More on change-making and related problems

Given a set of n integer-valued coin types and target value t, the well-known change-making problem asks for minimum number coins that sum to assuming an unlimited in each type. In more general all-targets version problem, we want summing j, every j=0,…,t. We obtain new results on these problems, including (i) algorithm with running time O˜(t4/3) (improving previous O˜(t3/2)-time algorithm), (ii) very simple O˜(u2+t)-time where u denotes maximum value, (iii) original (single-target) O˜(u) O˜(t)-time by Chan He (SOSA'20)). also describe applications (single-capacity) unbounded knapsack word break problem.