Question

I have two sets of elements and I want an optimal algorithm to find their differences or in math form: A U B – A ∩ B

One way I thought is

Bfound=0;
for (1->Na,i)
{
 flag=0;
 for (1->Nb,j)
 {
  if(A[i]==B[j])
  {
   flag=1;
   Bfound[j]=1;
  }

 }
 if (flag==0)
 print A[i]
}

for(1->Nb,i)
{
  if(Bfound[i]==0)
  print B[i]
}

Is this optimal?

Answer 1

To answer your question – no, this is not optimal. The complexity of your solution is O(nm) time, where n and m are the sizes of A and B, respectively. You can improve this time to O(nlogn + mlogm), if n ~ m.

1. Sort both arrays, in n log n + m log m time.

2. Find the intersection in n+m time:

   i = 0; 
   j = 0;
   while(i < n && j < m) {
     if (A[i] == B[j]) {
       print(A[i]);
       i++;
       j++;
     } else if (A[i] < B[j]) {
       i++;
     } else {
       j++;
     } 
   }