# algorithm

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This module implements some common generic algorithms.

# Basic usage

```import algorithm

type People = tuple
year: int
name: string

var a: seq[People]

# Sorting with default system.cmp
a.sort()
assert a == @[(year: 2000, name: "John"), (year: 2005, name: "Marie"),
(year: 2010, name: "Jane")]

proc myCmp(x, y: People): int =
if x.name < y.name: -1 else: 1

# Sorting with custom proc
a.sort(myCmp)
assert a == @[(year: 2010, name: "Jane"), (year: 2000, name: "John"),
(year: 2005, name: "Marie")]```

# Types

```SortOrder = enum
Descending, Ascending```
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# Procs

`proc `*`(x: int; order: SortOrder): int {...}{.inline, raises: [], tags: [].}`

Flips x if order == Descending. If order == Ascending then x is returned.

x is supposed to be the result of a comparator, i.e.

< 0 for less than,
== 0 for equal,
> 0 for greater than.

Examples:

```assert `*`(-123, Descending) == 123
assert `*`(123, Descending) == -123
assert `*`(-123, Ascending) == -123
assert `*`(123, Ascending) == 123```
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`proc fill[T](a: var openArray[T]; first, last: Natural; value: T)`

Fills the slice a[first..last] with value.

If an invalid range is passed, it raises IndexError.

Examples:

```var a: array[6, int]
a.fill(1, 3, 9)
assert a == [0, 9, 9, 9, 0, 0]
a.fill(3, 5, 7)
assert a == [0, 9, 9, 7, 7, 7]
doAssertRaises(IndexError, a.fill(1, 7, 9))```
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`proc fill[T](a: var openArray[T]; value: T)`
Fills the container a with value.

Examples:

```var a: array[6, int]
a.fill(9)
assert a == [9, 9, 9, 9, 9, 9]
a.fill(4)
assert a == [4, 4, 4, 4, 4, 4]```
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`proc reverse[T](a: var openArray[T]; first, last: Natural)`

Reverses the slice a[first..last].

If an invalid range is passed, it raises IndexError.

Examples:

```var a = [1, 2, 3, 4, 5, 6]
a.reverse(1, 3)
assert a == [1, 4, 3, 2, 5, 6]
a.reverse(1, 3)
assert a == [1, 2, 3, 4, 5, 6]
doAssertRaises(IndexError, a.reverse(1, 7))```
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`proc reverse[T](a: var openArray[T])`

Reverses the contents of the container a.

Examples:

```var a = [1, 2, 3, 4, 5, 6]
a.reverse()
assert a == [6, 5, 4, 3, 2, 1]
a.reverse()
assert a == [1, 2, 3, 4, 5, 6]```
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`proc reversed[T](a: openArray[T]; first: Natural; last: int): seq[T]`

Returns the reverse of the slice a[first..last].

If an invalid range is passed, it raises IndexError.

Examples:

```let
a = [1, 2, 3, 4, 5, 6]
b = a.reversed(1, 3)
assert b == @[4, 3, 2]```
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`proc reversed[T](a: openArray[T]): seq[T]`

Returns the reverse of the container a.

Examples:

```let
a = [1, 2, 3, 4, 5, 6]
b = reversed(a)
assert b == @[6, 5, 4, 3, 2, 1]```
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```proc binarySearch[T, K](a: openArray[T]; key: K;
cmp: proc (x: T; y: K): int {...}{.closure.}): int```

cmp is the comparator function to use, the expected return values are the same as that of system.cmp.

Examples:

```assert binarySearch(["a", "b", "c", "d"], "d", system.cmp[string]) == 3
assert binarySearch(["a", "b", "d", "c"], "d", system.cmp[string]) == 2```
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`proc binarySearch[T](a: openArray[T]; key: T): int`

