Flatten Fractional-Share Inventory and Record Trade Logs

Process customer buy and sell orders while keeping a firm's fractional-share inventory in [0,1) for every symbol after each order. The exchange trades only whole shares. Also return an inventory-perspective log of each exchange and customer transfer.

Implement fractional_inventory(orders: string[], inventory: string[]) -> string[][]. Return exactly two rows: the final inventory strings in input order, and the ordered log strings.

Input and Numeric Contract

• Inventory entries are SYMBOL/quantity, where integer quantity counts hundredths of a share. 50 means 0.50 shares. Symbols are unique, nonempty ASCII letters/digits/underscores. Initial quantities lie in [0,99].
• Orders are SYMBOL/B_OR_S/quantityOrDollars/price. B means the customer buys from inventory; S means the customer sells to inventory. Every symbol appears in the inventory input.
• An unprefixed integer quantity counts hundredths of a share. A quantity prefixed by $ counts cents of money. Price is positive integer cents per whole share. For dollar orders, share hundredths equal moneyCents * 100 / priceCents.
• The report does not define rounding. This practice contract admits only dollar orders whose conversion is an exact integer number of share hundredths. No fractional hundredth or rounding is required.
• At most 100000 orders and 1000 symbols. Numeric inputs are at most 1000000; use wide arithmetic for multiplication. Order quantities are positive.

Processing and Logging

Logs use SYMBOL/quantity/side/contra, where quantity is a positive integer in share hundredths, side is B or S from inventory's perspective, and contra is MARKET or CUSTOMER.

For a customer buy, obtain enough whole shares from the market first if current inventory is insufficient, then deliver the full requested quantity to the customer. Record a MARKET/B transfer only if needed, followed by a CUSTOMER/S transfer.

For a customer sell, record the CUSTOMER/B transfer first. Then sell all whole shares from inventory to the market, recording MARKET/S only if needed. Never emit zero-quantity logs. After either case, inventory must be nonnegative and below 100 hundredths.

This string-log encoding and transaction order are explicit practice choices that preserve the source's inventory perspective and example of buying from the market before delivering to a customer.

Example

inventory = ["ABC/0","XYZ/75"]
orders = ["ABC/B/150/1000","ABC/B/40/1000","ABC/S/75/1000"]
result = [["ABC/85","XYZ/75"],
 ["ABC/200/B/MARKET","ABC/150/S/CUSTOMER",
 "ABC/40/S/CUSTOMER","ABC/75/B/CUSTOMER"]]

With inventory ABC/20, a customer buy of 50 hundredths requires a market purchase of 100 and leaves ABC/70. With inventory ABC/75, a customer sell of 50 produces a customer buy log of 50, a market sell log of 100, and final inventory 25.

Explain how a single flattening invariant simplifies the cases and why language-specific negative-remainder behavior needs care. This exercise models quantity accounting only; it does not simulate prices, fees, settlement, or actual market execution.