A Comprehensive Study of the Key Enumeration Problem

. 2019 Oct 5;21(10):972. doi: 10.3390/e21100972

Algorithm 5 creates and initialises each node of the tree-like structure.

1:
functioninitialise( $i, f$ )
2:
if $f = i$ then
3:
$L^{i} \leftarrow (null, null, null, null, null, null, null, L^{i});$
4:
return $L^{i}$ ;
5:
else
6:
$q \leftarrow ⌊ \frac{i + f}{2} ⌋$ ;
7:
$N_{0}^{i, \dots, q} \leftarrow initialise (i, q)$ ;
8:
$N_{0}^{q + 1, \dots, f} \leftarrow initialise (q + 1, f)$ ;
9:
$N_{1}^{i, \dots, q} \leftarrow initialise (i, q)$ ;
10:
$N_{1}^{q + 1, \dots, f} \leftarrow initialise (q + 1, f)$ ;
11:
$c_{0}^{i, \dots, q} \leftarrow getCandidate (N_{0}^{i, \dots, q}, 0, 2)$ ;
12:
$c_{0}^{q + 1, \dots, f} \leftarrow getCandidate (N_{1}^{q + 1, \dots, f}, 0, 2)$ ;
13:
$Q^{i, \dots, f} . add ((c_{0}^{i, \dots, q}, c_{0}^{q + 1, \dots, f}, 0, 0))$ ;
14:
$X_{0}^{i, \dots, f} \leftarrow 1$ ; $Y_{0}^{i, \dots, f} \leftarrow 1$ ;
15:
$N^{i, \dots, f} \leftarrow (N_{0}^{i, \dots, q}, N_{0}^{q + 1, \dots, f}, N_{1}^{i, \dots, q}, N_{1}^{q + 1, \dots, f}, Q^{i, \dots, f}, X^{i, \dots, f}, Y^{i, \dots, f}, L^{i, \dots, f})$ ;
16:
return $N^{i, \dots, f}$ ;
17:
end if
18:
end function