algorithm

This module implements some common generic algorithms.

Basic usage

import algorithm

type People = tuple
  year: int
  name: string

var a: seq[People]

a.add((2000, "John"))
a.add((2005, "Marie"))
a.add((2010, "Jane"))

# 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
  elif x.name == y.name: 0
  else: 1

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

See also

• sequtils module for working with the built-in seq type
• tables module for sorting tables

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.

Example:

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 IndexDefect.

Example:

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(IndexDefect, a.fill(1, 7, 9))

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proc fill[T](a: var openArray[T]; value: T)

Fills the container a with value.

Example:

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 IndexDefect.

See also:

• reversed proc reverse a slice and returns a seq[T]
• reversed proc reverse and returns a seq[T]

Example:

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(IndexDefect, a.reverse(1, 7))

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proc reverse[T](a: var openArray[T])

Reverses the contents of the container a.

See also:

• reversed proc reverse a slice and returns a seq[T]
• reversed proc reverse and returns a seq[T]

Example:

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 IndexDefect.

See also:

• reverse proc reverse a slice
• reverse proc

Example:

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.

See also:

• reverse proc reverse a slice
• reverse proc

Example:

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

Binary search for key in a. Returns -1 if not found.

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

Example:

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

Binary search for key in a. Returns -1 if not found.

Example:

assert binarySearch([0, 1, 2, 3, 4], 4) == 4
assert binarySearch([0, 1, 4, 2, 3], 4) == 2

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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 IndexDefect.

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

See also:

• upperBound proc sorted by cmp in the specified order
• upperBound proc

Example:

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.

See also:

• upperBound proc sorted by cmp in the specified order
• upperBound proc

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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 IndexDefect.

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

See also:

• lowerBound proc sorted by cmp in the specified order
• lowerBound proc

Example:

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.

See also:

• lowerBound proc sorted by cmp in the specified order
• lowerBound proc

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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.

See also:

• sort func
• sorted proc sorted by cmp in the specified order
• sorted proc
• sortedByIt template

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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.

See also:

• sort func
• sort proc
• sortedByIt template

Example:

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.

See also:

• sort func
• sort proc
• sortedByIt template

Example:

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.

See also:

• isSorted func

Example:

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.

Example:

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.

See also:

• prevPermutation proc

Example:

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.

See also:

• nextPermutation proc

Example:

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 {...}{.
    discardable.}

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 IndexDefect.

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.

See also:

• rotateLeft proc for a version which rotates the whole container
• rotatedLeft proc for a version which returns a seq[T]

Example:

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(IndexDefect, 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.

See also:

• rotateLeft proc for a version which rotates a range
• rotatedLeft proc for a version which returns a seq[T]

Example:

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 IndexDefect.

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.

See also:

• rotateLeft proc for the in-place version of this proc
• rotatedLeft proc for a version which rotates the whole container

Example:

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.

See also:

• rotateLeft proc for the in-place version of this proc
• rotatedLeft proc for a version which rotates a range

Example:

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
# overload:
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)

See also:

• sort proc
• sorted proc sorted by cmp in the specified order
• sorted proc
• sortedByIt template

Example:

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.

See also:

• isSorted proc

Example:

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.

See also:

• sort func
• sort proc
• sorted proc sorted by cmp in the specified order
• sorted proc

Example:

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)]
# Nested sort
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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