Merge pull request keon#28 from vbyeh/master

add algorithm to backtrack

backtrack/word_search.py

@@ -0,0 +1,111 @@
+import unittest
+'''
+Given a matrix of words and a list of words to search, return a list of words that exists in the board
+This is Word Search II on LeetCode
+
+board = [
+         ['o','a','a','n'],
+         ['e','t','a','e'],
+         ['i','h','k','r'],
+         ['i','f','l','v']
+         ]
+
+words = ["oath","pea","eat","rain"]
+
+'''
+
+def find_words(board, words):
+    # make a trie structure that is essentially dictionaries of dictionaries that map each character to a potential next character
+    trie = {}
+    for word in words:
+        curr_trie = trie
+        for char in word:
+            if char not in curr_trie:
+                curr_trie[char] = {}
+            curr_trie = curr_trie[char]
+        curr_trie['#'] = '#'
+
+    # result is a set of found words since we do not want repeats
+    result = set()
+    used = [[False]*len(board[0]) for _ in range(len(board))]
+
+    for i in range(len(board)):
+        for j in range(len(board[0])):
+            backtrack(board, i, j, trie, '', used, result)
+    return list(result)
+
+'''
+backtrack tries to build each words from the board and return all words found
+@param: board, the passed in board of characters
+@param: i, the row index
+@param: j, the column index
+@param: trie, a trie of the passed in words
+@param: pre, a buffer of currently build string that differs by recursion stack
+@param: used, a replica of the board except in booleans to state whether a character has been used
+@param: result, the resulting set that contains all words found
+
+@return: list of words found
+'''
+
+def backtrack(board, i, j, trie, pre, used, result):
+    if '#' in trie:
+        result.add(pre)
+
+    if i < 0 or i >= len(board) or j < 0 or j >= len(board[0]):
+        return
+
+    if not used[i][j] and board[i][j] in trie:
+        used[i][j]=True
+        backtrack(board,i+1,j,trie[board[i][j]],pre+board[i][j], used, result)
+        backtrack(board,i,j+1,trie[board[i][j]],pre+board[i][j], used, result)
+        backtrack(board,i-1,j,trie[board[i][j]],pre+board[i][j], used, result)
+        backtrack(board,i,j-1,trie[board[i][j]],pre+board[i][j], used, result)
+        used[i][j]=False
+
+class MyTests(unittest.TestCase):
+    def test_normal(self):
+        board = [
+         ['o','a','a','n'],
+         ['e','t','a','e'],
+         ['i','h','k','r'],
+         ['i','f','l','v']
+         ]
+
+        words = ["oath","pea","eat","rain"]  
+        self.assertEqual(find_words(board, words), ['oath', 'eat'])
+
+    def test_none(self):
+        board = [
+         ['o','a','a','n'],
+         ['e','t','a','e'],
+         ['i','h','k','r'],
+         ['i','f','l','v']
+         ]
+
+        words = ["chicken", "nugget", "hello", "world"]  
+        self.assertEqual(find_words(board, words), [])
+
+    def test_empty(self):
+        board = []
+        words = []
+        self.assertEqual(find_words(board, words), [])
+
+    def test_uneven(self):
+        board = [
+         ['o','a','a','n'],
+         ['e','t','a','e']
+        ]
+        words = ["oath","pea","eat","rain"]  
+        self.assertEqual(find_words(board, words), ['eat'])
+
+    def test_repeat(self):
+        board = [
+        ['a','a','a'],
+        ['a','a','a'],
+        ['a','a','a']
+        ]
+        words = ["a", "aa", "aaa", "aaaa", "aaaaa"]
+        self.assertTrue(len(find_words(board, words))==5)
+
+if __name__=="__main__":
+    unittest.main()