Choose when a long agent session compacts its history

Agent buildMedium30 min

Your task

Your coding agent sends its whole history on every model call. A long session pays for the same tokens again and again, and can outgrow the context window. Compacting swaps the history for a short summary, but a compaction is a model call too, and it reads everything.

Write least_tokens(turns, system, summary, window) that returns the fewest tokens a session can spend.

Input and output:

turns: up to 1,000 whole numbers from 1 to 100,000. Turn i adds turns[i] tokens to the history.
system: the tokens of the system prompt, 0 to 100,000.
summary: the tokens of a compaction's summary, 0 to 100,000.
window: the most tokens one model call may read, 1 to 100,000,000.
Return a whole number: the fewest tokens, or -1 when no plan keeps every call within the window.

Rules:

The history starts empty. Each turn adds its tokens to the history, then makes one model call that reads system plus the whole history.
After any turn, the agent may compact. Compacting is one model call that reads system plus the whole history and writes summary tokens. The summary then replaces the history.
No model call may read more than window tokens.
A session spends every token any call reads, plus summary tokens for each compaction.

Examples

least_tokens(turns: list[int], system: int, summary: int, window: int) -> int

Example 1

Inputleast_tokens([100, 200, 300], 50, 40, 10000)

Output1150

Example 2

Inputleast_tokens([300, 300, 300], 50, 50, 700)

Output1850

Example 3

Inputleast_tokens([500, 600], 100, 0, 650)

Output-1