Module algorithm

This module implements some common generic algorithms.

Types

SortOrder = enum
  Descending, Ascending

sort order

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

proc fill[T](a: var openArray[T]; first, last: Natural; value: T)

fills the array a[first..last] with value.

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

fills the array a with value.

proc reverse[T](a: var openArray[T]; first, last: Natural)

reverses the array a[first..last].

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

reverses the array a.

proc reversed[T](a: openArray[T]; first: Natural; last: int): seq[T]

returns the reverse of the array a[first..last].

proc reversed[T](a: openArray[T]): seq[T]

returns the reverse of the array a.

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.

proc binarySearch[T](a: openArray[T]; key: T): int

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

proc smartBinarySearch[T](a: openArray[T]; key: T): int {...}{.deprecated.}

Deprecated since version 0.18.1; Use binarySearch instead.

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.

The first version uses cmp to compare the elements. The expected return values are the same as that of system.cmp. The second version uses the default comparison function cmp.

example:

var arr = @[1,2,3,5,6,7,8,9]
arr.insert(4, arr.lowerBound(4))
# after running the above arr is `[1,2,3,4,5,6,7,8,9]`

proc lowerBound[T](a: openArray[T]; key: T): int

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.

The first version uses cmp to compare the elements. The expected return values are the same as that of system.cmp. The second version uses the default comparison function cmp.

example:

var arr = @[1,2,3,4,6,7,8,9]
arr.insert(5, arr.upperBound(4))
# after running the above arr is `[1,2,3,4,5,6,7,8,9]`

proc upperBound[T](a: openArray[T]; key: T): int

proc 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. Currently Nim does not support a sensible default argument for cmp, so you have to provide one of your own. However, the system.cmp procs can be used:

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)

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.

proc 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

proc product[T](x: openArray[seq[T]]): seq[seq[T]]

produces the Cartesian product of the array. Warning: complexity may explode.

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.

var v = @[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
v.nextPermutation()
echo v # @[0, 1, 2, 3, 4, 5, 6, 7, 9, 8]

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.

var v = @[0, 1, 2, 3, 4, 5, 6, 7, 9, 8]
v.prevPermutation()
echo v # @[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

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.

proc rotateLeft[T](arg: var openArray[T]; dist: int): int

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

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

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

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. 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]

echo people.sortedByIt(it.name)

Because the underlying cmp() is defined for tuples you can do a nested sort like in the following example:

echo people.sortedByIt((it.age, it.name))