pebble | RocksDB/LevelDB inspired key-value database in Go | Database library

Input description

The first line of my input contains two numbers: 𝑛 and 𝑑, denoting respectively the number of containers (2 ≤ 𝑛 ≤ 20,000) and the number of deliveries (not more than 100,000)

In the following 𝑑 lines there are pairs of numbers: 𝑤 and 𝑧, where 𝑤 is the number of wagons in the delivery (no more than 20,000) and 𝑧 is the number of gravel in each wagon (no more than 20,000).

The total number of wagons from all deliveries will not exceed 1,000,000.
There will be no situation in any of the inputs where the container will contain more than 1,000,000,000 gravel.

Problem statement

Wagons are emptied one at a time, evenly into two consecutive containers. These are the rules for determining which two adjacent containers are chosen (where containers[] denotes a list of the n current container sizes):

1. Among all pairs (containers[i], containers[i+1]) with 0 <= i < n - 1, choose the pair which minimizes min(containers[i], containers[i+1])
2. If there is a tie, choose among the tied pairs, the pair which minimizes max(containers[i], containers[i+1]) (i.e. minimizes the second smallest element in the pair)
3. If there is still a tie, choose the pair (containers[i], containers[i+1]) with minimum index i among the tied pairs.

The gravel is distributed equally into the pair. If there is an odd number of gravel in a wagon, the container with the smaller ID gains the surplus (1 pebble).

At first, all containers are empty.

For example:

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