# Ranges and Progressions

Kotlin lets you easily create ranges of values using the `rangeTo()`

function from the `kotlin.ranges`

package and its operator form `..`

.
Usually, `rangeTo()`

is complemented by `in`

or `!in`

functions.

```
if (i in 1..4) { // equivalent of 1 <= i && i <= 4
print(i)
}
```

Integral type ranges (`IntRange`

, `LongRange`

, `CharRange`

) have an extra feature: they can be iterated over.
These ranges are also progressions of the corresponding integral types.
Such ranges are generally used for iteration in the `for`

loops.

```
fun main() {
//sampleStart
for (i in 1..4) print(i)
//sampleEnd
}
```

To iterate numbers in reverse order, use the `downTo`

function instead of `..`

.

```
fun main() {
//sampleStart
for (i in 4 downTo 1) print(i)
//sampleEnd
}
```

It is also possible to iterate over numbers with an arbitrary step (not necessarily 1). This is done via the `step`

function.

```
fun main() {
//sampleStart
for (i in 1..8 step 2) print(i)
println()
for (i in 8 downTo 1 step 2) print(i)
//sampleEnd
}
```

To iterate a number range which does not include its end element, use the `until`

function:

```
fun main() {
//sampleStart
for (i in 1 until 10) { // i in [1, 10), 10 is excluded
print(i)
}
//sampleEnd
}
```

## Range

A range defines a closed interval in the mathematical sense: it is defined by its two endpoint values which are both included in the range.
Ranges are defined for comparable types: having an order, you can define whether an arbitrary instance is in the range between two given instances.
The main operation on ranges is `contains`

, which is usually used in the form of `in`

and `!in`

operators.

To create a range for your class, call the `rangeTo()`

function on the range start value and provide the end value as an argument.
`rangeTo()`

is often called in its operator form `..`

.

```
class Version(val major: Int, val minor: Int): Comparable<Version> {
override fun compareTo(other: Version): Int {
if (this.major != other.major) {
return this.major - other.major
} else if (this.minor != other.minor) {
return this.minor - other.minor
} else return 0
}
}
fun main() {
//sampleStart
val versionRange = Version(1, 11)..Version(1, 30)
println(Version(0, 9) in versionRange)
println(Version(1, 20) in versionRange)
//sampleEnd
}
```

## Progression

As shown in the examples above, the ranges of integral types, such as `Int`

, `Long`

, and `Char`

, can be treated as arithmetic progressions of them.
In Kotlin, these progressions are defined by special types: `IntProgression`

, `LongProgression`

, and `CharProgression`

.

Progressions have three essential properties: the `first`

element, the `last`

element, and a non-zero `step`

.
The first element is `first`

, subsequent elements are the previous element plus a `step`

.
The last element is always hit by iteration unless the progression is empty.
Iteration over a progression with a positive step is equivalent to an indexed `for`

loop in Java/JavaScript.

```
for (int i = first; i <= last; i += step) {
// ...
}
```

When you create a progression implicitly by iterating a range, this progression's `first`

and `last`

elements are the range's endpoints, and the `step`

is 1.

```
fun main() {
//sampleStart
for (i in 1..10) print(i)
//sampleEnd
}
```

To define a custom progression step, use the `step`

function on a range.

```
fun main() {
//sampleStart
for (i in 1..8 step 2) print(i)
//sampleEnd
}
```

The last element of the progression is calculated to find the maximum value not greater than the end value for a positive step or the minimum value not less than the end value for a negative step such that `(last - first) % step == 0`

.

To create a progression for iterating in reverse order, use `downTo`

instead of `..`

when defining the range for it.

```
fun main() {
//sampleStart
for (i in 4 downTo 1) print(i)
//sampleEnd
}
```

Progressions implement `Iterable<N>`

, where `N`

is `Int`

, `Long`

, or `Char`

respectively, so you can use them in various collection functions like `map`

, `filter`

, and other.

```
fun main() {
//sampleStart
println((1..10).filter { it % 2 == 0 })
//sampleEnd
}
```