Time Complexity: G01 linear interpolation (cutting feed)
O(n)
0
0
G01 linear interpolation (cutting feed) in CNC Programming - Time & Space Complexity
Understanding Time Complexity
We want to understand how the time to complete a G01 linear move changes as the distance or number of moves increases.
How does the program's execution time grow when cutting longer or more lines?
Scenario Under Consideration
Analyze the time complexity of the following CNC program snippet using G01 commands.
N10 G01 X10 Y0 F100
N20 G01 X20 Y10
N30 G01 X30 Y20
N40 G01 X40 Y30
N50 G01 X50 Y40
This code moves the tool in straight lines from one point to the next at a set feed rate.
Identify Repeating Operations
Each G01 command moves the tool along a straight line.
- Primary operation: Executing each linear move command (G01).
- How many times: Once per line segment, so the number of moves equals the number of G01 commands.
How Execution Grows With Input
As you add more G01 commands, the total execution time grows roughly in direct proportion to the number of moves.
| Input Size (n) | Approx. Operations |
|---|---|
| 10 moves | 10 linear moves executed |
| 100 moves | 100 linear moves executed |
| 1000 moves | 1000 linear moves executed |
Pattern observation: Doubling the number of moves doubles the execution time.
Final Time Complexity
Time Complexity: O(n)
This means the time to complete all moves grows linearly with the number of G01 commands.
Common Mistake
[X] Wrong: "The time to execute G01 commands stays the same no matter how many moves there are."
[OK] Correct: Each G01 command requires the machine to move along a line, so more commands mean more moves and more time.
Interview Connect
Understanding how execution time grows with commands helps you write efficient CNC programs and shows you can reason about machine performance.
Self-Check
What if we combined multiple linear moves into one longer G01 command? How would the time complexity change?