Recursive pattern matching in C Sharp (C#) - Time & Space Complexity

Time Complexity: Recursive pattern matching

O(2^(m+n))

Understanding Time Complexity

When we use recursive pattern matching, the program calls itself to check parts of data step by step.

We want to know how the time it takes grows as the input gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

bool MatchPattern(string text, string pattern) {
    return (text, pattern) switch {
        ("", "") => true,
        (_, "") => false,
        (string t, string p) when p[0] == '*' =>
            MatchPattern(t, p[1..]) || (t != "" && MatchPattern(t[1..], p)),
        (string t, string p) when p[0] == '?' =>
            t != "" && MatchPattern(t[1..], p[1..]),
        (string t, string p) =>
            t != "" && t[0] == p[0] && MatchPattern(t[1..], p[1..])
    };
}
    

This code checks if a text matches a pattern with wildcards using recursion and pattern matching.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Recursive calls that reduce the text or pattern by one character.
• How many times: Up to the length of the text and pattern combined, but can branch due to '*'.

How Execution Grows With Input

Each recursive call tries to match smaller parts of the text and pattern, sometimes branching into two calls when '*' is found.

Input Size (n)	Approx. Operations
10	Up to about 2^10 (around 1000) calls in worst case
100	Up to about 2^100 calls (very large, impractical)
1000	Exponential growth, too large to compute

Pattern observation: The number of operations can grow very fast, doubling with each '*' in the pattern.

Final Time Complexity

Time Complexity: O(2^(m+n))

This means the time can grow exponentially with the combined length of text (m) and pattern (n), especially due to branching on '*'.

Common Mistake

[X] Wrong: "The recursion will always run in linear time because it reduces the input each call."

[OK] Correct: Sometimes the recursion splits into two calls (branching), causing the total calls to grow exponentially, not just linearly.

Interview Connect

Understanding recursive pattern matching helps you think about how recursion and branching affect performance, a key skill in many coding problems.

Self-Check

"What if we added memoization to store results of subproblems? How would the time complexity change?"

Practice

1. What is the main purpose of recursive pattern matching in C#?

easy

A. To break down complex data structures step-by-step

B. To create loops that run forever

C. To declare variables without types

D. To handle exceptions automatically

Solution

1. Step 1: Understand recursive pattern matching concept

   Recursive pattern matching is used to analyze data by breaking it down into smaller parts recursively.

2. Step 2: Identify the purpose from options

   To break down complex data structures step-by-step correctly states that it breaks down complex data structures step-by-step, which matches the concept.

3. Final Answer:

   To break down complex data structures step-by-step -> Option A

4. Quick Check:

   Recursive pattern matching = step-by-step data breakdown [OK]

Hint: Think: recursive means breaking down data stepwise [OK]

Common Mistakes:

• Confusing recursion with infinite loops
• Thinking it declares variables
• Assuming it handles exceptions

2. Which of the following is the correct syntax to use recursive pattern matching in a C# switch expression?

easy

A. case Node(var value, var next):

B. case Node[value, next]:

C. case Node->(value, next):

D. case Node[value; next]:

Solution

1. Step 1: Recall C# recursive pattern syntax

   In C#, recursive patterns use parentheses with variables inside, like Node(var value, var next).

2. Step 2: Compare options to correct syntax

   case Node(var value, var next): matches the correct syntax. Other options use invalid symbols like brackets or arrows.

3. Final Answer:

   case Node(var value, var next): -> Option A

4. Quick Check:

   Recursive pattern syntax uses parentheses ( ) [OK]

Hint: Look for parentheses with variables inside in case patterns [OK]

Common Mistakes:

• Using square brackets instead of parentheses
• Using arrows or semicolons incorrectly
• Missing 'var' keyword before variables

3. What will be the output of this C# code snippet?

record Node(int Value, Node? Next);
Node list = new(1, new(2, new(3, null)));

string PrintList(Node? node) => node switch
{
    null => "End",
    Node(var v, var n) => $"{v} -> " + PrintList(n)
};

Console.WriteLine(PrintList(list));

medium

A. 1 2 3 End

B. End

C. 1 -> 2 -> 3 -> End

D. 1 -> 2 -> 3

Solution

1. Step 1: Understand the recursive function PrintList

   PrintList prints the current node's value, then calls itself on the next node, until it reaches null and returns "End".

