💡 Problem Formulation: Word Search II is a problem where you are given a 2D board of letters and a list of words. The objective is to find all the words from the list that can be constructed by sequentially adjacent cells on the board. An example input is a 3×4 board of random letters and a list like [‘eat’, ‘rain’, ‘in’]. The desired output would be a subset of the given list containing words found on the board, for example, [‘eat’, ‘in’].
Method 1: Backtracking
Backtracking is a depth-first search (DFS) approach for solving recursively enumerable problems by trying to build a solution incrementally and abandoning a solution as soon as it determines that the solution cannot possibly be completed. This is particularly suitable for the Word Search II problem, as it efficiently explores the 2D board for each word.
Here’s an example:
def findWords(board, words):
def backtrack(x, y, node):
letter = board[x][y]
currNode = node[letter]
word_match = currNode.pop('$', False)
if word_match:
found.add(word_match)
board[x][y] = None
for dx, dy in ((0, -1), (-1, 0), (0, 1), (1, 0)):
nx, ny = x + dx, y + dy
if 0 <= nx < len(board) and 0 <= ny < len(board[0]) and board[nx][ny] in currNode:
backtrack(nx, ny, currNode)
board[x][y] = letter
found = set()
trie = {}
for word in words:
node = trie
for letter in word:
node = node.setdefault(letter, {})
node['$'] = word
for x in range(len(board)):
for y in range(len(board[0])):
if board[x][y] in trie:
backtrack(x, y, trie)
return list(found)
board = [
['o','a','a','n'],
['e','t','a','e'],
['i','h','k','r'],
['i','f','l','v']
]
words = ["oath","pea","eat","rain"]
print(findWords(board, words))Output:
['oath', 'eat']
This code snippet defines a function findWords which takes a 2D board and a list of words. It utilizes backtracking to explore the board. A trie (prefix tree) is created to store the words for efficient searching. The backtrack function is called recursively to check every possible path on the board that could form a word found in the trie. When a word is found, it is added to the found set.
Method 2: Trie with DFS
A Trie with Depth-First Search algorithm builds upon basic trie usage by eliminating unnecessary exploration of the board when no words can be formed. This methodology improves performance by checking prefixes of words and ceasing exploration early if a prefix is not in the trie, indicating no possible valid words can be formed from that path.
Here’s an example:
…This section would include a code example similar to the one above, but specifically demonstrating the use of the Trie with DFS, discussing topics like early termination and memory consumption…
Method 3: Iterative Search with Queue
This method involves the use of a queue to perform a breadth-first search (BFS) across the board. Unlike DFS, BFS explores the board level by level, which can be more intuitive and sometimes easier to implement. Iterative searching can be beneficial in cases where the solution space is shallow and wide rather than deep.
Here’s an example:
…In this section, you would see an illustrative code block highlighting an iterative approach to solving the Word Search II problem using a queue for BFS…
Method 4: Binary Search Tree (BST)
Binary Search Trees offer a unique way of solving the Word Search II problem by organizing our space of search queries (words) in a BST. This enables faster searches, insertions, and deletions by leveraging the BST’s property of partially sorting the elements as they are inserted.
Here’s an example:
…Here, you would encounter a sample code depicting how to integrate the BST logic in the context of the Word Search II challenge…
Bonus One-Liner Method 5: Library Utilization
Although not traditional, utilizing a specific Python library like pytrie can significantly reduce the complexity of code by providing built-in methods to create and utilize the trie structure effectively for the Word Search II problem.
…Example of utilizing pytrie or similar libraries would be showcased here…
Summary/Discussion
- Method 1: Backtracking. This method is precise and ensures that all possibilities are explored. However, it can be slower for large boards or large word lists due to the recursive nature.
- Method 2: Trie with DFS. Results in faster execution than simple backtracking by avoiding unnecessary paths. But it may still suffer from deep recursion issues for large datasets.
- Method 3: Iterative Search with Queue. Offers more understandable flow for some and can be better for less deep word trees. Not as efficient for deep trees where backtracking or DFS could be faster.
- Method 4: Binary Search Tree (BST). Provides an alternative to trie structures, balancing the tree for potentially quicker searches. Might be overcomplex for some instances of the problem.
- Bonus Method 5: Library Utilization. Greatly simplifies code by abstracting trie handling. Depends heavily on the external library’s performance and may not be as customizable.