کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4952500 | 1442039 | 2016 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Three-pile Sharing Nim and the quadratic time winning strategy
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
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چکیده انگلیسی
We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague-Grundy values is a palindrome. We establish a formula for P-positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague-Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Theoretical Computer Science - Volume 646, 20 September 2016, Pages 49-60
Journal: Theoretical Computer Science - Volume 646, 20 September 2016, Pages 49-60
نویسندگان
Nhan Bao Ho,