## lunchtime google code optimization.

Written by **Walter**

Well I had this question at job interview for google. They asked me to implement a set using arrays or std::vector. It contains only unique integers and I had to implement A union B \ A intersect B. I had only 20 minutes to solve it and only a pen and paper (no pc, no internet). And write proper c++ code that handles empty arrays and variable size arrays. The code I came up with was not optimal and larger than needed but it did work and you can take a peep at it here (as requested it had to handle empty and variable size arrays and did not have to be optimal code): intersect.cpp. Though I was not satisfied with the runtime complexity off O(N*M) for arrays A and B of lengths N and M respectively (because of the nested forloop used to get the intersection). So I came up with a more optimal solution. By just concatenating A and B, sorting it and then removing duplicates we have performed the same operation but then in O( (N+M) * log(N+M) ) average case (worst case for the sort can still be O( (N+M)^2 ).

typedef vector<int> array; void unionMinusIntersect( const array& a, const array& b, array& result ){ result.assign( a.begin(), a.end() ); // result = a; element copy result.insert( result.end(), b.begin(), b.end() ); // append elements in b to result sort( result.begin(), result.end() ); //sort to quickly find unique elements to remove //we loop and remove all duplicates (both elements so for 122466 we remove 22 and 66, leaving 14 array::iterator pos = result.begin(); while( pos!=result.end() ){ if( ((pos+1) != result.end()) && (*pos == *(pos+1)) ){ array::iterator newpos = pos-1; result.erase( pos, pos+2 ); //removes at pos and pos+1 pos = newpos; } pos++; } }Here is the complete optimized file optimized.cpp. And some output: walter-schreppers-computer:~ wschrep$ ./optimized A= 1 2 3 6 B= 2 3 5 6 unionMinusIntersect (A,B,result)= 1 5 testing empty inputs... done.