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.

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