Ruler Wrapping
Abstract
In 1985 Hopcroft, Joseph and Whitesides showed it is NP-complete to decide whether a carpenter's ruler with segments of given positive lengths can be folded into a line of at most a given length, such that the folded hinges alternate between 180 degrees clockwise and 180 degrees counter-clockwise. At the open-problem session of 33rd Canadian Conference on Computational Geometry (CCCG '21), O'Rourke proposed a natural variation of this problem called {\em ruler wrapping}, in which all folded hinges must be folded the same way. In this paper we show O'Rourke's variation has an linear-time solution. We also show how, given a sequence of positive numbers, in linear time we can partition it into the maximum number of substrings whose totals are non-decreasing.
Cite
@article{arxiv.2109.14497,
title = {Ruler Wrapping},
author = {Travis Gagie and Mozhgan Saeidi and Allan Sapucaia},
journal= {arXiv preprint arXiv:2109.14497},
year = {2022}
}