Update examples/How_to_count_tokens_with_tiktoken.ipynb

[ChenyangLi4288]

Summary

This PR adds comprehensive examples for counting tokens with structured responses to the existing "How to count tokens with tiktoken" notebook, addressing issue #2102. The addition includes a new function for calculating token overhead from structured response schemas, practical examples comparing different response formats, and API verification to ensure accuracy.

Motivation

The existing notebook provided excellent coverage for counting tokens in regular messages and tool calls, but lacked examples for structured responses - a key feature that adds token overhead due to schema definitions and validation instructions. This gap left developers without guidance on how to estimate token consumption when using structured outputs, which is increasingly important as more applications adopt structured response formats for better data consistency and parsing.

The new examples fill this gap by:

• Providing a dedicated function to calculate structured response token overhead
• Demonstrating both simple JSON object format and complex structured schemas
• Showing how schema complexity directly impacts token consumption
• Including API verification to validate the token counting estimates
• Following the same educational pattern as existing sections for consistency

This addition makes the cookbook more complete and helps developers make informed decisions about when and how to use structured responses based on their token budget considerations.

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