Cut a Numeric String into Required Pieces

We study the problem of cutting a length-\(n\) string of positive real numbers into \(k\) pieces so that every piece has sum at least \(b\). The problem can also be phrased as transforming such a string into a new one by merging adjacent numbers. We discuss connections with other problems and present several algorithms in connection with the problem: an \(O(n)\)-time greedy algorithm, an \(O(kn\log n)\)-time dynamic programming algorithm, and an \(O(n+ k \log n + 2^kk)\)-time FPT algorithm for \(n-k\) pieces.