Examples:

```assert binarySearch([0, 1, 2, 3, 4], 4) == 4
assert binarySearch([0, 1, 4, 2, 3], 4) == 2```
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```proc smartBinarySearch[T](a: openArray[T]; key: T): int {...}{.
deprecated: "Deprecated since v0.18.1; Use \'binarySearch\'".}```
Deprecated: Deprecated since v0.18.1; Use 'binarySearch'
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`proc lowerBound[T, K](a: openArray[T]; key: K; cmp: proc (x: T; k: K): int {...}{.closure.}): int`

Returns a position to the first element in the a that is greater than key, or last if no such element is found. In other words if you have a sorted sequence and you call insert(thing, elm, lowerBound(thing, elm)) the sequence will still be sorted.

If an invalid range is passed, it raises IndexError.

The version uses cmp to compare the elements. The expected return values are the same as that of system.cmp.

Examples:

```var arr = @[1, 2, 3, 5, 6, 7, 8, 9]
assert arr.lowerBound(3, system.cmp[int]) == 2
assert arr.lowerBound(4, system.cmp[int]) == 3
assert arr.lowerBound(5, system.cmp[int]) == 3
arr.insert(4, arr.lowerBound(4, system.cmp[int]))
assert arr == [1, 2, 3, 4, 5, 6, 7, 8, 9]```
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`proc lowerBound[T](a: openArray[T]; key: T): int`

Returns a position to the first element in the a that is greater than key, or last if no such element is found. In other words if you have a sorted sequence and you call insert(thing, elm, lowerBound(thing, elm)) the sequence will still be sorted.

The version uses the default comparison function cmp.

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`proc upperBound[T, K](a: openArray[T]; key: K; cmp: proc (x: T; k: K): int {...}{.closure.}): int`

Returns a position to the first element in the a that is not less (i.e. greater or equal to) than key, or last if no such element is found. In other words if you have a sorted sequence and you call insert(thing, elm, upperBound(thing, elm)) the sequence will still be sorted.

If an invalid range is passed, it raises IndexError.

The version uses cmp to compare the elements. The expected return values are the same as that of system.cmp.

Examples:

```var arr = @[1, 2, 3, 5, 6, 7, 8, 9]
assert arr.upperBound(2, system.cmp[int]) == 2
assert arr.upperBound(3, system.cmp[int]) == 3
assert arr.upperBound(4, system.cmp[int]) == 3
arr.insert(4, arr.upperBound(3, system.cmp[int]))
assert arr == [1, 2, 3, 4, 5, 6, 7, 8, 9]```
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`proc upperBound[T](a: openArray[T]; key: T): int`

Returns a position to the first element in the a that is not less (i.e. greater or equal to) than key, or last if no such element is found. In other words if you have a sorted sequence and you call insert(thing, elm, upperBound(thing, elm)) the sequence will still be sorted.

The version uses the default comparison function cmp.

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`proc sort[T](a: var openArray[T]; order = SortOrder.Ascending)`

Shortcut version of sort that uses system.cmp[T] as the comparison function.

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```proc sorted[T](a: openArray[T]; cmp: proc (x, y: T): int {...}{.closure.};
order = SortOrder.Ascending): seq[T]```

Returns a sorted by cmp in the specified order.

Examples:

```let
a = [2, 3, 1, 5, 4]
b = sorted(a, system.cmp[int])
c = sorted(a, system.cmp[int], Descending)
d = sorted(["adam", "dande", "brian", "cat"], system.cmp[string])
assert b == @[1, 2, 3, 4, 5]
assert c == @[5, 4, 3, 2, 1]
assert d == @["adam", "brian", "cat", "dande"]```
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`proc sorted[T](a: openArray[T]; order = SortOrder.Ascending): seq[T]`

Shortcut version of sorted that uses system.cmp[T] as the comparison function.

