Design a token manager with lazy expiration

Problem

Design a token manager that tracks authentication tokens with a fixed time-to-live (TTL). Each token is valid in the half-open time interval [createdTime, createdTime + timeToLive).

You must support the following operations:

• TokenManager(timeToLive) : initialize the manager with a positive integer TTL.
• generate(tokenId, currentTime) : create a new token with id tokenId at currentTime . If tokenId already exists, overwrite it with the new creation time.
• renew(tokenId, currentTime) : if tokenId exists and is unexpired at currentTime , update its creation time to currentTime (thus extending its expiry). If it does not exist or is expired, do nothing.
• countUnexpiredTokens(currentTime) : return the number of tokens that are unexpired at currentTime .

Requirement: implement efficiently using a lazy deletion strategy for expired tokens (i.e., remove expired entries only when needed, rather than scanning all tokens each time).

Constraints

• 1 <= timeToLive <= 10^8
• Up to 2 * 10^5 total operations
• 1 <= currentTime <= 10^9
• tokenId is a string of length 1..20 containing letters/digits

Example

Assume timeToLive = 5.

• generate("abc", 1) → token abc valid until time 6
• renew("abc", 5) → token abc valid until time 10
• countUnexpiredTokens(6) → returns 1
• countUnexpiredTokens(10) → returns 0 (expires at 10 )