Merge branch 'TheAlgorithms:main' into main

Author: SatinWukerORIG

DIRECTORY.md

@@ -6,6 +6,11 @@
   * [Catalan Numbers](dynamic_programming/catalan_numbers.nim)
   * [Viterbi](dynamic_programming/viterbi.nim)
 
+## Maths
+  * [Absolute value](maths/abs.nim)
+  * [Aliquot sum](maths/aliquot_sum.nim)
+  * [Bitwise Addition](maths/bitwise_addition.nim)
+
 ## Strings
   * [Check Anagram](strings/check_anagram.nim)
 

README.md

@@ -1,40 +1,40 @@
-<div align="center">
-<!-- Title: -->
-  <a href="https://github.com/TheAlgorithms/">
-    <img src="https://raw.githubusercontent.com/TheAlgorithms/website/1cd824df116b27029f17c2d1b42d81731f28a920/public/logo.svg" height="100">
-  </a>
-  <h1><a href="https://github.com/TheAlgorithms/">The Algorithms</a> - Nim</h1>
-<!-- Labels: -->
-  <!-- First row: -->
-  <a href="https://gitpod.io/#https://github.com/TheAlgorithms/Nim">
-    <img src="https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod&style=flat-square" height="20" alt="Gitpod Ready-to-Code">
-  </a>
-  <a href="https://github.com/TheAlgorithms/Nim/blob/master/CONTRIBUTING.md">
-    <img src="https://img.shields.io/static/v1.svg?label=Contributions&message=Welcome&color=0059b3&style=flat-square" height="20" alt="Contributions Welcome">
-  </a>
-  <img src="https://img.shields.io/github/repo-size/TheAlgorithms/Nim.svg?label=Repo%20size&style=flat-square" height="20">
-  <a href="https://the-algorithms.com/discord">
-    <img src="https://img.shields.io/discord/808045925556682782.svg?logo=discord&colorB=7289DA&style=flat-square" height="20" alt="Discord chat">
-  </a>
-  <a href="https://gitter.im/TheAlgorithms">
-    <img src="https://img.shields.io/badge/Chat-Gitter-ff69b4.svg?label=Chat&logo=gitter&style=flat-square" height="20" alt="Gitter chat">
-  </a>
-  <!-- Second row: -->
-  <br>
-<!-- Short description: -->
-  <h3>Algorithms collection implemented in Nim - for education</h3>
-</div>
+# <a href="https://github.com/TheAlgorithms/">The Algorithms</a> – Nim&nbsp;<img src="https://raw.githubusercontent.com/nim-lang/assets/master/Art/logo-crown.png" height="28px"/><a href="https://github.com/TheAlgorithms/"><img align="right" src="https://raw.githubusercontent.com/TheAlgorithms/website/main/public/logo.svg" height="100"></a>
+
+[![Gitpod Ready-to-Code][badge-gitpod]](https://gitpod.io/#https://github.com/TheAlgorithms/Nim)
+[![Contributions Welcome][badge-contributions]](https://github.com/TheAlgorithms/Nim/blob/master/CONTRIBUTING.md)
+![Repo size][badge-reposize]
+</br>
+[![Discord chat][badge-discord]][chat-discord]
+[![Gitter chat][badge-gitter]][chat-gitter]
+[![Matrix room][badge-matrix]][chat-matrix]
+
+## Algorithms collection implemented in Nim - for education
 
 Implementations are for learning purposes only. They may be less efficient than the implementations in the [Nim standard library](https://nim-lang.org/docs/lib.html) or [Nimble packages](https://nimble.directory/). Use them at your discretion.
 
 ## Getting Started
 
 Read through our [Contribution Guidelines](CONTRIBUTING.md) before you contribute.
 
+## List of Algorithms
+
+See our [directory](DIRECTORY.md) for easier navigation and a better overview of the project.
+
+You can also browse the implementations on [the website](https://the-algorithms.com/language/nim).
+
 ## Community Channels
 
-We are on [Discord](https://the-algorithms.com/discord) and [Gitter](https://gitter.im/TheAlgorithms)! Community channels are a great way for you to ask questions and get help. Please join us!
+We are on [Discord](https://the-algorithms.com/discord) and [Gitter][chat-gitter]/[Matrix][chat-matrix]!
 
-## List of Algorithms
+Community channels are a great way for you to ask questions and get help. Please join us!
 
-See our [directory](DIRECTORY.md) for easier navigation and a better overview of the project.
+<!-- links -->
+[chat-discord]: https://the-algorithms.com/discord 
+[chat-gitter]: https://gitter.im/#TheAlgorithms_community:gitter.im
+[chat-matrix]: https://matrix.to/#/#TheAlgorithms_community:gitter.im
+[badge-contributions]: https://img.shields.io/static/v1.svg?label=Contributions&message=Welcome&color=0059b3&style=flat-square
+[badge-discord]: https://img.shields.io/discord/808045925556682782.svg?logo=discord&colorB=7289DA&style=flat-square
+[badge-matrix]: https://img.shields.io/badge/matrix-TheAlgorithms_community-0dbd8b?logo=matrix
+[badge-gitpod]: https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod&style=flat-square
+[badge-gitter]: https://img.shields.io/badge/Chat-Gitter-ff69b4.svg?label=Chat&logo=gitter&style=flat-square
+[badge-reposize]: https://img.shields.io/github/repo-size/TheAlgorithms/Nim.svg?label=Repo%20size&style=flat-square

config.nims

@@ -13,6 +13,8 @@ import std/[os, sequtils]
 from std/strutils import startsWith, endsWith
 from std/strformat import `&`
 
