Counting Solutions (n-Queens Problem)
Revision as of 10:26, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Counting Solutions (n-Queens Problem)}} == Description == How many ways can one put $n$ queens on an $n \times n$ chessboard so that no two queens attack each other? In other words, how many points can be placed on an $n \times n$ grid so that no two are on the same row, column, or diagonal? == Related Problems == Related: Constructing Solutions, n-Queens Completion == Parameters == <pre>n: number of queens, size of chessboard</pre> == Tab...")
Description
How many ways can one put $n$ queens on an $n \times n$ chessboard so that no two queens attack each other? In other words, how many points can be placed on an $n \times n$ grid so that no two are on the same row, column, or diagonal?
Related Problems
Related: Constructing Solutions, n-Queens Completion
Parameters
n: number of queens, size of chessboard
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Rivin, Zabih | 1992 | $O({8}^n*poly(n)$) | $O({8}^n*n^{2})$ | Exact | Deterministic | Time & Space |
Time Complexity graph
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Space Complexity graph
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Pareto Decades graph
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References/Citation
https://dl-acm-org.ezproxy.canberra.edu.au/citation.cfm?id=1243380