1. Letter Combinations of a Phone Number

# Letter Combinations of a Phone Number
# Given a string containing digits from 2-9 inclusive, 
# return all possible letter combinations represent.
# mapping of digit to letters is given.

class Solution:
    def letterCombinations(self, digits):
        if not digits:
            return []
        dic = {"2":"abc", "3":"def", "4":"ghi", "5":"jkl", "6":"mno", "7":"pqrs", "8":"tuv", "9":"wxyz"}
        res = []
        self.dfs(digits, dic, 0, "", res)
        return res

    def dfs(self, digits, dic, index, path, res):
        if len(path) == len(digits):
            res.append(path)  #深度搜索到的每条str
            return 
        for i in range(index, len(digits)):
            for j in dic[digits[i]]:  # 数字逐位 遍历深入 至串长达到
                self.dfs(digits, dic, i+1, path+j, res)  # index & strPath

2. Word Search II

# Word Search II
# Given a 2D board and a list of words from the dictionary, 
# find all words in the board.

# sequentially adjacent cell, 
# "adjacent": horizontally or vertically neighboring. 
# same letter not be used more than once in a word.

class Solution:
    def findWords(self, board: List[List[str]], words: List[str]) -> List[str]:
        WORD_KEY = '$'
        
        trie = {}
        for word in words:
            node = trie
            for letter in word:
                # retrieve the next node; If not found, create a empty node.
                node = node.setdefault(letter, {})
            # mark the existence of a word in trie node
            node[WORD_KEY] = word
        
        rowNum = len(board)
        colNum = len(board[0])
        
        matchedWords = []
        
        def backtracking(row, col, parent):    
            
            letter = board[row][col]
            currNode = parent[letter]
            
            # check if we find a match of word
            word_match = currNode.pop(WORD_KEY, False)
            if word_match:
                # also we removed the matched word to avoid duplicates,
                #   as well as avoiding using set() for results.
                matchedWords.append(word_match)
            
            # Before the EXPLORATION, mark the cell as visited 
            board[row][col] = '#'
            
            # Explore the neighbors in 4 directions, i.e. up, right, down, left
            for (rowOffset, colOffset) in [(-1, 0), (0, 1), (1, 0), (0, -1)]:
                newRow, newCol = row + rowOffset, col + colOffset     
                if newRow < 0 or newRow >= rowNum or newCol < 0 or newCol >= colNum:
                    continue
                if not board[newRow][newCol] in currNode:
                    continue
                backtracking(newRow, newCol, currNode)
        
            # End of EXPLORATION, we restore the cell
            board[row][col] = letter
        
            # Optimization: incrementally remove the matched leaf node in Trie.
            if not currNode:
                parent.pop(letter)

        for row in range(rowNum):
            for col in range(colNum):
                # starting from each of the cells
                if board[row][col] in trie:
                    backtracking(row, col, trie)
        
        return matchedWords    

3. WildCard Matching

# WildCard Matching
# s; pattern p; wildcard pattern ? *
class Solution:
    def isMatch(self, s, p):
        length = len(s)
        if len(p) - p.count('*') > length:
            return False
        dp = [True] + [False]*length
        for i in p:
            if i != '*':
                for n in reversed(range(length)):
                    dp[n+1] = dp[n] and (i == s[n] or i == '?')
            else:
                for n in range(1, length+1):
                    dp[n] = dp[n-1] or dp[n]
            dp[0] = dp[0] and i == '*'
        return dp[-1]

4. Regular Expression Matching

# 10. Regular Expression Matching
# Input: string (s) and a pattern (p)
# support for '.' and '*'
# Input:
# s = "aab"
# p = "c*a*b"
# Output: true
# Explanation: c can be repeated 0 times, a can be repeated 1 time. Therefore, it matches "aab".

class Solution:
    def isMatch(self, s: str, p: str) -> bool:
        dp = [[False] * (len(s) + 1) for _ in range(len(p) + 1)]
        dp[0][0] = True
        for i in range(1, len(p)):
            dp[i + 1][0] = dp[i - 1][0] and p[i] == '*'
        for i in range(len(p)):
            for j in range(len(s)):
                if p[i] == '*':
                    dp[i + 1][j + 1] = dp[i - 1][j + 1] or dp[i][j + 1]
                    if p[i - 1] == s[j] or p[i - 1] == '.':
                        dp[i + 1][j + 1] |= dp[i + 1][j]
                else:
                    dp[i + 1][j + 1] = dp[i][j] and (p[i] == s[j] or p[i] == '.')
        return dp[-1][-1]