|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 |
""" bktree.py, by bearophile Fast Levenshtein distance and BK-tree implementations in Python. The following functions are designed for Psyco, they are too much slow without it. """ def editDistance(s1, s2): """Computes the Levenshtein distance between two arrays (strings too). Such distance is the minimum number of operations needed to transform one array into the other, where an operation is an insertion, deletion, or substitution of a single item (like a char). This implementation (Wagner-Fischer algorithm with just 2 lines) uses O(min(|s1|, |s2|)) space. editDistance([], []) 0 >>> editDistance([1, 2, 3], [2, 3, 5]) 2 >>> tests = [["", ""], ["a", ""], ["", "a"], ["a", "a"], ["x", "a"], ... ["aa", ""], ["", "aa"], ["aa", "aa"], ["ax", "aa"], ["a", "aa"], ["aa", "a"], ... ["abcdef", ""], ["", "abcdef"], ["abcdef", "abcdef"], ... ["vintner", "writers"], ["vintners", "writers"]]; >>> [editDistance(s1, s2) for s1,s2 in tests] [0, 1, 1, 0, 1, 2, 2, 0, 1, 1, 1, 6, 6, 0, 5, 4] """ # This function is designed for Psyco if s1 == s2: return 0 # this is fast in Python if len(s1) > len(s2): s1, s2 = s2, s1 r1 = range(len(s2) + 1) r2 = [0] * len(r1) i = 0 for c1 in s1: r2[0] = i + 1 j = 0 for c2 in s2: if c1 == c2: r2[j+1] = r1[j] else: a1 = r2[j] a2 = r1[j] a3 = r1[j+1] if a1 > a2: if a2 > a3: r2[j+1] = 1 + a3 else: r2[j+1] = 1 + a2 else: if a1 > a3: r2[j+1] = 1 + a3 else: r2[j+1] = 1 + a1 j += 1 aux = r1; r1 = r2; r2 = aux i += 1 return r1[-1] def editDistanceFast(s1, s2, r1=[0]*35, r2=[0]*35): """Computes the Levenshtein distance between two arrays (strings too). Such distance is the minimum number of operations needed to transform one array into the other, where an operation is an insertion, deletion, or substitution of a single item (like a char). This implementation (Wagner-Fischer algorithm with just 2 lines) uses O(min(|s1|, |s2|)) space. This version is a bit faster but it works only with strings up to 34 items long. editDistanceFast([], []) 0 >>> editDistanceFast([1, 2, 3], [2, 3, 5]) 2 >>> tests = [["", ""], ["a", ""], ["", "a"], ["a", "a"], ["x", "a"], ... ["aa", ""], ["", "aa"], ["aa", "aa"], ["ax", "aa"], ["a", "aa"], ["aa", "a"], ... ["abcdef", ""], ["", "abcdef"], ["abcdef", "abcdef"], ... ["vintner", "writers"], ["vintners", "writers"]]; >>> [editDistanceFast(s1, s2) for s1,s2 in tests] [0, 1, 1, 0, 1, 2, 2, 0, 1, 1, 1, 6, 6, 0, 5, 4] """ # This function is designed for Psyco if s1 == s2: return 0 # this is fast in Python if len(s1) > len(s2): s1, s2 = s2, s1 len_s2 = len(s2) assert len(s2) <= 34, "Error: one input sequence is too much long (> 34), use editDistance()." for i in xrange(len_s2 + 1): r1[i] = i r2[i] = 0 i = 0 for c1 in s1: r2[0] = i + 1 j = 0 for c2 in s2: if c1 == c2: r2[j+1] = r1[j] else: a1 = r2[j] a2 = r1[j] a3 = r1[j+1] if a1 > a2: if a2 > a3: r2[j+1] = 1 + a3 else: r2[j+1] = 1 + a2 else: if a1 > a3: r2[j+1] = 1 + a3 else: r2[j+1] = 1 + a1 j += 1 aux = r1; r1 = r2; r2 = aux i += 1 return r1[len_s2] import gc try: import psyco psyco.bind(editDistance) psyco.bind(editDistanceFast) from psyco.classes import psyobj except ImportError: psyobj = object class BKtree(psyobj): """ BKtree(items, distance, usegc=False): inputs are an iterable of hashable items that must allow the next() method too, and a callable that computes the distance (that mets the positivity, symmetry and triangle inequality conditions) between two items. It allows a fast search of similar items. The indexing phase may be slow, so this is useful only if you want to perform many searches. It raises a AttributeError if items doesn't have the .next() method. It can be used with strings, using editDistance()/editDistanceFast() Once initialized, you can retrieve items using xfind/find, giving an item and a threshold distance. You can disable the GC during the indexing phase to speed it up (default disabled), enabling it you may save some memory. If you have Psyco you can use it to speed up editDistanceFast. You can speed up this class with (but not binding it with Psyco): from psyco.classes import __metaclass__ You can also use the psyco metaclass just for this BKtree class, with psyobj. >>> t = BKtree([], distance=editDistanceFast) Traceback (most recent call last): ... AttributeError: 'list' object has no attribute 'next' >>> t = BKtree(iter([]), distance=editDistanceFast) >>> t.find("hello", 1), t.find("", 0) ([], []) >>> ws = "abyss almond clump cubic cuba adopt abused chronic abutted cube clown admix almsman" >>> t = BKtree(iter(ws.split()), distance=editDistanceFast) >>> [len(t.find("cuba", th)) for th in range(7)] [1, 2, 3, 4, 5, 9, 13] >>> [t.find("cuba", th) for th in range(4)] [['cuba'], ['cuba', 'cube'], ['cubic', 'cuba', 'cube'], ['clump', 'cubic', 'cuba', 'cube']] >>> [len(t.find("abyss", th)) for th in range(7)] [1, 1, 1, 2, 4, 12, 12] >>> [t.find("abyss", th) for th in range(4)] [['abyss'], ['abyss'], ['abyss'], ['abyss', 'abused']] """ def __init__(self, items, distance, usegc=False): self.distance = distance self.nodes = {} try: self.root = items.next() except StopIteration: self.root = "" return self.nodes[self.root] = [] # the value is a list of tuples (word, distance) gc_on = gc.isenabled() if not usegc: gc.disable() for el in items: if el not in self.nodes: # do not add duplicates self._addLeaf(self.root, el) if gc_on: gc.enable() def _addLeaf(self, root, item): dist = self.distance(root, item) if dist > 0: for arc in self.nodes[root]: if dist == arc[1]: self._addLeaf(arc[0], item) break else: if item not in self.nodes: self.nodes[item] = [] self.nodes[root].append((item, dist)) def find(self, item, threshold): "Return an array with all the items found with distance <= threshold from item." result = [] if self.nodes: self._finder(self.root, item, threshold, result) return result def _finder(self, root, item, threshold, result): dist = self.distance(root, item) if dist <= threshold: result.append(root) dmin = dist - threshold dmax = dist + threshold for arc in self.nodes[root]: if dmin <= arc[1] <= dmax: self._finder(arc[0], item, threshold, result) def xfind(self, item, threshold): "Like find, but yields items lazily. This is slower than find if you need a list." if self.nodes: return self._xfinder(self.root, item, threshold) def _xfinder(self, root, item, threshold): dist = self.distance(root, item) if dist <= threshold: yield root dmin = dist - threshold dmax = dist + threshold for arc in self.nodes[root]: if dmin <= arc[1] <= dmax: for node in self._xfinder(arc[0], item, threshold): yield node if __name__ == "__main__": import doctest doctest.testmod() print "Tests finished." # You need a list of words #words = file("somewordlist.txt").read().split() words = iter("""periclean germs progressed laughing allying wasting harassing nonsynchronous grumbled ledgers schelling shod mutating statewide schuman following reddened nairobi cultivate malted overpowering mechanic paraphrase lucerne plugged wick complimented roarer supercomputer impromptu cormorant abandons equalized channing chill bacon nonnumerical cabana amazing rheumatism""".split()) tree = BKtree(words, editDistanceFast) print tree.find("cube", 4) # ['cabana', 'wick', 'chill', 'shod'] for thresh in xrange(12): print thresh, len(tree.find("cube", thresh)) |
