Infinite loops in Go - Time & Space Complexity

Time Complexity: Infinite loops

O(∞)

Understanding Time Complexity

Infinite loops run without stopping, so their execution time keeps growing forever.

We want to understand what happens to the running time when a loop never ends.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

package main

func main() {
    for {
        // do something simple
    }
}

This code runs a loop that never stops, repeating the same action endlessly.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The infinite for loop repeating the inner action.
• How many times: Forever, with no end.

How Execution Grows With Input

Since the loop never stops, the number of operations keeps increasing without limit.

Input Size (n)	Approx. Operations
10	Very large, keeps growing
100	Even larger, keeps growing
1000	Much larger, keeps growing

Pattern observation: The operations grow endlessly, never stopping or slowing down.

Final Time Complexity

Time Complexity: O(∞)

This means the program runs forever, so the time needed is infinite and never finishes.

Common Mistake

[X] Wrong: "The loop will finish eventually because computers are fast."

[OK] Correct: An infinite loop has no stopping point, so no matter how fast the computer is, it never ends.

Interview Connect

Understanding infinite loops helps you spot when code might run forever, which is important for writing reliable programs.

Self-Check

"What if we add a condition inside the loop to stop after n times? How would the time complexity change?"