Consider an instance of the stable marriage problem given by the ranking

matrix

For each of its marriage matchings, indicate whether it is stable or not.

For the unstable matchings, specify a blocking pair. For the stable match$-$

ings, indicate whether they are man$-$optimal, woman$-$optimal, or neither.

$($Assume that the Greek and Roman letters denote the men and women,

respectively.$)$

Design a simple algorithm for checking whether a given marriage matching

is stable and determine its time efficiency class.