Question

I have three algorithms for computing the reflexive transitive closure of R*

R*={(a,b): a,b ε A and there is a path from a to b in R}

Algorithm #1

Initially R*:= 0
for i=1,.....,n do
for each tuple(b1,....,bi) ε A^i do
if(b1,....,bi) is a path in R then add (b1,bi) to R*

Algorithm #2

Initially R* := R U {(ai,ai) :ai ε A}
while there are three elements ai,aj,ak ε A such that
(ai,aj),(aj,ak)ε R* but(ai,ak) not ε R* do:
add(ai,ak) to R*

Answer 1

Algorithm #3

Initially R* := R U {(ai,ai): ai ε A }
for each j=1,2,....,n do
for each i=1,2,....,n do
if(ai,aj),(aj,ak) ε R* but (ai,ak) not ε R* then add (ai,ak) to R*


Could you please explain those algorithms to me and send a code(in java or c) for each of them?
Thank you!