```
pub trait Ord: Eq + PartialOrd {
// Required method
fn cmp(&self, other: &Self) -> Ordering;
// Provided methods
fn max(self, other: Self) -> Self
where Self: Sized { ... }
fn min(self, other: Self) -> Self
where Self: Sized { ... }
fn clamp(self, min: Self, max: Self) -> Self
where Self: Sized { ... }
}
```

## Expand description

Trait for types that form a total order.

Implementations must be consistent with the `PartialOrd`

implementation, and ensure `max`

,
`min`

, and `clamp`

are consistent with `cmp`

:

`partial_cmp(a, b) == Some(cmp(a, b))`

.`max(a, b) == max_by(a, b, cmp)`

(ensured by the default implementation).`min(a, b) == min_by(a, b, cmp)`

(ensured by the default implementation).- For
`a.clamp(min, max)`

, see the method docs (ensured by the default implementation).

Violating these requirements is a logic error. The behavior resulting from a logic error is not
specified, but users of the trait must ensure that such logic errors do *not* result in
undefined behavior. This means that `unsafe`

code **must not** rely on the correctness of these
methods.

### §Corollaries

From the above and the requirements of `PartialOrd`

, it follows that for all `a`

, `b`

and `c`

:

- exactly one of
`a < b`

,`a == b`

or`a > b`

is true; and `<`

is transitive:`a < b`

and`b < c`

implies`a < c`

. The same must hold for both`==`

and`>`

.

Mathematically speaking, the `<`

operator defines a strict weak order. In cases where `==`

conforms to mathematical equality, it also defines a strict total order.

### §Derivable

This trait can be used with `#[derive]`

.

When `derive`

d on structs, it will produce a
lexicographic ordering based on the
top-to-bottom declaration order of the struct’s members.

When `derive`

d on enums, variants are ordered primarily by their discriminants. Secondarily,
they are ordered by their fields. By default, the discriminant is smallest for variants at the
top, and largest for variants at the bottom. Here’s an example:

However, manually setting the discriminants can override this default behavior:

```
#[derive(PartialEq, Eq, PartialOrd, Ord)]
enum E {
Top = 2,
Bottom = 1,
}
assert!(E::Bottom < E::Top);
```

### §Lexicographical comparison

Lexicographical comparison is an operation with the following properties:

- Two sequences are compared element by element.
- The first mismatching element defines which sequence is lexicographically less or greater than the other.
- If one sequence is a prefix of another, the shorter sequence is lexicographically less than the other.
- If two sequences have equivalent elements and are of the same length, then the sequences are lexicographically equal.
- An empty sequence is lexicographically less than any non-empty sequence.
- Two empty sequences are lexicographically equal.

### §How can I implement `Ord`

?

`Ord`

requires that the type also be `PartialOrd`

, `PartialEq`

, and `Eq`

.

Because `Ord`

implies a stronger ordering relationship than `PartialOrd`

, and both `Ord`

and
`PartialOrd`

must agree, you must choose how to implement `Ord`

**first**. You can choose to
derive it, or implement it manually. If you derive it, you should derive all four traits. If you
implement it manually, you should manually implement all four traits, based on the
implementation of `Ord`

.

Here’s an example where you want to define the `Character`

comparison by `health`

and
`experience`

only, disregarding the field `mana`

:

```
use std::cmp::Ordering;
struct Character {
health: u32,
experience: u32,
mana: f32,
}
impl Ord for Character {
fn cmp(&self, other: &Self) -> std::cmp::Ordering {
self.experience
.cmp(&other.experience)
.then(self.health.cmp(&other.health))
}
}
impl PartialOrd for Character {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl PartialEq for Character {
fn eq(&self, other: &Self) -> bool {
self.health == other.health && self.experience == other.experience
}
}
impl Eq for Character {}
```

If all you need is to `slice::sort`

a type by a field value, it can be simpler to use
`slice::sort_by_key`

.

### §Examples of incorrect `Ord`

implementations

```
use std::cmp::Ordering;
#[derive(Debug)]
struct Character {
health: f32,
}
impl Ord for Character {
fn cmp(&self, other: &Self) -> std::cmp::Ordering {
if self.health < other.health {
Ordering::Less
} else if self.health > other.health {
Ordering::Greater
} else {
Ordering::Equal
}
}
}
impl PartialOrd for Character {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl PartialEq for Character {
fn eq(&self, other: &Self) -> bool {
self.health == other.health
}
}
impl Eq for Character {}
let a = Character { health: 4.5 };
let b = Character { health: f32::NAN };
// Mistake: floating-point values do not form a total order and using the built-in comparison
// operands to implement `Ord` irregardless of that reality does not change it. Use
// `f32::total_cmp` if you need a total order for floating-point values.
// Reflexivity requirement of `Ord` is not given.
assert!(a == a);
assert!(b != b);
// Antisymmetry requirement of `Ord` is not given. Only one of a < c and c < a is allowed to be
// true, not both or neither.
assert_eq!((a < b) as u8 + (b < a) as u8, 0);
```

```
use std::cmp::Ordering;
#[derive(Debug)]
struct Character {
health: u32,
experience: u32,
}
impl PartialOrd for Character {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for Character {
fn cmp(&self, other: &Self) -> std::cmp::Ordering {
if self.health < 50 {
self.health.cmp(&other.health)
} else {
self.experience.cmp(&other.experience)
}
}
}
// For performance reasons implementing `PartialEq` this way is not the idiomatic way, but it
// ensures consistent behavior between `PartialEq`, `PartialOrd` and `Ord` in this example.
impl PartialEq for Character {
fn eq(&self, other: &Self) -> bool {
self.cmp(other) == Ordering::Equal
}
}
impl Eq for Character {}
let a = Character {
health: 3,
experience: 5,
};
let b = Character {
health: 10,
experience: 77,
};
let c = Character {
health: 143,
experience: 2,
};
// Mistake: The implementation of `Ord` compares different fields depending on the value of
// `self.health`, the resulting order is not total.
// Transitivity requirement of `Ord` is not given. If a is smaller than b and b is smaller than
// c, by transitive property a must also be smaller than c.
assert!(a < b && b < c && c < a);
// Antisymmetry requirement of `Ord` is not given. Only one of a < c and c < a is allowed to be
// true, not both or neither.
assert_eq!((a < c) as u8 + (c < a) as u8, 2);
```

