Problem Description

You are tasked with calculating the total charge for a customer based on their usage intervals and a single, temporary price override.

Definitions

• Usage Record: An interval [start, end), where start is inclusive and end is exclusive.
• defaultPrice: The price per unit time (e.g., per day) applied when no override is active.
• Price Override: Defined by:
  • override.period = [overrideStart, overrideEnd): The specific time interval during which the override is active.
  • override.price: The price per unit time applicable during the override.period.

Task

Given the following inputs:

• usageRecords: []Interval (each Interval is [start, end))
• defaultPrice: int
• override: PriceOverride

Compute the total charge across all usage time. The billing rules are:

• Any portion of usage that overlaps with override.period is billed at override.price.
• Any portion of usage outside override.period is billed at defaultPrice.

The total charge should be returned as an integer.

Notes and Edge Cases

• Usage records may be entirely outside, entirely inside, or partially overlap the override period.
• Assume all inputs are valid (e.g., start < end, prices are non-negative).
• Crucially, clarify whether usageRecords can overlap each other. If they can, your solution must ensure that overlapping usage time is not double-billed (e.g., by first merging overlapping usage intervals).

Example

Consider defaultPrice = 10, an override period [2, 6) with override.price = 5, and a usage record [1, 4).

• The interval [1, 2) falls outside the override period and is billed at 10.
• The interval [2, 4) falls within the override period and is billed at 5.

The total charge would be calculated based on these segments.