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The Problem

The Problem

I have an n by n binary matrix and three operations. I can zero out a row or column that has exactly one solitary one in it and I can zero out a row if it has an exact copy. How can I apply these operations repeatedly until none of them can be applied in O(n^2) time?

Problem:

I need to find the length of the longest repeating pattern in a sequence of beads represented as a string. The string can be up to 1 million characters long. What is the most efficient algorithm for solving this problem, ideally running in linear time O(n) or close to it?

An algorithm is a step-by-step set of instructions designed to perform a specific task or solve a particular problem. It is a fundamental concept in computer science and mathematics, used to guide computers and humans in problem-solving and decision-making processes.
give me some more information

I am currently working on a problem at work where we have paint buckets of different sizes and we need to create a calculator that given a required quantity of paint it will calculate the required quantity of each bucket size minimising wastage. It needs to use the biggest size possible but minimising wastage. I am sure this sort of algorithm has a name but I can’t find it. I found the Knapsack Algorithm and the Coin Change Algorithm but they are not exactly the same.
Any idea about the name of this algorithm? It seems a fairly generic problem. I am sure an algorithm exists already.

(examples are in zig, but I guess this is a general noob algorithmic question)