What is the name of the algorithm in which a given segment is assembled from a set of segments of smaller length?

Question

Algorithms

Actually, there is a set of segments of different lengths, and there is a line of a given length, along which these segments must be laid so as to completely fill it (i.e. from the very beginning to the very end - no more, no less). What is the name of the algorithm by which this can be done?

For example, there is a set of Markov chains (phrases of 1, 2, 3 words) and a sentence of, for example, 12 words. It is necessary to put all these phrases in a sentence so that each of them must be found in the sentence. Those. the entire set must be used.
Or, for example, in architecture: we have a given length of the facade and a set of typical blocks of 2, 3 and 6 meters that need to be laid out along this facade.

For some reason I can’t formulate a request to Google in order to find algorithms for solving this problem :(

Answer 1

This is either a tiling problem or a coin exchange problem. In a particularly confusing case, this will be a cutting task.