Question

Given the following problem , I’d appreciate for any corrections since I have no solution
for the current question (taken from one of my professor’s exams !!!) :

Remark: this is no homework !

Problem:

Given two sorted arrays A (with length n) & B (with length m) , where each

element (in both arrays) is a real number , and a number X (also a real number) ,

we’d like to know whether or not exists a ∈ A and b ∈ B , such as :

a + b = X , in O(n+m) running time .

Solution :

First , we start to check from the end of both arrays , since we don’t need the numbers that are bigger than X :

• i = n

• k = m

• while A[i] > X , i = i -1

• while B[k] > X , k = k -1

Define j = 0 .
Now start running from the current i in A , and from j in B :

• while i > 0 , j < k :
• if A[i]+B[j] == X , then return both cells
• else j = j+1 , i = i -1

In the end we’d have either the two elements , or we’d reach out of bounds in one
or both of the arrays , which means that no two elements such a + b = X are indeed exist .

Any remarks would be much appreciated

Thanks

Answer 1

You shouldn’t adjust i and j at the same time. If the sum is too big, you should decrease i. If it is too small, increase j.