Splitting models for print bed fit in 3D Printing - Time & Space Complexity

Time Complexity: Splitting models for print bed fit

O(n)

Understanding Time Complexity

When splitting a 3D model to fit a print bed, it's important to understand how the time to split grows as the model size increases.

We want to know how the work needed changes when the model gets bigger or more complex.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function splitModel(modelParts, bedSize) {
  let splitParts = [];
  for (let part of modelParts) {
    if (part.size > bedSize) {
      let halves = splitPart(part);
      splitParts.push(...halves);
    } else {
      splitParts.push(part);
    }
  }
  return splitParts;
}

function splitPart(part) {
  // Splits part into two smaller parts
  return [part.slice(0, part.size / 2), part.slice(part.size / 2)];
}
    

This code checks each part of a model and splits it if it is too big to fit on the print bed.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each model part and splitting parts that are too large.
• How many times: The loop runs once for each part, and splitting can cause more parts to be added and checked again.

How Execution Grows With Input

As the number of parts increases, the time to check and possibly split each part grows.

Input Size (n)	Approx. Operations
10	About 10 checks and some splits if needed
100	About 100 checks and more splits, possibly doubling parts
1000	About 1000 checks and many splits, increasing parts significantly

Pattern observation: The work grows roughly in proportion to the number of parts, but splitting can increase parts, making the work grow faster.

Final Time Complexity

Time Complexity: O(n)

This means the time to split models grows roughly in direct proportion to the number of parts to check and split.

Common Mistake

[X] Wrong: "Splitting a model always takes the same time no matter how big it is."

[OK] Correct: Larger or more complex models have more parts to check and split, so the time needed grows with model size.

Interview Connect

Understanding how splitting models scales with size shows you can think about how tasks grow and manage complexity, a useful skill in many technical roles.

Self-Check

"What if the splitting function split parts into three smaller parts instead of two? How would the time complexity change?"