Fractional Inventory

Fractional Stock Inventory

You are given two lists that are both sorted by stock symbol: a list of pending orders and a list representing your current fractional stock holdings. Write a function solve(inventory, orders) that processes each order in sequence and returns the updated inventory after all orders have been handled, keeping the result sorted by symbol.

Each order is an array of the form [symbol, type, quantity, unit_price]:

• symbol: a ticker string (e.g., "AAPL").
• type: "B" for a buy order, "S" for a sell order.
• quantity: either a plain integer (representing a share fraction in hundredths) or a dollar amount string starting with "$" (also in hundredths).
• unit_price: the current price of one share, expressed in hundredths.

Each inventory entry is a pair [symbol, amount] where amount is an integer between 0 and 99 inclusive, representing the current fractional share count in hundredths. For example, an inventory entry ["AAPL", 50] means you hold 0.50 shares of AAPL.

Important: the last two digits of every integer are the decimal part. For instance, an order ["AAPL", "B", "42", "100"] means you want to buy 0.42 shares of AAPL at $1.00 per share. A dollar-based order like ["AAPL", "B", "$50", "100"] means you want to spend $0.50; at $1.00 per share this buys 0.50 shares. An inventory value of 50 means 0.50 shares.

Your inventory always holds strictly less than one whole share of any stock. This invariant must be maintained after each order is processed: if the fraction reaches 100 or more, discard the whole‑share part and keep only the remainder modulo 100.

Processing rules:

• Buy order:
  If the current fractional inventory for that symbol is sufficient to cover the demanded quantity, simply subtract the order amount from the inventory. If the inventory is insufficient, calculate the shortfall, purchase enough whole shares to cover it, subtract the ordered quantity, and keep whatever remains as the new fractional inventory (which will be less than 100).

• Sell order:
  Add the sold quantity to the existing fractional inventory. Then remove any whole shares by taking the result modulo 100, leaving only the fractional part.

When the order quantity is a dollar amount, first convert it to a share quantity by dividing the dollar amount by the unit price (both in hundredths). Use integer arithmetic carefully to preserve the conversion.

After processing all orders, return the inventory as a list of [symbol, amount] pairs, sorted by symbol.

Example 1:

Input: orders = [["AAPL", "B", "42", "100"], ["GOOG", "S", "$80", "160"]], inventory = [["AAPL", "99"], ["GOOG", "60"]]
Output: [["AAPL", "57"], ["GOOG", "10"]]

Explanation:

• The first order is a buy of 0.42 AAPL shares. The current AAPL inventory is 0.99 shares, which is enough to cover the purchase. Subtract 42 from 99, leaving 57 (0.57 shares).
• The second order is a sell, expressed as $0.80 worth of GOOG. At a price of $1.60 per share, this converts to 0.50 shares (80 * 100 / 160 = 50 in hundredths). Add the 50 to the existing GOOG inventory of 60, giving 110. Because 110 ≥ 100, we keep only the fractional part: 110 mod 100 = 10, resulting in 0.10 shares.

inventory = [['AAPL', '99'], ['GOOG', '60']]
orders = [['AAPL', 'B', '42', '100'], ['GOOG', 'S', '$80', '160']]

[['AAPL', '57'], ['GOOG', '10']]

Example 2:

Input: orders = [["AAPL","B","$42","100"]], inventory = [["AAPL","50"]]
Output: [["AAPL","8"]]

Example 3:

Input: orders = [["AAPL","S","75","100"]], inventory = [["AAPL","60"]]
Output: [["AAPL","35"]]

Constraints:

• The input lists are sorted by stock symbol.
• Every inventory quantity is an integer in the range [0, 99].
• Order quantities are either plain integers in hundredths or dollar‑amount strings like "$42" (also in hundredths).
• Unit prices are integer hundredths.
• For dollar‑based orders, the conversion to shares uses integer division; the problem guarantees that the conversion yields a valid whole‑share quantity.
• The function must maintain the invariant that after each order the fractional inventory is strictly less than 100 (i.e., amount < 100).
• The returned inventory must be sorted by symbol.