Time complexity and space complexity are two fundamental concepts in the analysis of algorithms that help us understand how an algorithm performs as the input size grows. Time complexity measures how the runtime of an algorithm scales with the size of the input data. It's expressed in Big O notation, such as O(n), O(log n), or O(n^2), where 'n' represents the size of the input. For example, if an algorithm has a time complexity of O(n), its runtime will grow linearly as the input size increases. On the other hand, if an algorithm has a time complexity of O(n^2), its runtime will grow quadratically, meaning the time taken will increase much more rapidly. Space complexity, on the other hand, measures how much memory an algorithm requires as the input size grows. This includes the memory required for the input data as well as any extra memory the algorithm uses during execution (e.g., for variables, recursion stacks, or data structures). Space complexity is also expressed in Big O notation. For example, if an algorithm has a space complexity of O(1), it means that the algorithm uses a constant amount of memory, regardless of the input size. If the space complexity is O(n), it means that the memory usage grows linearly with the size of the input. Optimizing both time and space complexity is crucial because more efficient algorithms can handle larger inputs or perform tasks faster. A trade-off often exists between the two: optimizing for time may require more memory and vice versa. Understanding these complexities helps in designing algorithms that can scale efficiently, especially in applications where performance is critical, such as big data processing or real-time systems. When you're choosing or writing an algorithm, it's important to consider both its time and space complexity to ensure that it can handle the expected workload efficiently.