Approach

To effectively solve the wildcard matching problem using dynamic programming, follow this structured framework:

1. Understand the Problem Statement: The goal is to determine if a given string matches a pattern that includes wildcard characters. The wildcard characters are:

• ? which matches any single character.

• * which matches zero or more characters.

• Define Subproblems: The matching can be broken down into smaller subproblems where we check matching between the string and the pattern at different indices.

• Set Up a DP Table: Create a 2D boolean array dp where dp[i][j] indicates whether the first i characters of the string match the first j characters of the pattern.

• Initialize Base Cases: Define initial values for when either the string or pattern is empty.

• Fill the DP Table: Use a nested loop to fill in the dp table based on the matching rules for characters and wildcards.

• Return the Result: The final value in the dp table will indicate whether the entire string matches the entire pattern.

Key Points

• Dynamic Programming: This approach leverages the overlapping subproblems property of dynamic programming, optimizing the matching process.

• Initialization: Correctly initializing the dp table is crucial for accurate results.

• Iterative Filling: Ensure all possible matches are considered through careful iteration over string and pattern characters.

• Final Output: The solution should return a boolean value indicating whether there is a match.

Standard Response

Here’s a sample implementation of the wildcard matching problem using dynamic programming in Python:

def isMatch(s: str, p: str) -> bool:
 # Initialize the DP table
 dp = [[False] * (len(p) + 1) for _ in range(len(s) + 1)]
 dp[0][0] = True # Both string and pattern are empty

 # Handle patterns with leading '*'
 for j in range(1, len(p) + 1):
 if p[j - 1] == '*':
 dp[0][j] = dp[0][j - 1]

 # Fill the DP table
 for i in range(1, len(s) + 1):
 for j in range(1, len(p) + 1):
 if p[j - 1] == '*':
 # '*' matches zero characters (dp[i][j-1]) or one character (dp[i-1][j])
 dp[i][j] = dp[i][j - 1] or dp[i - 1][j]
 elif p[j - 1] == '?' or s[i - 1] == p[j - 1]:
 # Either '?' matches any character or characters are equal
 dp[i][j] = dp[i - 1][j - 1]

 # The result is in the bottom-right corner of the DP table
 return dp[len(s)][len(p)]

# Example usage:
s = "adceb"
p = "*a*b"
print(isMatch(s, p)) # Output: True

Tips & Variations

Common Mistakes to Avoid

• Incorrect Initialization: Failing to account for patterns that start with * can lead to incorrect results.

• Off-by-One Errors: Ensure that loops iterate correctly to avoid accessing out-of-bounds indices.

• Neglecting Edge Cases: Consider edge cases, such as empty strings and patterns.

Alternative Ways to Answer

• For a recursive approach, one can recursively check each character against the pattern and handle wildcards accordingly.

• A backtracking approach can also be used, though it may not be as efficient as dynamic programming for larger strings and patterns.

Role-Specific Variations

• For Technical Interviews: Emphasize your understanding of dynamic programming principles and complexity analysis.

• For Managerial Roles: Discuss your problem-solving process and how you would lead a team to implement such algorithms effectively.

• For Creative Positions: Highlight your ability to think outside the box in algorithm design, perhaps considering unconventional matching strategies.

Follow-Up Questions

• How would you optimize this solution further?

• Can you explain the time and space complexity of your approach?

• How would you handle a situation where the pattern contains multiple consecutive wildcards?

By following this structured approach and employing the provided tips, job seekers can effectively demonstrate their problem-solving skills in technical interviews, particularly in coding challenges related to dynamic programming and algorithms