module Algorithms::Search

Binary Search: This search finds an item in log(n) time provided that the container is already sorted. The method returns the item if it is found, or nil if it is not. If there are duplicates, the first one found is returned, and this is not guaranteed to be the smallest or largest item.

Complexity: O(lg N)

Algorithms::Search.binary_search([1, 2, 3], 1) #=> 1
Algorithms::Search.binary_search([1, 2, 3], 4) #=> nil

# File lib/algorithms/search.rb, line 14
def self.binary_search(container, item)
  return nil if item.nil?
  low = 0
  high = container.size - 1
  while low <= high
    mid = (low + high) / 2
    val = container[mid]
    if val > item
      high = mid - 1
    elsif val < item
      low = mid + 1
    else
      return val
    end
  end
  nil
end

Knuth-Morris-Pratt Algorithm substring search algorithm: Efficiently finds the starting position of a substring in a string. The algorithm calculates the best position to resume searching from if a failure occurs.

The method returns the index of the starting position in the string where the substring is found. If there is no match, nil is returned.

Complexity: O(n + k), where n is the length of the string and k is the length of the substring.

Algorithms::Search.kmp_search("ABC ABCDAB ABCDABCDABDE", "ABCDABD") #=> 15
Algorithms::Search.kmp_search("ABC ABCDAB ABCDABCDABDE", "ABCDEF") #=> nil

# File lib/algorithms/search.rb, line 43
def self.kmp_search(string, substring)
  return nil if string.nil? or substring.nil?
  
  # create failure function table
  pos = 2
  cnd = 0
  failure_table = [-1, 0]
  while pos < substring.length
    if substring[pos - 1] == substring[cnd]
      failure_table[pos] = cnd + 1
      pos += 1
      cnd += 1
    elsif cnd > 0
      cnd = failure_table[cnd]
    else
      failure_table[pos] = 0
      pos += 1
    end
  end

  m = i = 0
  while m + i < string.length
    if substring[i] == string[m + i]
      i += 1
      return m if i == substring.length
    else
      m = m + i - failure_table[i]
      i = failure_table[i] if i > 0
    end
  end
  return nil
end