>(const Mod &b) const = default;
constexpr bool operator!=(Mod b) const { return (val != b.val); }
constexpr bool operator<(Mod b) const { return (val < b.val); }
constexpr bool operator>(Mod b) const { return (val > b.val); }
constexpr bool operator<=(Mod b) const { return (val <= b.val); }
constexpr bool operator>=(Mod b) const { return (val >= b.val); }
// io
friend std::istream &operator>>(std::istream &in, Mod &a) {
V v;
in >> v;
a = Mod(v);
return in;
}
friend std::ostream &operator<<(std::ostream &out, const Mod &a) {
out << a.val;
return out;
}
// conversion
explicit constexpr operator T() const { return val; }
constexpr const T &operator()() const { return val; }
constexpr Mod operator-() const { return Mod(-val); }
};
constexpr int MOD = (int)1e9 + 7;
using Mint = Mod<std::integral_constant<std::decay<decltype(MOD)>::type, MOD>>;
std::vector<Mint> fac, ifac;
void init(int n) {
fac.assign(n + 1, 0);
ifac.assign(n + 1, 0);
fac[0] = 1;
for (int i = 1; i <= n; ++i) {
fac[i] = fac[i - 1] * i;
}
ifac.back() = fac.back().inv();
for (int i = n - 1; i >= 0; --i) {
ifac[i] = ifac[i + 1] * (i + 1);
}
}
Mint C(int n, int k) {
if (n < k || n < 0 || k < 0) {
return 0;
}
return fac[n] * ifac[n - k] * ifac[k];
}
Mint P(int n, int k) {
if (n < k || n < 0 || k < 0) {
return 0;
}
return fac[n] * ifac[n - k];
}
int main() {
#ifndef LOCAL
std::cin.tie(nullptr)->sync_with_stdio(false);
#endif
int n, m;
int64_t k;
std::cin >> n >> m >> k;
init(n);
std::vector<Mint> pk(n + 1);
pk[0] = 1;
for (int i = 1; i <= n; ++i) {
pk[i] = pk[i - 1] * k;
}
std::vector<Mint> kp(n + 1);
kp[0] = 1;
for (int i = 1; i <= n; ++i) {
kp[i] = kp[i - 1] * (k - i + 1);
}
auto ck = [&](int b) -> Mint {
if (b < 0 || k < b) {
return 0;
}
return kp[b] * ifac[b];
};
std::vector<std::vector<Mint>> dp(
m + 1, std::vector<Mint>(std::min<int64_t>(m, k) + 1));
dp[0][0] = 1;
for (int i = 1; i <= m; ++i) {
for (int j = 1; j <= (int)std::min<int64_t>(i, k); ++j) {
dp[i][j] = dp[i - 1][j - 1] * i;
if (i > 1) {
dp[i][j] += dp[i - 2][j - 1] * C(i, 2);
}
}
dp[i].resize(m + 1);
}
std::vector<Mint> num(m / 2 + 1);
for (int i = 1; i <= m / 2; ++i) {
int j = m - 2 * i;
Mint prod = 1;
for (int l = 0; l < i; ++l) {
prod *= k - l;
}
for (int d = 0; d <= j; ++d) {
num[i] += prod * dp[j][d] * ck(d);
prod *= Mint(k - d).inv() * (k - d - i);
}
}
Mint ans = 0;
{
Mint sum = 0;
for (int j = 1; j <= m; ++j) {
sum += dp[m][j] * ck(j);
}
for (int j = 1; j <= m / 2; ++j) {
sum -= num[j];
}
ans += sum * (n - m + 1) * pk[n - m];
}
for (int i = 1; i <= m / 2; ++i) {
int j = m - 2 * i;
for (int sz = m, mul = 1; sz <= n; sz += i + j, mul *= -1) {
ans += num[i] * mul * (n - sz + 1) * pk[n - sz];
}
}
std::cout << ans << '\n';
}
Details
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Test #1:
score: 100
Accepted
time: 1ms
memory: 3616kb
input:
4 2 3
output:
228
result:
ok 1 number(s): "228"
Test #2:
score: 0
Accepted
time: 108ms
memory: 34460kb
input:
999999 1999 12345678
output:
52352722
result:
ok 1 number(s): "52352722"
Test #3:
score: -100
Runtime Error
input:
7 4 2