Question

In need of help to solve this problem.

Theory 1. Assume you are given two linear lists LI and L2 with nl, n2 elements, respectively. Consider the problem of determining whether any element of L is an element of L2 (not value, element!) (a) Derive a lower bound for this problem. (b) Design an algorithm for this problem. Derive its time complexity. It should be as close to your lower bound as possible.

Answer 1

(a) Lower bound must be O(n1 + n2) as you need to see each element at least once.

(b)

Find(e1) { // where e1 is an element in L1

for each element E in L2 do

hash = HashFunction(E);

HashTable[hash] = E;

done

hash = HashFunction(e1);

if (HashTable[hash] == e1)

printf "element found"

else

print "element not found"

return

}