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I think that if the maximum frequency is at most the total number of other characters + 1, then the arrangement exists. We can construct the solution by starting with the character with the maximum frequency and decrementing its counter, then adding the next different character with the maximum frequency and decrementing and so on. If many chars have the same frequency any one of them can be chosen. Keeping track only if that arrangement exists would be O(1) time and space for each character from the infinite sequence, while constructing the solution with the algorithm above would be O(n) time (the max-heap's size does not depend on the input size) and O(1) space.
- ppp August 31, 2017