Find the fastest algorithm

[Guest]

**Problem:** A metal worker can cut a metal rod of length x into two smaller pieces in [tex]x[/tex] minutes. One day, a customer comes to the metalsmith's shop with an order for n metal bars. The client specifies the length [tex]z_k[/tex]of each bar k. The metalworker must cut a metal rod of total length to fulfill the customer's order. **Question:** What is the fastest algorithm for the metallurgist to cut the metal bars and fulfill the customer's order? Prove that your algorithm is the fastest.

[Guest]

Sort the lengths of the metal bars ([tex]z_k[/tex]) in decreasing order.

Initialize a list of remaining lengths starting with a single rod of length 0.

For each metal bar length in decreasing order:
Try to fit the current bar length into the remaining lengths:

Start from the beginning of the list.
If a segment is found where the bar length fits, cut it from that segment.
If no suitable segment is found, add a new segment of the current bar length.

The number of cuts made during this process is the minimum number required to fulfill the customer's order.