SSH and RDP access in Azure - Time & Space Complexity

Time Complexity: SSH and RDP access

O(n)

Understanding Time Complexity

When connecting to virtual machines using SSH or RDP, it's important to understand how the number of connections affects the system.

We want to know how the time to establish access grows as more machines or users are involved.

Scenario Under Consideration

Analyze the time complexity of opening SSH or RDP sessions to multiple Azure VMs.

// Pseudocode for opening SSH or RDP sessions
for (int i = 0; i < vmCount; i++) {
    ConnectToVM(vmList[i]);
}

void ConnectToVM(string vm) {
    // Establish network connection
    // Authenticate user
    // Open session
}
    

This sequence opens a remote access session to each VM one by one.

Identify Repeating Operations

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

• Primary operation: Establishing a remote connection (SSH or RDP) to a VM.
• How many times: Once per VM, repeated for each VM in the list.

How Execution Grows With Input

Each additional VM requires a new connection, so the total time grows as you add more VMs.

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

Pattern observation: The number of connection operations grows directly with the number of VMs.

Final Time Complexity

Time Complexity: O(n)

This means the time to establish access grows linearly with the number of VMs you connect to.

Common Mistake

[X] Wrong: "Opening multiple SSH or RDP sessions happens all at once and takes the same time as one session."

[OK] Correct: Each connection requires its own setup time, so more sessions mean more total time.

Interview Connect

Understanding how connection time scales helps you design systems that handle many users or machines efficiently.

Self-Check

"What if connections were opened in parallel instead of one after another? How would the time complexity change?"