Stock Price Fluctuation

You are given a live stream of stock price updates arriving one at a time, and you must build a small system that keeps track of them and answers questions about the current state of the stock.

Each update is a pair (timestamp, price), meaning that at the given timestamp the stock traded at the given price. Updates for the same timestamp can arrive more than once, and a later update overwrites the price recorded for that timestamp (it does not create a second record). Updates do not necessarily arrive in increasing order of timestamp — an update for an earlier timestamp can show up after one for a later timestamp.

Design a class StockPrice that supports:

• StockPrice() — initializes the object, with no price data recorded yet.
• update(timestamp, price) — records that at timestamp the price was price, overwriting any price previously recorded for that same timestamp.
• current() — returns the price at the latest timestamp seen so far (latest meaning the largest timestamp value recorded via update, not the order calls were made).
• maximum() — returns the highest price recorded across all timestamps seen so far, using the most up-to-date value for each timestamp.
• minimum() — returns the lowest price recorded across all timestamps seen so far, using the most up-to-date value for each timestamp.

Notes to keep in mind:

• A correction to an old timestamp must be reflected immediately in current, maximum, and minimum — stale prices should never be counted once they've been overwritten.
• current() is based on the largest timestamp value ever given to update, regardless of call order.
• It is guaranteed that current(), maximum(), and minimum() are only called after at least one update call has happened.

Examples

Example 1:

Input:

["StockPrice", "update", "update", "current", "maximum", "update", "maximum", "update", "minimum"]
[[], [2, 50], [4, 80], [], [], [3, 65], [], [4, 30], []]

Output:

[null, null, null, 80, 80, null, 80, null, 30]

Explanation:

• update(2, 50) and update(4, 80) record two prices.
• current() returns 80, the price at timestamp 4, the largest timestamp so far.
• maximum() returns 80 (the max of 50 and 80).
• update(3, 65) adds a third timestamp; maximum() is still 80.
• update(4, 30) corrects the earlier price of 80 at timestamp 4 down to 30.
• minimum() now returns 30, since the recorded prices are 50, 65, and 30.

Example 2:

Input:

["StockPrice", "update", "update", "update", "current", "update", "current"]
[[], [5, 100], [1, 20], [5, 40], [], [1, 90], []]

Output:

[null, null, null, null, 40, null, 40]

Explanation:

• After the first three updates, timestamp 5 holds price 40 (it was corrected from 100), and timestamp 1 holds 20.
• current() returns 40 because timestamp 5 is still the largest timestamp recorded, even though it arrived out of order.
• update(1, 90) corrects an older timestamp, which does not change what the latest timestamp is, so current() still returns 40.

Constraints

• 1 <= timestamp, price <= 10^9
• At most 10^5 total calls will be made to update, current, maximum, and minimum combined.
• current, maximum, and minimum are called only after update has been called at least once.