# 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]

    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 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

  Source Edit

# 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.

  See also:

  - reversed proc reverse a slice and returns a `seq[T]`
  - reversed proc reverse and returns a `seq[T]`

  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`.

  See also:

  - reversed proc reverse a slice and returns a `seq[T]`
  - reversed proc reverse and returns a `seq[T]`

  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.

  See also:

  - reverse proc reverse a slice
  - reverse proc

  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`.

  See also:

  - reverse proc reverse a slice
  - reverse proc

  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

  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.

  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

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

  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'
  Source Edit

    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`.

  See also:

  - upperBound proc sorted by `cmp` in the specified order
  - upperBound proc

  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]

  Source Edit

    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
  Source Edit

    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`.

  See also:

  - lowerBound proc sorted by `cmp` in the specified order
  - lowerBound proc

  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]

  Source Edit

    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
  Source Edit

    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
  Source Edit

    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

  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"]

  Source Edit

    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

  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.

  See also:

  - isSorted func

  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.

  See also:

  - prevPermutation proc

  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.

  See also:

  - nextPermutation proc

  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]

  Source Edit

    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 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.

  See also:

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

  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))

  Source Edit

    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]`

  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]

  Source Edit

    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.

  See also:

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

  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]

  Source Edit

    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

  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
      # 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

  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"]

  Source Edit

    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

  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.

  See also:

  - sort func
  - sort proc
  - sorted proc sorted by `cmp` in the specified order
  - sorted proc

  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)]

  Source Edit