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#[doc(hidden)]
#[macro_export]
macro_rules! impl_number_utils_for {
($type: ty) => {
impl NumberUtils for $type {
fn factorial(&self) -> Self {
if self <= &1 {
1
} else if self == &2 {
2
} else {
(3..=*self).fold(2, |x, y| x * y)
}
}
fn permutation(&self, k: u32) -> Self {
let k = k as $type;
if self < &k {
0
} else if self == &0 || k == 0 {
1
} else {
let self_k_1 = self - k + &1;
(self_k_1 + &1..=*self).fold(self_k_1, |x, y| x * y)
}
}
fn combination(&self, k: u32) -> Self {
let k = k as $type;
if self < &k {
0
} else if self == &0 || k == 0 || self == &k {
1
} else if k == 1 {
*self
} else {
self.permutation(k as u32) / k.factorial()
}
}
fn gcd(&self, mut m: Self) -> Self {
let mut n = *self;
if n == 0 {
return m;
}
if m == 0 {
return n;
}
let gcd_exponent_on_two = (n | m).trailing_zeros();
n >>= n.trailing_zeros();
m >>= m.trailing_zeros();
while n != m {
if n < m {
std::mem::swap(&mut n, &mut m);
}
n -= m;
n >>= n.trailing_zeros();
}
n << gcd_exponent_on_two
}
fn lcm(&self, m: Self) -> Self {
self / self.gcd(m) * m
}
fn isqrt(&self) -> Self {
if self < &2 {
return *self;
}
let mut shift = 2;
while self >> shift != 0 {
shift += 2;
}
let mut result = 0;
while shift >= 0 {
result <<= 1;
let large_cand = result + 1;
if large_cand * large_cand <= self >> shift {
result = large_cand;
}
shift -= 2;
}
result
}
fn checked_factorial(&self) -> Option<Self> {
if self <= &1 {
Some(1)
} else if self == &2 {
Some(2)
} else {
let mut result: $type = 2;
for i in 3..=*self {
result = result.checked_mul(i)?;
}
Some(result)
}
}
fn checked_permutation(&self, k: u32) -> Option<Self> {
let k = k as $type;
if self < &k {
Some(0)
} else if self == &0 || k == 0 {
Some(1)
} else {
let self_k_1 = self.checked_sub(k)?.checked_add(1)?;
let mut result = self_k_1;
for i in self_k_1 + 1..=*self {
result = result.checked_mul(i)?;
}
Some(result)
}
}
fn checked_combination(&self, k: u32) -> Option<Self> {
let k = k as $type;
if self < &k {
Some(0)
} else if self == &0 || k == 0 || self == &k {
Some(1)
} else if k == 1 {
Some(*self)
} else {
self.checked_permutation(k as u32)?.checked_div(k.checked_factorial()?)
}
}
fn digits(&self) -> Self {
if self == &0 {
1
} else {
(self.ilog10() + 1) as $type
}
}
}
};
( $($type: ty),* ) => {
$( impl_number_utils_for!($type); )*
}
}