Welcome to the world of dynamic programming! In this lesson, we will explore the concept of dynamic programming and its significance in programming interviews.

Dynamic programming is a powerful technique used to solve complex problems by breaking them down into simpler subproblems and solving each subproblem only once. It employs a bottom-up approach, where solutions to subproblems are stored in an array or table and used to build the solution to the main problem.

By utilizing memoization or tabulation, dynamic programming optimizes the time complexity of the problem, often reducing it from exponential to polynomial time.

For example, let's consider the Fibonacci sequence. The naive recursive approach to calculate the nth Fibonacci number has an exponential time complexity of O(2^n), as it recomputes the same subproblems multiple times. However, by applying dynamic programming, the time complexity can be reduced to linear or even constant time.

So why is dynamic programming important in programming interviews? Well, it allows us to solve complex problems efficiently, showcasing our problem-solving skills and understanding of algorithmic optimizations. It demonstrates our ability to think critically and break down problems into manageable chunks.

In the upcoming lessons, we will dive deeper into applying dynamic programming to solve various problems, starting with the Fibonacci sequence. So, let's get started and unlock the power of dynamic programming!