Ruby实现的最短编辑距离计算方法

利用动态规划算法，实现最短编辑距离的计算。

#encoding: utf-8
#author: xu jin
#date: nov 12, 2012
#editdistance
#to find the minimum cost by using editdistance algorithm
#example output:
#  "please input a string: "
#  exponential
#  "please input the other string: "
#  polynomial
#  "the expected cost is 6"
#  the result is :
#    ["e", "x", "p", "o", "n", "e", "n", "-", "t", "i", "a", "l"]
#    ["-", "-", "p", "o", "l", "y", "n", "o", "m", "i", "a", "l"]

p "please input a string: "
x = gets.chop.chars.map{|c| c}
p "please input the other string: "
y = gets.chop.chars.map{|c| c}
x.unshift(" ")
y.unshift(" ")
e = array.new(x.size){array.new(y.size)}
flag = array.new(x.size){array.new(y.size)}
del, ins, cha, fit = (1..4).to_a  #deleat, insert, change, and fit
 
def edit_distance(x, y, e, flag)
  (0..x.length - 1).each{|i| e[i][0] = i}
  (0..y.length - 1).each{|j| e[0][j] = j}
  diff = array.new(x.size){array.new(y.size)}
  for i in(1..x.length - 1) do
    for j in(1..y.length - 1) do
      diff[i][j] = (x[i] == y[j])? 0: 1
      e[i][j] = [e[i-1][j] + 1, e[i][j - 1] + 1, e[i-1][j - 1] + diff[i][j]].min
      if e[i][j] == e[i-1][j] + 1
        flag[i][j] = del
      elsif e[i][j] == e[i-1][j - 1] + 1
        flag[i][j] = cha
      elsif e[i][j] == e[i][j - 1] + 1
        flag[i][j] = ins      
      else flag[i][j] = fit
      end    
    end
  end 
end

out_x, out_y = [], []

def solution_structure(x, y, flag, i, j, out_x, out_y)
  case flag[i][j]
  when fit
    out_x.unshift(x[i])
    out_y.unshift(y[j]) 
    solution_structure(x, y, flag, i - 1, j - 1, out_x, out_y)
  when del
    out_x.unshift(x[i])
    out_y.unshift('-')
    solution_structure(x, y, flag, i - 1, j, out_x, out_y)
  when ins
    out_x.unshift('-')
    out_y.unshift(y[j])
    solution_structure(x, y, flag, i, j - 1, out_x, out_y)
  when cha
    out_x.unshift(x[i])
    out_y.unshift(y[j])
    solution_structure(x, y, flag, i - 1, j - 1, out_x, out_y)
  end
  #if flag[i][j] == nil ,go here
  return if i == 0 && j == 0   
  if j == 0
      out_y.unshift('-')
      out_x.unshift(x[i])
      solution_structure(x, y, flag, i - 1, j, out_x, out_y)
  elsif i == 0
      out_x.unshift('-')
      out_y.unshift(y[j])
      solution_structure(x, y, flag, i, j - 1, out_x, out_y)
  end
end

edit_distance(x, y, e, flag)
p "the expected edit distance is #{e[x.length - 1][y.length - 1]}"
solution_structure(x, y, flag, x.length - 1, y.length - 1, out_x, out_y)
puts "the result is : \n  #{out_x}\n  #{out_y}"