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 an 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:
The above program can be optimized by memoization using decorators.
1. A function called memoize_factorial has been defined. It’s 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 output of this program.
- Decorators in Python
- Decorators with parameters in Python
- Function Decorators in Python | Set 1 (Introduction)
- Memoization (1D, 2D and 3D)
- Water Jug Problem using Memoization
- Edit Distance | DP using Memoization
- Longest Common Subsequence | DP using Memoization
- Important differences between Python 2.x and Python 3.x with examples
- Python | Sort Python Dictionaries by Key or Value
- Python | Set 4 (Dictionary, Keywords in Python)
- SQL using Python | Set 1
- bin() in Python
- Python Set | pop()
- max() and min() in Python
- Any & All in Python
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.