Count Algorithm Operations

1) What you are counting

When an algorithm question asks for the number of operations, the goal is to express how much work the algorithm does as an exact count or a simplified total. An operation can be a comparison, assignment, arithmetic step, or another basic action depending on the exercise.

2) Count systematically

• Read the algorithm line by line.
• Decide which statements are executed once, which repeat, and which depend on a condition.
• For repeated parts, count how many times each loop runs.
• Multiply the number of executions by the number of operations inside the repeated block.
• Add all separate counts together.

3) Simplify the result

If the total is given as an expression, combine like terms and reduce it fully. Keep coefficients and constants accurate. If the exercise involves parameters such as n, leave the answer in simplified algebraic form unless a numerical value is requested.

4) Check your count

A good check is to test a small input size and verify that your expression matches the actual number of steps. Make sure you did not double-count operations inside nested repetition or forget the last comparison in a loop.

5) Common mistakes

• Counting a loop body only once instead of once per iteration.
• Forgetting setup or final check operations.
• Simplifying before finishing the full count.

Use a careful, step-by-step tally, then simplify at the end.