Public IP addresses in Azure - Time & Space Complexity

Time Complexity: Public IP addresses

O(n)

Understanding Time Complexity

When creating public IP addresses in Azure, it's important to understand how the time to complete this task changes as you create more addresses.

We want to know: how does the number of public IPs affect the total time and operations needed?

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

// Create multiple public IP addresses in Azure
for (int i = 0; i < n; i++) {
    var publicIp = new PublicIPAddress($"publicIp-{i}")
        .WithRegion("eastus")
        .WithExistingResourceGroup("myResourceGroup")
        .WithDynamicIP()
        .Create();
}
    

This sequence creates n public IP addresses one after another in a specified resource group and region.

Identify Repeating Operations

Identify the API calls, resource provisioning, data transfers that repeat.

• Primary operation: Creating a single public IP address resource via Azure API.
• How many times: Exactly n times, once per public IP address.

How Execution Grows With Input

Each new public IP requires a separate creation call, so the total work grows directly with the number of IPs.

Input Size (n)	Approx. API Calls/Operations
10	10
100	100
1000	1000

Pattern observation: Doubling the number of IPs doubles the number of API calls and total time roughly.

Final Time Complexity

Time Complexity: O(n)

This means the time to create public IP addresses grows linearly with how many you create.

Common Mistake

[X] Wrong: "Creating multiple public IPs happens all at once, so time stays the same no matter how many I create."

[OK] Correct: Each public IP creation is a separate call and provisioning step, so more IPs mean more total time.

Interview Connect

Understanding how resource creation scales helps you design efficient cloud deployments and estimate wait times realistically.

Self-Check

What if we created all public IP addresses in parallel instead of one after another? How would the time complexity change?