g++ ./DynamicProgramming/fibonacci.cpp ./DynamicProgramming/fibonacci.cpp -o fibonacci 

g++ -std=c++11 ./DynamicProgramming/fibonacci.cpp -o ./DynamicProgramming/fibonacci.cpp -o fibonacci 
g++ -std=c++11 ./DynamicProgramming/lcs.cpp -o ./DynamicProgramming/lcs.cpp -o lcs 

./fibonacci
./lcs

how to implement the Fibonacci sequence in modern C++ using different methods: a naive recursive approach (This is a simple recursive implementation, but it has exponential time complexity O(2^n), which makes it inefficient for larger values of n) memoization (This approach has a time complexity of O(n) and avoids recomputation by storing intermediate results.), and iterative approach with space optimization (This approach has a time complexity of O(n) and space complexity of O(1) because it only stores the last two Fibonacci numbers at any given time.) and Modern C++ Lambda

Try to follow in this order to understand progression:

1. Naive Recursive: Simple but inefficient due to redundant calculations.
2. Memoization: Stores previously calculated results, improving efficiency to O(n).
3. Iterative: Space-optimized version with O(1) space complexity.
4. Modern C++ Lambda: Compact, elegant solution leveraging lambdas and memoization.