Flips the sign of 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

Binary search for key in a. Return the index of key or -1 if not found. Assumes that a is sorted according to cmp.

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

Example:

assert binarySearch(["a", "b", "c", "d"], "d", system.cmp[string]) == 3
assert binarySearch(["a", "b", "c", "d"], "c", system.cmp[string]) == 2

Example:

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

Assigns value to all elements of the slice a[first..last].

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))

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]

Checks to see whether a is already sorted in order using cmp for the comparison. The parameters are 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

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

Returns the index of the first element in a that is not less than (i.e. greater or equal to) 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. Assumes that a is sorted according to cmp.

If an invalid range is passed, it raises IndexDefect.

This version uses cmp to compare the elements. The expected return values are the same as those 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]

Returns the index of the first element in a that is not less than (i.e. greater or equal to) 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. Assumes that a is sorted.

This version uses the default comparison function cmp.

See also:

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

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

See also:

• merge proc

Example:

let x = [5, 10, 15, 20, 25]
let y = [50, 40, 30, 20, 10].sorted

var merged: seq[int]
merged.merge(x, y)
assert merged.isSorted
assert merged == @[5, 10, 10, 15, 20, 20, 25, 30, 40, 50]

See also:

• merge proc

Example:

let x = @[1, 3, 6]
let y = @[2, 3, 4]

block:
  var merged = @[7] # new data is appended to merged sequence
  merged.merge(x, y, system.cmp[int])
  assert merged == @[7, 1, 2, 3, 3, 4, 6]

block:
  var merged = @[7] # if you only want new data, clear merged sequence first
  merged.setLen(0)
  merged.merge(x, y, system.cmp[int])
  assert merged.isSorted
  assert merged == @[1, 2, 3, 3, 4, 6]

import std/sugar

var res: seq[(int, int)]
res.merge([(1, 1)], [(1, 2)], (a, b) => a[0] - b[0])
assert res == @[(1, 1), (1, 2)]

assert seq[int].default.dup(merge([1, 3], [2, 4])) == @[1, 2, 3, 4]

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 the 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]

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]

Example:

assert product(@[@[1], @[2]]) == @[@[1, 2]]
assert product(@[@["A", "K"], @["Q"]]) == @[@["K", "Q"], @["A", "Q"]]

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]

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))

Returns the elements of a in reverse order.

See also:

• reverse proc

Example:

assert [10, 11, 12].reversed == @[12, 11, 10]
assert seq[string].default.reversed == @[]

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]

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]

Same as rotateLeft, but with 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]

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))

Default Nim sort (an implementation of merge sort). The sorting is guaranteed to be stable (that is, equal elements stay in the same order) and the worst case is guaranteed to be O(n log n). Sorts by cmp in the specified order.

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"]

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

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"]

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"]

Returns the index of the first element in 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, upperBound(thing, elm)) the sequence will still be sorted. Assumes that a is sorted according to cmp.

If an invalid range is passed, it raises IndexDefect.

This version uses cmp to compare the elements. The expected return values are the same as those 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]

Returns the index of the first element in 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, upperBound(thing, elm)) the sequence will still be sorted. Assumes that a is sorted.

This version uses the default comparison function cmp.

See also:

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

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 also 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)]