Examples:

```let
a = [2, 3, 1, 5, 4]
b = sorted(a)
c = sorted(a, Descending)
d = sorted(["adam", "dande", "brian", "cat"])
assert b == @[1, 2, 3, 4, 5]
assert c == @[5, 4, 3, 2, 1]
assert d == @["adam", "brian", "cat", "dande"]```
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`proc isSorted[T](a: openArray[T]; order = SortOrder.Ascending): bool`

Shortcut version of isSorted that uses system.cmp[T] as the comparison function.

Examples:

```let
a = [2, 3, 1, 5, 4]
b = [1, 2, 3, 4, 5]
c = [5, 4, 3, 2, 1]
d = ["adam", "brian", "cat", "dande"]
e = ["adam", "dande", "brian", "cat"]
assert isSorted(a) == false
assert isSorted(b) == true
assert isSorted(c) == false
assert isSorted(c, Descending) == true
assert isSorted(d) == true
assert isSorted(e) == false```
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`proc product[T](x: openArray[seq[T]]): seq[seq[T]]`
Produces the Cartesian product of the array. Warning: complexity may explode.

Examples:

```assert product(@[@[1], @[2]]) == @[@[1, 2]]
assert product(@[@["A", "K"], @["Q"]]) == @[@["K", "Q"], @["A", "Q"]]```
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`proc nextPermutation[T](x: var openArray[T]): bool {...}{.discardable.}`

Calculates the next lexicographic permutation, directly modifying x. The result is whether a permutation happened, otherwise we have reached the last-ordered permutation.

If you start with an unsorted array/seq, the repeated permutations will not give you all permutations but stop with last.

Examples:

```var v = @[0, 1, 2, 3]
assert v.nextPermutation() == true
assert v == @[0, 1, 3, 2]
assert v.nextPermutation() == true
assert v == @[0, 2, 1, 3]
assert v.prevPermutation() == true
assert v == @[0, 1, 3, 2]
v = @[3, 2, 1, 0]
assert v.nextPermutation() == false
assert v == @[3, 2, 1, 0]```
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`proc prevPermutation[T](x: var openArray[T]): bool {...}{.discardable.}`

Calculates the previous lexicographic permutation, directly modifying x. The result is whether a permutation happened, otherwise we have reached the first-ordered permutation.

Examples:

```var v = @[0, 1, 2, 3]
assert v.prevPermutation() == false
assert v == @[0, 1, 2, 3]
assert v.nextPermutation() == true
assert v == @[0, 1, 3, 2]
assert v.prevPermutation() == true
assert v == @[0, 1, 2, 3]```
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```proc rotateLeft[T](arg: var openArray[T]; slice: HSlice[int, int]; dist: int): int {...}{.
Performs a left rotation on a range of elements. If you want to rotate right, use a negative dist. Specifically, rotateLeft rotates the elements at slice by dist positions.

The element at index slice.a + dist will be at index slice.a.
The element at index slice.b will be at slice.a + dist -1.
The element at index slice.a will be at slice.b + 1 - dist.
The element at index slice.a + dist - 1 will be at slice.b.

Elements outside of slice will be left unchanged. The time complexity is linear to slice.b - slice.a + 1. If an invalid range (HSlice) is passed, it raises IndexError.

slice
The indices of the element range that should be rotated.
dist
The distance in amount of elements that the data should be rotated. Can be negative, can be any number.

Examples:

```var a = [0, 1, 2, 3, 4, 5]
a.rotateLeft(1 .. 4, 3)
assert a == [0, 4, 1, 2, 3, 5]
a.rotateLeft(1 .. 4, 3)
assert a == [0, 3, 4, 1, 2, 5]
a.rotateLeft(1 .. 4, -3)
assert a == [0, 4, 1, 2, 3, 5]
doAssertRaises(IndexError, a.rotateLeft(1 .. 7, 2))```
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`proc rotateLeft[T](arg: var openArray[T]; dist: int): int {...}{.discardable.}`

Default arguments for slice, so that this procedure operates on the entire arg, and not just on a part of it.

