Recursion is a programming technique where a function calls itself repeatedly till a termination condition is met. Some of the examples where recursion is used are calculation of fibonacci series, factorial, etc. But the issue with them is that in the recursion tree, there can be chances that the sub-problem that is already solved is being solved again, which adds to overhead.
Memoization is a technique of recording the intermediate results so that it can be used to avoid repeated calculations and speed up the programs. It can be used to optimize the programs that use recursion. In Python, memoization can be done with the help of function decorators.
Let us take the example of calculating the factorial of a number. The simple program below uses recursion to solve the problem:
Python3
# Simple recursive program to find factorialdef facto(num): if num == 1: return 1 else: return num * facto(num-1) print(facto(5))print(facto(5)) # again performing same calculation |
120 120
The above program can be optimized by memoization using decorators.
Python3
# Factorial program with memoization using# decorators.# A decorator function for function 'f' passed# as parametermemory = {}def memoize_factorial(f): # This inner function has access to memory # and 'f' def inner(num): if num not in memory: memory[num] = f(num) print('result saved in memory') else: print('returning result from saved memory') return memory[num] return inner @memoize_factorialdef facto(num): if num == 1: return 1 else: return num * facto(num-1)print(facto(5))print(facto(5)) # directly coming from saved memory |
result saved in memory result saved in memory result saved in memory result saved in memory result saved in memory 120 returning result from saved memory 120
Explanation:
1. A function called memoize_factorial has been defined. Its main purpose is to store the intermediate results in the variable called memory.
2. The second function called facto is the function to calculate the factorial. It has been annotated by a decorator(the function memoize_factorial). The facto has access to the memory variable as a result of the concept of closures. The annotation is equivalent to writing,
facto = memoize_factorial(facto)
3. When facto(5) is called, the recursive operations take place in addition to the storage of intermediate results. Every time a calculation needs to be done, it is checked if the result is available in memory. If yes, then it is used, else, the value is calculated and is stored in memory.
4. We can verify the fact that memoization actually works, please see the output of this program.
