Factorial table
(Mylib/Combinatorics/factorial_table.cpp)
Operations
-
factorial_table(int N)
- $0!$ ~ $N!$とその逆数を計算する。
- Time complexity $O(N)$
-
factorial(int i)
: return $i!$
-
inv_factorial(int i)
: return $\frac{1}{i!}$
-
P(int n, int k)
: return $_nP_k$
-
C(int n, int k)
: return $_nC_k$
-
H(int n, int k)
: return $_nH_k = _{n+k-1}C_k$
Requirements
Notes
Problems
References
Required by
Verified with
Code
#pragma once
#include <cassert>
#include <cstdint>
#include <vector>
namespace haar_lib {
template <typename T>
class factorial_table {
public:
using value_type = T;
private:
int N_;
std::vector<T> f_table_, if_table_;
public:
factorial_table() {}
factorial_table(int N) : N_(N) {
f_table_.assign(N + 1, 1);
if_table_.assign(N + 1, 1);
for (int i = 1; i <= N; ++i) {
f_table_[i] = f_table_[i - 1] * i;
}
if_table_[N] = f_table_[N].inv();
for (int i = N; --i >= 0;) {
if_table_[i] = if_table_[i + 1] * (i + 1);
}
}
T factorial(int64_t i) const {
assert(0 <= i and i <= N_);
return f_table_[i];
}
T inv_factorial(int64_t i) const {
assert(0 <= i and i <= N_);
return if_table_[i];
}
T P(int64_t n, int64_t k) const {
if (n < k or n < 0 or k < 0) return 0;
return factorial(n) * inv_factorial(n - k);
}
T C(int64_t n, int64_t k) const {
if (n < k or n < 0 or k < 0) return 0;
return P(n, k) * inv_factorial(k);
}
T H(int64_t n, int64_t k) const {
if (n == 0 and k == 0) return 1;
return C(n + k - 1, k);
}
};
} // namespace haar_lib
#line 2 "Mylib/Combinatorics/factorial_table.cpp"
#include <cassert>
#include <cstdint>
#include <vector>
namespace haar_lib {
template <typename T>
class factorial_table {
public:
using value_type = T;
private:
int N_;
std::vector<T> f_table_, if_table_;
public:
factorial_table() {}
factorial_table(int N) : N_(N) {
f_table_.assign(N + 1, 1);
if_table_.assign(N + 1, 1);
for (int i = 1; i <= N; ++i) {
f_table_[i] = f_table_[i - 1] * i;
}
if_table_[N] = f_table_[N].inv();
for (int i = N; --i >= 0;) {
if_table_[i] = if_table_[i + 1] * (i + 1);
}
}
T factorial(int64_t i) const {
assert(0 <= i and i <= N_);
return f_table_[i];
}
T inv_factorial(int64_t i) const {
assert(0 <= i and i <= N_);
return if_table_[i];
}
T P(int64_t n, int64_t k) const {
if (n < k or n < 0 or k < 0) return 0;
return factorial(n) * inv_factorial(n - k);
}
T C(int64_t n, int64_t k) const {
if (n < k or n < 0 or k < 0) return 0;
return P(n, k) * inv_factorial(k);
}
T H(int64_t n, int64_t k) const {
if (n == 0 and k == 0) return 1;
return C(n + k - 1, k);
}
};
} // namespace haar_lib
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