Examples:

```var a = [1, 2, 3, 4, 5]
a.rotateLeft(2)
assert a == [3, 4, 5, 1, 2]
a.rotateLeft(4)
assert a == [2, 3, 4, 5, 1]
a.rotateLeft(-6)
assert a == [1, 2, 3, 4, 5]```
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`proc rotatedLeft[T](arg: openArray[T]; slice: HSlice[int, int]; dist: int): seq[T]`

Same as rotateLeft, just with the difference that it does not modify the argument. It creates a new seq instead.

Elements outside of slice will be left unchanged. If an invalid range (HSlice) is passed, it raises IndexError.

slice
The indices of the element range that should be rotated.
dist
The distance in amount of elements that the data should be rotated. Can be negative, can be any number.

Examples:

```var a = @[1, 2, 3, 4, 5]
a = rotatedLeft(a, 1 .. 4, 3)
assert a == @[1, 5, 2, 3, 4]
a = rotatedLeft(a, 1 .. 3, 2)
assert a == @[1, 3, 5, 2, 4]
a = rotatedLeft(a, 1 .. 3, -2)
assert a == @[1, 5, 2, 3, 4]```
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`proc rotatedLeft[T](arg: openArray[T]; dist: int): seq[T]`

Same as rotateLeft, just with the difference that it does not modify the argument. It creates a new seq instead.

Examples:

```var a = @[1, 2, 3, 4, 5]
a = rotatedLeft(a, 2)
assert a == @[3, 4, 5, 1, 2]
a = rotatedLeft(a, 4)
assert a == @[2, 3, 4, 5, 1]
a = rotatedLeft(a, -6)
assert a == @[1, 2, 3, 4, 5]```
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# Funcs

```func sort[T](a: var openArray[T]; cmp: proc (x, y: T): int {...}{.closure.};
order = SortOrder.Ascending)```

Default Nim sort (an implementation of merge sort). The sorting is guaranteed to be stable and the worst case is guaranteed to be O(n log n).

The current implementation uses an iterative mergesort to achieve this. It uses a temporary sequence of length a.len div 2. If you do not wish to provide your own cmp, you may use system.cmp or instead call the overloaded version of sort, which uses system.cmp.

```sort(myIntArray, system.cmp[int])
# do not use cmp[string] here as we want to use the specialized
sort(myStrArray, system.cmp)```

You can inline adhoc comparison procs with the do notation. Example:

```people.sort do (x, y: Person) -> int:
result = cmp(x.surname, y.surname)
if result == 0:
result = cmp(x.name, y.name)```

Examples:

```var d = ["boo", "fo", "barr", "qux"]
proc myCmp(x, y: string): int =
if x.len() > y.len() or x.len() == y.len():
1
else:
-1

sort(d, myCmp)
assert d == ["fo", "qux", "boo", "barr"]```
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```func isSorted[T](a: openArray[T]; cmp: proc (x, y: T): int {...}{.closure.};
order = SortOrder.Ascending): bool```

Checks to see whether a is already sorted in order using cmp for the comparison. Parameters identical to sort. Requires O(n) time.

Examples:

```let
a = [2, 3, 1, 5, 4]
b = [1, 2, 3, 4, 5]
c = [5, 4, 3, 2, 1]
d = ["adam", "brian", "cat", "dande"]
e = ["adam", "dande", "brian", "cat"]
assert isSorted(a) == false
assert isSorted(b) == true
assert isSorted(c) == false
assert isSorted(c, Descending) == true
assert isSorted(d) == true
assert isSorted(e) == false```
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# Templates

`template sortedByIt(seq1, op: untyped): untyped`

Convenience template around the sorted proc to reduce typing.

The template injects the it variable which you can use directly in an expression.

Because the underlying cmp() is defined for tuples you can do a nested sort.

Examples:

```type
Person = tuple[name: string, age: int]
var
p1: Person = (name: "p1", age: 60)
p2: Person = (name: "p2", age: 20)
p3: Person = (name: "p3", age: 30)
p4: Person = (name: "p4", age: 30)
people = @[p1, p2, p4, p3]
assert people.sortedByIt(it.name) ==
@[(name: "p1", age: 60), (name: "p2", age: 20), (name: "p3", age: 30),
(name: "p4", age: 30)]
assert people.sortedByIt((it.age, it.name)) ==
@[(name: "p2", age: 20), (name: "p3", age: 30), (name: "p4", age: 30),
(name: "p1", age: 60)]```
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