2. Step 2: Trace the output for list nodes 1, 2, 3

   It prints "1 -> " + PrintList(2), then "2 -> " + PrintList(3), then "3 -> " + PrintList(null), which returns "End".

3. Final Answer:

   1 -> 2 -> 3 -> End -> Option C

4. Quick Check:

   Recursive print with null base case = 1 -> 2 -> 3 -> End [OK]

Hint: Follow recursion calls and base case carefully [OK]

Common Mistakes:

• Ignoring the base case output
• Missing arrows in output
• Confusing spaces with arrows

4. Identify the error in this recursive pattern matching code:

record Node(int Value, Node? Next);
string PrintList(Node? node) => node switch
{
    Node(var v, var n) => $"{v} -> " + PrintList(n),
    null => "End"
};

medium

A. Missing semicolon after switch expression

B. No error, code works correctly

C. The pattern 'Node(var v, var n)' is invalid syntax

D. The order of cases should have 'null' before 'Node' to avoid errors

Solution

1. Step 1: Check switch expression order and syntax

   In C#, switch expressions check patterns top to bottom. Here, 'Node' pattern matches non-null nodes, and 'null' matches null nodes. The order is valid.

2. Step 2: Verify syntax correctness

   The pattern syntax and semicolons are correct. No syntax errors exist.

3. Final Answer:

   No error, code works correctly -> Option B

4. Quick Check:

   Pattern order and syntax are valid [OK]

Hint: Null pattern can be last in switch expressions [OK]

Common Mistakes:

• Thinking null must come first
• Assuming missing semicolon error
• Misreading pattern syntax

5. Given a binary tree defined as:

record TreeNode(int Value, TreeNode? Left, TreeNode? Right);

Write a recursive pattern matching expression to calculate the sum of all values in the tree. Which of the following switch expressions correctly implements this?

hard

A. node switch { null => 0, TreeNode(v, l, r) => v + Sum(l) + Sum(r) }

B. node switch { TreeNode(v, l, r) => v + Sum(l) + Sum(r), null => 0 }

C. node switch { null => 0, TreeNode(var v, var l) => v + Sum(l) }

D. node switch { null => 0, TreeNode(var v, var l, var r) => v + Sum(l) + Sum(r) }

Solution

1. Step 1: Understand the tree structure and sum logic

   The tree node has three parts: Value, Left, and Right. The sum should add the current value plus sums of left and right subtrees.

2. Step 2: Check each option for correct pattern and order

   node switch { null => 0, TreeNode(var v, var l, var r) => v + Sum(l) + Sum(r) } correctly matches null first (base case) and then TreeNode with three variables (value, left, right). It sums value + Sum(left) + Sum(right). node switch { TreeNode(v, l, r) => v + Sum(l) + Sum(r), null => 0 } misses 'var' keywords, which is required. node switch { null => 0, TreeNode(v, l, r) => v + Sum(l) + Sum(r) } misses 'var' keywords, which is required. node switch { null => 0, TreeNode(var v, var l) => v + Sum(l) } misses the right subtree.

3. Final Answer:

   node switch { null => 0, TreeNode(var v, var l, var r) => v + Sum(l) + Sum(r) } -> Option D

4. Quick Check:

   Correct pattern with all parts and base case first [OK]

Hint: Include all node parts and base case null first [OK]

Common Mistakes:

• Omitting 'var' in pattern variables
• Missing one subtree in sum
• Placing null case after non-null without care