Polynomial Time Algorithms

Polynomial time algorithms are methods for solving problems that can be completed efficiently, meaning the time required increases at a manageable rate as the problem size grows. Specifically, their running time can be expressed as a polynomial function of the input size (like n, n², n³, etc.), which means they remain practical for larger problems. These algorithms are important because they ensure solutions can be found within reasonable timeframes, making them suitable for real-world applications where quick processing is essential. In contrast, problems requiring super-polynomial or exponential time become increasingly impractical as input size increases.