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Code Explanation:
1. Importing the Cache Function
from functools import cache
- Imports cache from Python's built-in functools module.
- It is used to store previously calculated function results.
- It helps avoid repeated calculations for the same arguments.
2. Applying the Cache Decorator
@cache
- Applies caching to the mystery() function.
- Stores each function's return value based on its arguments.
- Unlike lru_cache, cache has no maximum storage limit.
3. Defining the Recursive Function
def mystery(n):
- Defines a recursive function named mystery().
- Accepts an integer argument n.
- The function calls itself with smaller values of n.
4. Checking the Base Condition
if n < 2:
- Checks whether n is smaller than 2.
- This condition stops the recursion when n reaches 0 or 1.
- It prevents infinite recursive calls.
5. Returning the Base Value
return n
- Returns n directly when the base condition is satisfied.
- Therefore, mystery(0) returns 0.
- mystery(1) returns 1.
6. Performing Recursive Calculations
return mystery(n-1) + mystery(n-2)
- Calls the same function with n-1 and n-2.
- Adds the two returned values.
- This follows the Fibonacci sequence.
- Previously calculated results are retrieved from the cache instead of being recalculated.
7. First Function Call
print(mystery(6))
- Calls the function with n = 6.
- Calculates the Fibonacci value using recursive calls.
- The calculation is:
mystery(6) = mystery(5) + mystery(4)
= 5 + 3 = 8
- The result 8 is printed and cached.
8. Second Function Call
print(mystery(5))
- Calls the function with n = 5.
- This result was already calculated during mystery(6).
- Python retrieves the cached value 5.
- No new recursive calculation is required.
- Prints 5.
9. Checking Cache Information
print(mystery.cache_info().hits)
- cache_info() provides information about the cache.
- .hits returns the number of times a cached result was successfully reused.
- During the first call, the recursive calculation produces 5 cache hits.
- The second call to mystery(5) adds one more cache hit.
- Therefore, the total number of cache hits is 6.
Understanding Cache Execution
Function call Result Cache behavior
mystery(6) 8 Calculates recursively
mystery(5) 5 Uses cached result
cache_info().hits 6 Counts cache hits
Final Output
Correct Output
8 5 6
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