The fibonacci series using memoization

Another algorithm today...
This is the Fibonacci series implemented with memoization .

int fibonacci(int n){
 int prev=0;
 int next=1;
 int val=0;
 for(int i=2;i<=n;i++){
  val=next+prev;
  prev=next;
  next=val;
 }
 return val;
}

Typically, If you are designing a maths library, you would implement a caching mechanism to avoid reprocessing again. A better  way in term of performance would be :

int fibonacci(int n){
 static vector<int> cache(0);
 //check if we have already processed
 if(n<cache.size()){
  cout<<"from cache: ";
  return cache.at(n);
 }
 
 //initial values 
 if(cache.size()==0){
  cache.push_back(0);
  cache.push_back(1);
 }
 
 //we calculate the fibonacci from where the cache end to the number requested
 for(int i=cache.size()-1;i<=n;i++){
  cache.push_back( cache.at(i) + cache.at(i-1) );
 }
 cout<<"Calculated : ";
 return cache.at(n);
}

the cout is embedded for simple debugging.