Counting Solutions

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

Parameters

$n$ : number of queens, size of chessboard

Filters

Computational Model

Randomization

Approximation

Algorithms Table

Displaying 6 of 6 algorithms


Rivin, Zabih	1992	$O(8^n \text{poly}(n))$	$O(8^n n^2)$
Dijkstra	1972	$O(n!)$	$O(n)$
Method of determinants	1874	$O(n!)$
Gunther Determinants solution	1874	$O(n!)$	$O(n!)$
Naive + 1 queen per row restriction	1850	$O(n!)$	$O(n)$
Naive Algorithm	1848	$O(n^n)$	$O(n)$

Reductions Table

Insuffient Data to display table

Other relevant algorithms