研究生: |
胡淑琼 Hu Shu-chiung |
---|---|
論文名稱: |
2×n踩地雷一致性問題之研究 On The Study of |
指導教授: |
林順喜
Lin, Shun-Shii |
學位類別: |
碩士 Master |
系所名稱: |
資訊工程學系 Department of Computer Science and Information Engineering |
論文出版年: | 2006 |
畢業學年度: | 94 |
語文別: | 英文 |
論文頁數: | 32 |
中文關鍵詞: | 踩地雷 、踩地雷一致性問題 、有限狀態機 、P |
英文關鍵詞: | Minesweeper, Minesweeper consistency problem, finite automata, P |
論文種類: | 學術論文 |
相關次數: | 點閱:172 下載:10 |
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踩地雷是微軟作業系統上非常流行的一套單人電腦遊戲,自從Richard Kaye在2000年證明了踩地雷問題是NP-complete之後,近年來有許多學者投入這方面的研究。Meredith Kadlac提出了一維的踩地雷遊戲,並証明了一維踩地雷一致性問題(One-dimensional Minesweeper Consistency Problem)是非常容易處理的,且可以用一個決定性的有限狀態機(DFA)來判斷一個一維踩地雷的盤面是否一致。我們將此一致性問題延伸至2×n踩地雷盤面上,2×n踩地雷是二維的,但其中一個維度被限定為2。我們發現這個問題也是可克服的,我們成功的設計了一個有限狀態機,其可在線性時間內解出2n踩地雷一致性問題,因此,我們證明了2×n踩地雷一致性問題的複雜度亦為P。
Minesweeper is a popular single-player game included with Windows operating systems. Since Richard Kaye proved that Minesweeper is NP-complete in 2000, it has been recently studied by many researchers. Meredith Kadlac had showed that one-dimensional Minesweeper consistency problem is regular and can be recognized by a deterministic finite automata. We extend the consistency problem to 2×n Minesweeper, which is two-dimensional but with its one dimension restricted to 2. We find that this problem is also tractable and design a finite automata which can solve 2n Minesweeper consistency problem in linear time. Hence, we are able to show that 2×n Minesweeper consistency problem is also in P.
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