Relational patterns in C Sharp (C#) - Time & Space Complexity

Time Complexity: Relational patterns

O(n)

Understanding Time Complexity

We want to understand how fast a program runs when it uses relational patterns in C#.

Specifically, we ask: how does the program's work grow when the input changes size?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int[] numbers = {1, 5, 10, 15, 20};
int threshold = 10;

foreach (int num in numbers)
{
    if (num is > threshold)
    {
        Console.WriteLine($"{num} is greater than {threshold}");
    }
}
    

This code checks each number to see if it is greater than a threshold and prints it if true.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each number in the array.
• How many times: Once for every number in the array.

How Execution Grows With Input

As the list of numbers gets bigger, the program checks more numbers one by one.

Input Size (n)	Approx. Operations
10	10 checks
100	100 checks
1000	1000 checks

Pattern observation: The work grows directly with the number of items.

Final Time Complexity

Time Complexity: O(n)

This means the program takes longer in a straight line as the input list grows.

Common Mistake

[X] Wrong: "Relational patterns make the program faster because they are special checks."

[OK] Correct: Relational patterns are just a way to write conditions clearly; the program still checks each item one by one.

Interview Connect

Understanding how loops and conditions affect speed helps you explain your code clearly and shows you know how programs grow with input.

Self-Check

"What if we replaced the array with a sorted list and stopped checking after the first number greater than the threshold? How would the time complexity change?"

Practice

1. What does the relational pattern is > 10 check in C#?

easy

A. If a value is greater than 10

B. If a value is equal to 10

C. If a value is less than 10

D. If a value is not equal to 10

Solution

1. Step 1: Understand the relational pattern syntax

   The pattern is > 10 checks if a value is greater than 10.

2. Step 2: Compare with other options

   Options A, B, and D check less than, equality, or inequality, which are different from > 10.

3. Final Answer:

   If a value is greater than 10 -> Option A

4. Quick Check:

   Relational pattern is > 10 means greater than 10 [OK]

Hint: Relational patterns use normal math signs like >, <, == [OK]

Common Mistakes:

• Confusing > with >= or ==.
• Thinking it checks equality instead of comparison.
• Mixing up less than and greater than signs.

2. Which of the following is the correct syntax to check if an integer n is less than or equal to 5 using a relational pattern?

easy

A. if (n is <= 5) { }

B. if (n <= 5) { }

C. if (n is < = 5) { }

D. if (n is <=5) { }

Solution

1. Step 1: Identify correct relational pattern syntax

   The relational pattern syntax uses is followed by the operator and value without spaces inside the operator, like is <= 5.

2. Step 2: Check each option

   if (n is <= 5) { } uses correct syntax: if (n is <= 5). if (n <= 5) { } is normal comparison, not a relational pattern. if (n is < = 5) { } has a space between < and = which is invalid. if (n is <=5) { } misses a space after is, which is required.

3. Final Answer:

   if (n is <= 5) { } -> Option A

4. Quick Check:

   Relational pattern syntax: is <= value [OK]

Hint: Relational patterns need 'is' then operator with no spaces inside operator [OK]

Common Mistakes:

• Using normal comparison without 'is'.
• Adding spaces inside the operator like '< ='.
• Omitting space after 'is'.

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

int x = 7;
if (x is >= 5 and < 10)
    Console.WriteLine("In range");
else
    Console.WriteLine("Out of range");

medium

A. No output

B. Out of range

C. In range

D. Compilation error

Solution

1. Step 1: Evaluate the relational pattern condition

   The condition x is >= 5 and < 10 checks if x is between 5 and 9 inclusive. Since x = 7, it satisfies both parts.

2. Step 2: Determine which branch runs

   Because the condition is true, the Console.WriteLine("In range") runs, printing "In range".

3. Final Answer:

   In range -> Option C

4. Quick Check:

   7 is between 5 and 10, so output is "In range" [OK]

Hint: Check both parts of 'and' relational pattern carefully [OK]

Common Mistakes:

• Thinking 'and' means 'or'.
• Ignoring one part of the condition.
• Assuming syntax error due to 'and'.

4. Identify the error in this code snippet using relational patterns:

int score = 85;
switch (score)
{
    case is > 90:
        Console.WriteLine("Excellent");
        break;
    case is >= 80 and < 90:
        Console.WriteLine("Good");
        break;
    default:
        Console.WriteLine("Average");
        break;
}

medium

A. The 'and' keyword is not allowed in switch case patterns

B. Missing braces around case blocks

C. Relational patterns cannot be used in switch cases

D. The pattern 'is > 90' should be 'case > 90:' without 'is'

Solution

1. Step 1: Identify the syntax error in switch case patterns

   Relational patterns in switch statements use syntax like case > 90:, without the is keyword. The code incorrectly uses case is > 90: and case is >= 80 and < 90:.

2. Step 2: Evaluate the options

   The 'and' keyword is not allowed in switch case patterns is incorrect; and is allowed to combine patterns like case >= 80 and < 90:. The pattern 'is > 90' should be 'case > 90:' without 'is' correctly identifies the misuse of is. Relational patterns cannot be used in switch cases is false; relational patterns are supported in switch cases. Missing braces around case blocks is wrong; braces are not required around case contents.

3. Final Answer:

   The pattern 'is > 90' should be 'case > 90:' without 'is' -> Option D

4. Quick Check:

   Switch case relational pattern: case > value, no is [OK]

Hint: No 'is' keyword needed for relational patterns in switch cases [OK]

Common Mistakes:

• Adding 'is' before relational operators in switch cases.
• Thinking 'and' cannot combine patterns in switch cases.
• Confusing switch statements with 'is' patterns.

5. You want to write a method that returns "Child", "Teen", or "Adult" based on age using relational patterns. Which of these switch expressions correctly implements this?

string GetAgeGroup(int age) => age switch
{
    < 13 => "Child",
    >= 13 and < 20 => "Teen",
    _ => "Adult"
};

hard

A. Replace 'and' with '&&' in the second pattern

B. Correct as is

C. Use nested if statements instead of switch

D. Add parentheses around '>= 13 and < 20'

Solution

1. Step 1: Analyze the switch expression with relational patterns

   The switch expression uses relational patterns correctly: < 13 for "Child", combined pattern >= 13 and < 20 for "Teen", and default for "Adult".

2. Step 2: Confirm syntax correctness

   The 'and' keyword is valid in switch expressions for combining patterns. No parentheses or '&&' are needed here.

3. Final Answer:

   Correct as is -> Option B

4. Quick Check:

   Switch expressions support 'and' for combined relational patterns [OK]

Hint: Use 'and' to combine relational patterns in switch expressions [OK]

Common Mistakes:

• Replacing 'and' with '&&' which is invalid in patterns.
• Adding unnecessary parentheses.
• Thinking switch expressions don't support relational patterns.