Question

Could you please help me with this one? :
“Let A and B are an incrementally ordered arrays of natural numbers and K be some arbitrary natural number. Find an effective algorithm which determines all possible pairs of indexes (i,j) such that A[i]+B[j]=K. Prove algorithm’s correctness and estimate its complexity.”

Should I just iterate over the first array and do a binary search on the other one?
Thanks 🙂

Answer 1

No!

Both arrays are ordered, so you do the following:

• Place an iterator itA on the beginning of A
• Place an iterator itB on the end of B
• Move iterators in opposite directions, testing *itA + *itB at each iteration. If the value is equal to K, return both indexes. If the value is smaller than K, increment itA. Else, decrement itB.

When you go through both arrays, you are done, in linear time.