The documentation of `PartialOrd`

contains further examples, for example it’s wrong for
`PartialOrd`

and `PartialEq`

to disagree.

## Required Methods§

## Provided Methods§

1.21.0 · source#### fn max(self, other: Self) -> Selfwhere
Self: Sized,

#### fn max(self, other: Self) -> Selfwhere
Self: Sized,

Compares and returns the maximum of two values.

Returns the second argument if the comparison determines them to be equal.

##### §Examples

1.21.0 · source#### fn min(self, other: Self) -> Selfwhere
Self: Sized,

#### fn min(self, other: Self) -> Selfwhere
Self: Sized,

Compares and returns the minimum of two values.

Returns the first argument if the comparison determines them to be equal.

##### §Examples

## Object Safety§

**not**object safe.

## Implementors§

### impl Ord for AsciiChar

### impl Ord for Infallible

### impl Ord for ErrorKind

### impl Ord for IpAddr

### impl Ord for SocketAddr

### impl Ord for Ordering

### impl Ord for bool

### impl Ord for char

### impl Ord for i8

### impl Ord for i16

### impl Ord for i32

### impl Ord for i64

### impl Ord for i128

### impl Ord for isize

### impl Ord for !

### impl Ord for str

Implements ordering of strings.

Strings are ordered lexicographically by their byte values. This orders Unicode code
points based on their positions in the code charts. This is not necessarily the same as
“alphabetical” order, which varies by language and locale. Sorting strings according to
culturally-accepted standards requires locale-specific data that is outside the scope of
the `str`

type.

### impl Ord for u8

### impl Ord for u16

### impl Ord for u32

### impl Ord for u64

### impl Ord for u128

### impl Ord for ()

### impl Ord for usize

### impl Ord for CpuidResult

### impl Ord for TypeId

### impl Ord for CStr

### impl Ord for CString

### impl Ord for OsStr

### impl Ord for OsString

### impl Ord for Error

### impl Ord for PhantomPinned

### impl Ord for Ipv4Addr

### impl Ord for Ipv6Addr

### impl Ord for SocketAddrV4

### impl Ord for SocketAddrV6

### impl Ord for Components<'_>

### impl Ord for Path

### impl Ord for PathBuf

### impl Ord for PrefixComponent<'_>

### impl Ord for Alignment

### impl Ord for String

### impl Ord for Duration

### impl Ord for Instant

### impl Ord for SystemTime

### impl<'a> Ord for Component<'a>

### impl<'a> Ord for Prefix<'a>

### impl<'a> Ord for Location<'a>

### impl<A> Ord for &A

### impl<A> Ord for &mut A

### impl<B> Ord for Cow<'_, B>

### impl<Dyn> Ord for DynMetadata<Dyn>where
Dyn: ?Sized,

### impl<F> Ord for Fwhere
F: FnPtr,

### impl<K, V, A> Ord for BTreeMap<K, V, A>

### impl<Ptr> Ord for Pin<Ptr>

### impl<T> Ord for Option<T>where
T: Ord,

### impl<T> Ord for Poll<T>where
T: Ord,

### impl<T> Ord for *const Twhere
T: ?Sized,

### impl<T> Ord for *mut Twhere
T: ?Sized,

### impl<T> Ord for [T]where
T: Ord,

Implements comparison of slices lexicographically.

### impl<T> Ord for (T₁, T₂, …, Tₙ)

This trait is implemented for tuples up to twelve items long.

### impl<T> Ord for Cell<T>

### impl<T> Ord for RefCell<T>

### impl<T> Ord for PhantomData<T>where
T: ?Sized,

### impl<T> Ord for ManuallyDrop<T>

### impl<T> Ord for NonZero<T>where
T: ZeroablePrimitive + Ord,

### impl<T> Ord for Saturating<T>where
T: Ord,

### impl<T> Ord for Wrapping<T>where
T: Ord,

### impl<T> Ord for NonNull<T>where
T: ?Sized,

### impl<T> Ord for Reverse<T>where
T: Ord,

### impl<T, A> Ord for Box<T, A>

### impl<T, A> Ord for BTreeSet<T, A>

### impl<T, A> Ord for LinkedList<T, A>

### impl<T, A> Ord for VecDeque<T, A>

### impl<T, A> Ord for Rc<T, A>

### impl<T, A> Ord for Arc<T, A>

### impl<T, A> Ord for Vec<T, A>

Implements ordering of vectors, lexicographically.

### impl<T, E> Ord for Result<T, E>

### impl<T, const N: usize> Ord for [T; N]where
T: Ord,

Implements comparison of arrays lexicographically.