Split parcels into the most balanced shipments

Parcels sit on a conveyor in a fixed order, and weights[i] is the weight of the i-th parcel. You must cut the line into contiguous shipments so that every parcel belongs to exactly one shipment.

A shipment is balanced if the weight of its last parcel is strictly less than the heaviest weight in that shipment.

Implement max_balanced_shipments(weights: list[int]) -> int. It returns the largest number of shipments in a split where every shipment is balanced. If no such split exists, it returns 0.

Constraints

• 0 <= n <= 10^5
• 1 <= weights[i] <= 10^9
• Aim for O(n) time.

Example 1

weights = [4, 9, 2, 7, 7, 1]
output  = 2

One optimal split is [4, 9, 2] | [7, 7, 1]. Both shipments end lighter than their heaviest parcel. Three shipments are impossible.

Example 2

weights = [5, 1, 3, 2, 4]
output  = 1

[5, 1] | [3, 2, 4] fails because the second shipment ends on its heaviest parcel. The only valid split is the whole line as one shipment.

Example 3

weights = [1, 2, 3]
output  = 0

Any shipment that ends with the 3 has 3 as its maximum, so it can never be balanced.