I am practicing algorithms for upcoming job interviews and I am having trouble correctly implementing this one. I am trying to also maximize efficiency as well. Here is the problem:

Maximize the profit of your business selling metal rods. If you sell N metal rods of length L, you receive N * L * metal_price. The remaining smaller metal rods will be trashed. To cut metal rods, you need to pay cost_per_cut for every cut. What is the max profit you can make?

constraints:
lengths will be 1 to 50 elements, inclusive.
each element of length will lie in range [1,10000]
1 <= metal_price, cost_per_cut <=1000

sample input:

cost_per_cut =1metal_price =10lengths = [26,103, 59]return: 1770

how the book solved this is that the most optimal length of rod is 6. so we cut 4 pieces of length 6 from 1st rod, and throw piece of length 2 from it. next we cut 17 pieces of length 6 from 2nd rod, and throw away piece of length 1. for the third, we cut 9 pieces of length 6, and throw a piece of length 5. so in total we have made 30 cuts. therefore, 30*6*10 - 30*1 - 1770

Here is my attempt so far:

def  maxProfit( cost_per_cut,  metal_price,  lengths):profit =0for num in lengths:

I'm just not really sure how to go about doing this. Should I iterate over the numbers and see what the lowest number they're divisible by and use that? Any ideas?

Since the input ranges are quite small, can you not just brute force this

    static int getProfit(int[] rods, int cutCost, int metalPrice, int L){int profit = 0;foreach (int rod in rods){if (rod % L == 0){profit += (metalPrice * rod - (rod / L - 1) * cutCost);}else{profit += (metalPrice * (rod - rod % L) - (rod / L) * cutCost);}}return profit;}static void Main(string[] args){int[] rods = new int[] { 26,103,59};int cutCost =1;int metalPrice=10;int maxProfit = 0;for (int L = 1; L <= 10000; ++L){int profit= getProfit(rods, cutCost, metalPrice, L);if (profit > maxProfit){maxProfit = profit;}}Console.WriteLine(maxProfit);}