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

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