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Use of Memoization in Recursion

Memoization can be used to reduce function calls or computations. In the following example of Fibonacci series generation through C++, I will use normal recursion and then will change the same for memoization( http://en.wikipedia.org/wiki/Memoization ) to show the reduction of the function call. This is a simple demo implementation. 
static int counter = 0;
int normalfibrecursion(int n)
{
 if( n < 1)
 {
  return 0;
 }

 if(n == 1)
 {
  return 1;
 }

 if(n < 3)
 {
  return 1;
 }
 else
 {
  cout << "Call normalfibrecursion(" << n-2 << ") and normalfibrecursion(" << n-1 << ")\n";
  counter++;
  return normalfibrecursion(n-2) + normalfibrecursion(n-1);
 }
}
In the above-mentioned simple prototype implementation for the Fibonacci series of n=10, the total function call comes to (54*2) times. This is usually very high and it will grow exponentially as n increases. Below mentioned picture demonstrates the fact: USE OF MEMOIZATION: - The following example shows the use of memoization to optimize function calls. 
static int counter = 0;
int fib(int n, int *memoid)
{
 if(memoid[n - 1] != -1)
 {
  return memoid[n - 1];
 }
 
 cout << "Call fib(" << n-2 << ") and fib(" << n-1 << ").\n";
 memoid[n - 1] = fib(n-2, memoid) + fib(n-1, memoid);
 counter++;
 return memoid[n - 1];
}

int  memoidfib(int n, int *memoid)
{   
    for(int i = 0; i < n; i++)
    {
        memoid[i] = -1;
    }
    memoid[0]=0;
    memoid[1]=1;

    return fib(n,memoid);
}
If we call "memoidfib" function from our client code, definitely there will be a much-reduced function call and in this case, it is reduced to (8*2) function calls. Please follow the picture below:

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