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arXiv · 2109.14497

Ruler Wrapping

Travis Gagie·Mozhgan Saeidi·Allan Sapucaia
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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.

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Travis Gagie, Mozhgan Saeidi, Allan Sapucaia. 2021-09-29. Ruler Wrapping. https://arxiv.org/abs/2109.14497

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