+--mm:arc # TODO: check if still needs to be below imports on Nim > 1.6.12
+
 const IgnorePathPrefixes = ["."]
 
 func isIgnored(path: string): bool =
@@ -27,12 +29,13 @@ iterator modules(dir: string = getCurrentDir()): string =
 
 ############ Tasks
 task test, "Test everything":
+  --warning: "BareExcept:off"
   --hints: off
   var failedUnits: seq[string]
 
   for path in modules():
     echo &"Testing {path}:"
-    try: exec(&"nim --hints:off r \"{path}\"")
+    try: selfExec(&"-f --warning[BareExcept]:off --hints:off r \"{path}\"")
     except OSError:
       failedUnits.add(path)
   if failedUnits.len > 0:

maths/abs.nim

@@ -0,0 +1,120 @@
+## Absolute value
+{.push raises: [].}
+import std/strutils
+
+runnableExamples:
+  assert absVal(-5.1) == 5.1
+  assert absMin(@[-1, 2, -3]) == 1
+  assert absMax(@[-1, 2, -3]) == 3
+  assert signedMinAbs(@[3, -10, -2]) == -2
+  assert signedMaxAbs(@[3, -10, -2]) == -10
+
+func absVal*[T: SomeFloat](num: T): T =
+  ## Returns the absolute value of a number.
+  ## Use `math.abs <https://nim-lang.org/docs/system.html#abs%2CT>`_ instead!
+  return if num < 0.0: -num else: num
+
+# Same for Integers but returns a Natural
+func absVal*[T: SomeInteger](num: T): Natural = (if num < 0: -num else: num)
+
+func absMin*(x: openArray[int]): Natural {.raises: [ValueError].} =
+  ## Returns the smallest element in absolute value in a sequence.
+  if x.len == 0:
+    raise newException(ValueError, """Cannot find absolute minimum
+     of an empty sequence""".unindent)
+  result = absVal(x[0])
+  for i in 1 ..< x.len:
+    if absVal(x[i]) < result:
+      result = absVal(x[i])
+
+func absMax*(x: openArray[int]): Natural {.raises: [ValueError].} =
+  ## Returns the largest element in absolute value in a sequence.
+  if x.len == 0:
+    raise newException(ValueError, """Cannot find absolute maximum of an empty
+   sequence""".unindent)
+  result = absVal(x[0])
+  for i in 1 ..< x.len:
+    if absVal(x[i]) > result:
+      result = absVal(x[i])
+
+func signedMinAbs*(x: openArray[int]): int {.raises: [ValueError].} =
+  ## Returns the first signed element whose absolute value
+  ## is the smallest in a sequence.
+  if x.len == 0:
+    raise newException(ValueError, """Cannot find absolute maximum of an empty
+   sequence""".unindent)
+  var (min, minAbs) = (x[0], absVal(x[0]))
+  for n in x:
+    let nAbs = absVal(n)
+    if nAbs < minAbs: (min, minAbs) = (n, nAbs)
+  min
+
+func signedMaxAbs*(x: openArray[int]): int {.raises: [ValueError].} =
+  ## Returns the first signed element whose absolute value
+  ## is the largest in a sequence.
+  if x.len == 0:
+    raise newException(ValueError, """Cannot find absolute maximum of an empty
+   sequence""".unindent)
+  var (max, maxAbs) = (x[0], absVal(x[0]))
+  for n in x:
+    let nAbs = absVal(n)
+    if nAbs > maxAbs: (max, maxAbs) = (n, nAbs)
+  max
+
+when isMainModule:
+  import std/[unittest, random]
+  randomize()
+
+  suite "Check absVal":
+    test "Check absVal":
+      check:
+        absVal(11.2) == 11.2
+        absVal(5) == 5
+        absVal(-5.1) == 5.1
+        absVal(-5) == absVal(5)
+        absVal(0) == 0
+
+  suite "Check absMin":
+    test "Check absMin":
+      check:
+        absMin(@[-1, 2, -3]) == 1
+        absMin(@[0, 5, 1, 11]) == 0
+        absMin(@[3, -10, -2]) == 2
+        absMin([-1, 2, -3]) == 1
+        absMin([0, 5, 1, 11]) == 0
+        absMin([3, -10, -2]) == 2
+
+    test "absMin on empty sequence raises ValueError":
+      doAssertRaises(ValueError):
+        discard absMin(@[])
+
+  suite "Check absMax":
+    test "Check absMax":
+      check:
+        absMax(@[0, 5, 1, 11]) == 11
+        absMax(@[3, -10, -2]) == 10
+        absMax(@[-1, 2, -3]) == 3
+
+    test "`absMax` on empty sequence raises ValueError":
+      doAssertRaises(ValueError):
+        discard absMax(@[])
+
+  suite "Check signedMinAbs":
+    test "Check signedMinAbs":
+      check:
+        signedMinAbs(@[0, 5, 1, 11]) == 0
+        signedMinAbs(@[3, -2, 1, -4, 5, -6]) == 1
+        signedMinAbs(@[3, -2, -1, -4, 5, -6]) == -1
+
+    test "Among two minimal elements, the first one is returned":
+      check signedMinAbs(@[3, -2, 1, -4, 5, -6, -1]) == 1
+
+  suite "Check signedMaxAbs":
+    test "Check signedMaxAbs":
+      check:
+        signedMaxAbs(@[3, -2, 1, -4, 5, -6]) == -6
+        signedMaxAbs(@[0, 5, 1, 11]) == 11
+
+    test "signedMaxAbs on empty sequence raises ValueError":
+      doAssertRaises(ValueError):
+        discard signedMaxAbs(@[])

