Chat Billing Calculation (Monthly Billing by Token Usage and Plan Switching)

Problem: Chat Billing Calculation (Token Usage + Plan Switching) Implement a billing function to compute each user's total charges for a given month based on chat session token usage. Input You are given an array of strings sessions, where each string represents one chat session during the month in the format: "user_id,input_tokens,output_tokens,plan" user_id: user identifier (string) input_tokens: number of input tokens for the session (non-negative integer) output_tokens: number of output tokens for the session (non-negative integer) plan: plan used for this session, either: payg (pay-as-you-go) fixed A user may appear multiple times (multiple sessions in the month). Output Return an array of strings result, each formatted as: "user_id: $x.xx" representing the user's total spend for the month (rounded/formatted to 2 decimals). Requirements: Sort the output array alphabetically by user_id. Users with total spend < $1.00 must still appear (e.g., $0.00, $0.87). Billing rules Common rule: bill in 100-token blocks Tokens are billed in blocks of 100. Only full 100-token blocks are counted; any partial block is not billed/charged. Example: 0–99 => 0 blocks; 100–199 => 1 block; 200–299 => 2 blocks. Requirement 1: payg pricing (test cases 0–4) If plan = payg: Input tokens cost $0.03 per 100 tokens Output tokens cost $0.04 per 100 tokens For each session: input charge = floor(input_tokens / 100) * 0.03 output charge = floor(output_tokens / 100) * 0.04 Monthly total is the sum over all sessions. Requirement 2: fixed plan (test cases 5–9) If the user uses fixed for the month: Monthly fee: $15.00 Included allowance: 40000 tokens per month (counted in 100-token blocks) Any usage above the included allowance (overage) is charged at payg rates ($0.03/100 for input, $0.04/100 for output). Allowance and overage calculations must also follow the full 100-token block rule. Requirement 3: Plan switching and proration by sessions (test cases 10–13) Users may switch plans within a billing cycle (some sessions payg, some fixed). If the user has N total sessions in the month, and F of them are fixed: Prorate the fixed monthly fee by session count: fixed_fee = 15.00 * (F / N) Prorate the fixed allowance similarly: fixed_allowance = 40000 * (F / N) tokens (still subject to 100-token block counting) Billing constraints: Token blocks must be computed separately per plan. payg sessions are charged directly using Requirement 1. fixed sessions first consume the prorated fixed_allowance; any excess is charged at payg rates. The final monthly spend is: payg_charges + fixed_fee + fixed_overage_charges.