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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