## 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.