This question tests your understanding of modal verbs and perfect infinitives in English grammar, specifically for expressing unnecessary past actions.

The sentence structure indicates a past situation where someone did something that wasn't necessary: "You ________________ for me; I could have found the way all right."

The correct grammatical structure for expressing that an action was performed in the past but was unnecessary is: needn't have + past participle.

Let's analyze the options:

Option 1: Couldn't have wait - Incorrect because "couldn't have" requires a past participle ("waited"), not base form ("wait")

Option 2: Don't have to wait - Incorrect because this refers to present/future necessity, not past unnecessary action

Option 3: Needn't have waited - CORRECT - This perfectly expresses that the waiting action was unnecessary in the past

Option 4: Didn't needed to wait - Incorrect because after "didn't" we need the base form "need," not "needed"

Related Grammar Concepts

Modal Perfect Structures: These are used to talk about past situations with modal verbs. The pattern is: modal + have + past participle.

Need as a semi-modal: "Need" can function both as a regular verb and as a modal verb. In "needn't have," it acts as a modal verb.

Key Formula

To express unnecessary past action: Needn't have + past participle

Example: You needn't have brought your umbrella (but you did bring it unnecessarily)

Contrast with: Didn't need to + base verb (which means the action wasn't necessary and may or may not have been performed)