maths/aliquot_sum.nim

@@ -0,0 +1,31 @@
+## Aliquot sum
+## In number theory, the aliquot sum s(n) of a positive integer n is the sum of
+## all proper divisors of n, that is, all divisors of n other than n itself.
+## https://en.wikipedia.org/wiki/Aliquot_sum
+
+runnableExamples:
+  import std/strformat
+  const expected = [16, 117]
+  for i, number in [12, 100].pairs():
+    let sum = aliquotSum(number)
+    assert sum == expected[i]
+    echo fmt"The sum of all the proper divisors of {number} is {sum}"
+
+func aliquotSum*(number: Positive): Natural =
+  ## Returns the sum of all the proper divisors of the number
+  ## Example: aliquotSum(12) = 1 + 2 + 3 + 4 + 6 = 16
+  result = 0
+  for divisor in 1 .. (number div 2):
+    if number mod divisor == 0:
+      result += divisor
+
+when isMainModule:
+  import std/unittest
+  suite "Check aliquotSum":
+    test "aliquotSum on small values":
+      var
+        input = @[1, 2, 9, 12, 27, 100]
+        expected = @[0, 1, 4, 16, 13, 117]
+      for i in 0 ..< input.len:
+        check:
+          aliquotSum(input[i]) == expected[i]

maths/arc_length.nim

@@ -0,0 +1,34 @@
+# Arc Length of a Circle
+## https://en.wikipedia.org/wiki/Arc_length
+import std/math
+{.push raises: [].}
+
+func arcLengthDegree(radius: float, angle: float): float =
+  ## Calculate the length of an arc given the `radius` and `angle` in degrees.
+  return PI * radius * (angle / 180)
+
+func arcLengthRadian(radius: float, angle: float): float =
+  ## Calculate the length of an arc given the `radius` and `angle` in radians.
+  return radius * angle
+
+when isMainModule:
+  import std/unittest
+  const UnitsInLastPlace = 1
+  suite "Arc Length":
+    test "radius 5, angle 45":
+      check almostEqual(arcLengthDegree(5, 45), 3.926990816987241, UnitsInLastPlace)
+    test "radius 15, angle 120":
+      check almostEqual(arcLengthDegree(15, 120), 31.41592653589793, UnitsInLastPlace)
+    test "radius 10, angle 90":
+      check almostEqual(arcLengthDegree(10, 90), 15.70796326794897, UnitsInLastPlace)
+
+  suite "Arc Length":
+    test "radius 5, angle 45":
+      check almostEqual(arcLengthRadian(5, degToRad(45.0)), 3.926990816987241,
+       UnitsInLastPlace)
+    test "radius 15, angle 120":
+      check almostEqual(arcLengthRadian(15, degToRad(120.0)), 31.41592653589793,
+       UnitsInLastPlace)
+    test "radius 10, angle 90":
+      check almostEqual(arcLengthRadian(10, degToRad(90.0)), 15.70796326794897,
+       UnitsInLastPlace)

maths/bitwise_addition.nim

@@ -0,0 +1,38 @@
+## Bitwise Addition
+## Illustrate how to implement addition of integers using bitwise operations
+## See https://en.wikipedia.org/wiki/Bitwise_operation#Applications
+runnableExamples:
+  import std/strformat
+  var
+    a = 5
+    b = 6
+  echo fmt"The sum of {a} and {b} is {add(a,b)}"
+
+func add*(first: int, second: int): int =
+  ## Implementation of addition of integer with `and`, `xor` and `shl`
+  ## boolean operators.
+  var first = first
+  var second = second
+  while second != 0:
+    var c = first and second
+    first = first xor second
+    second = c shl 1
+  return first
+
+when isMainModule:
+  import std/unittest
+
+  suite "Check addition":
+    test "Addition of two positive numbers":
+      check:
+        add(3, 5) == 8
+        add(13, 5) == 18
+    test "Addition of two negative numbers":
+      check:
+        add(-7, -2) == -9
+        add(-321, -0) == -321
+    test "Addition of one positive and one negative number":
+      check:
+        add(-7, 2) == -5
+        add(-13, 5) == -8
+        add(13, -5) == 8