How do quantum algorithms such as Shor's algorithm and Grover's algorithm offer exponential speedup for certain computational tasks compared to classical algorithms?

Quantum algorithms such as Shor’s algorithm and Grover’s algorithm leverage quantum parallelism and superposition to achieve exponential speedup for certain computational tasks compared to classical algorithms. Shor’s algorithm enables efficient factorization of large composite numbers, posing a threat to classical public-key cryptography systems. Grover’s algorithm accelerates the search of unsorted databases or search spaces, providing quadratic speedup over classical search algorithms.