Manacher's Algorithm

strings/Manacher.nim

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+## Manacher's algorithm
+## --------------------
+##
+## Determine the longest palindrome in a string in linear time in its length
+## with Manacher's algorithm.
+## Inspired from:
+## https://github.com/jilljenn/tryalgo/blob/master/tryalgo/manacher.py
+## https://en.wikipedia.org/wiki/Longest_palindromic_substring
+##
+## :time complexity: O(n) where n is the string's length.
+
+import std/[strutils, sequtils, sets]
+{.push raises: [].}
+
+runnableExamples:
+  let example1 = "cabbbab"
+  doAssert(manacherString(example1) == "abbba")
+  doAssert(manacherIndex(example1) == 1 .. 5)
+  doAssert(manacherLength(example1) == 5)
+
+func manacherIndex*(s: string): HSlice[int, int] {.raises: [ValueError].} =
+  ## Longest palindrome in a string by Manacher
+  ## :param s: string, lowercase ascii, no whitespace
+  ## :returns: indexes i,j such that s\[i:j\] is the longest palindrome in s
+  ## :time complexity: O(n) where n is the string's length.
+  ## All the indexes refer to an intermediate string t
+  ## of the form "^#a#b#a#a#$" for s="abaa"
+  if s.len == 0:
+    raise newException(ValueError, "Empty string")
+  let extraSymbols = toHashSet(['$', '^', '#'])
+  let letters = toHashSet(s.toLowerAscii)
+  assert disjoint(extraSymbols, letters) # Forbidden letters
+  if s == "":
+    return 0 .. 1
+  let s = "^#" & join(s, "#") & "#$"
+  var
+    center = 1
+    distance = 1
+    p = repeat(0, len(s)) # Palindrome radii for each index in s
+  for index in 2 ..< len(s)-1:
+    # reflect index with respect to center
+    let mirror = 2 * center - index # = center - (index - center)
+    p[index] = max(0, min(distance - index, p[mirror]))
+    # grow palindrome centered in i
+    while s[index + 1 + p[index]] == s[index - 1 - p[index]]:
+      p[index] += 1
+    # adjust center if necessary
+    if index + p[index] > distance:
+      center = index
+      distance = index + p[index]
+  # find the argmax index in p
+  var
+    j = maxIndex(p)
+    k = p[j]
+  return (j - k) div 2 ..< (j + k) div 2 # extract solution
+
+func manacherString*(s: string): string {.raises: [ValueError].} =
+  ## Returns the greatest palindromic substring in `s`.
+  return s[manacherIndex(s)]
+
+func manacherLength*(s: string): int {.raises: [ValueError].} =
+  ## Returns the length of the greatest palindromic substring in `s`.
+  let
+    res = manacherIndex(s)
+    (i, j) = (res.a, res.b)
+  return j - i + 1
+
+when isMainModule:
+  import std/unittest
+  suite "Manacher's algorithm":
+    test "Simple palindrome":
+      check manacherIndex("abbbab") == 0 .. 4
+      check manacherLength("abbbab") == 5
+      check manacherString("abbbab") == "abbba"
+
+    test "Single letter palindrome":
+      check manacherIndex("abcab") == 0 .. 0
+      check manacherLength("abcab") == 1
+      check manacherString("abcab") == "a"
+
+    test "Palindrome is full string":
+      check manacherIndex("telet") == 0 .. 4
+      check manacherLength("telet") == 5
+      check manacherString("telet") == "telet"
+
+    test "Empty string":
+      doAssertRaises(ValueError):
+        discard manacherIndex("")
+      doAssertRaises(ValueError):
+        discard manacherLength("")
+      doAssertRaises(ValueError):
+        discard manacherString("")

strings/manacher.nim

@@ -0,0 +1,91 @@
+## Manacher's algorithm
+##
+## Determine the longest palindrome in a string in linear time in its length
+## with Manacher's algorithm.
+##
+## Inspired from:
+## https://github.com/jilljenn/tryalgo/blob/master/tryalgo/manacher.py
+## https://en.wikipedia.org/wiki/Longest_palindromic_substring
+##
+import std/[strutils, sequtils, sets]
+{.push raises: [].}
+
+runnableExamples:
+  let example1 = "cabbbab"
+  doAssert(manacherString(example1) == "abbba")
+  doAssert(manacherIndex(example1) == 1 .. 5)
+  doAssert(manacherLength(example1) == 5)
+
+func manacherIndex*(s: string): HSlice[int, int] {.raises: [ValueError].} =
+  ## Find the start and stop index for the longest palindrome in a string by Manacher
+  ##
+  ## :returns: indexes i and j such that s\[i:j\] is the longest palindrome in s
+  ## :param s: string, lowercase ascii, no whitespace
+  ## :time complexity: O(len(s))
+  ## All the indexes refer to an intermediate string t
+  ## of the form "^#a#b#a#a#$" for s="abaa"
+  if s.len == 0:
+    raise newException(ValueError, "Empty string")
+  let extraSymbols = toHashSet(['$', '^', '#'])
+  let letters = toHashSet(s.toLowerAscii)
+  assert disjoint(extraSymbols, letters) # Forbidden letters
+  if s == "":
+    return 0 .. 1
+  let s = "^#" & join(s, "#") & "#$"
+  var
+    center = 1
+    distance = 1
+    p = repeat(0, len(s)) # Palindrome radii for each index in s
+  for index in 2 ..< len(s)-1:
+    # reflect index with respect to center
+    let mirror = 2 * center - index # = center - (index - center)
+    p[index] = max(0, min(distance - index, p[mirror]))
+    # grow palindrome centered in i
+    while s[index + 1 + p[index]] == s[index - 1 - p[index]]:
+      p[index] += 1
+    # adjust center if necessary
+    if index + p[index] > distance:
+      center = index
+      distance = index + p[index]
+  # find the argmax index in p
+  var
+    j = maxIndex(p)
+    k = p[j]
+  return (j - k) div 2 ..< (j + k) div 2 # extract solution
+
+func manacherString*(s: string): string {.raises: [ValueError].} =
+  ## Returns the longest palindrome
+  return s[manacherIndex(s)]
+
+func manacherLength*(s: string): int {.raises: [ValueError].} =
+  ## Returns the length of the longest palindrome
+  let
+    res = manacherIndex(s)
+    (i, j) = (res.a, res.b)
+  return j - i + 1
+
+when isMainModule:
+  import std/unittest
+  suite "Manacher's algorithm":
+    test "Simple palindrome":
+      check manacherIndex("abbbab") == 0 .. 4
+      check manacherLength("abbbab") == 5
+      check manacherString("abbbab") == "abbba"
+
+    test "Single letter palindrome":
+      check manacherIndex("abcab") == 0 .. 0
+      check manacherLength("abcab") == 1
+      check manacherString("abcab") == "a"
+
+    test "Palindrome is full string":
+      check manacherIndex("telet") == 0 .. 4
+      check manacherLength("telet") == 5
+      check manacherString("telet") == "telet"
+
+    test "Empty string":
+      doAssertRaises(ValueError):
+        discard manacherIndex("")
+      doAssertRaises(ValueError):
+        discard manacherLength("")
+      doAssertRaises(ValueError):
+        discard manacherString("")