Answer:
Computational complexity refers to the study of how the efficiency of algorithms and computational problems is affected by the size of the input. In other words, it focuses on understanding the amount of time and space required by an algorithm to solve a problem as the input grows larger.
One way to measure computational complexity is through time complexity, which quantifies the number of operations an algorithm performs as a function of the input size. Time complexity is often expressed using big O notation, which gives an upper bound on the growth rate of the algorithm's running time. For example, an algorithm with a time complexity of O(n^2) means that its running time grows quadratically with the input size.
Another measure of computational complexity is space complexity, which measures the amount of memory or storage an algorithm requires as the input size increases. Space complexity is also expressed using big O notation, similar to time complexity. For example, an algorithm with a space complexity of O(n) means that it requires a linear amount of memory with respect to the input size.
Understanding computational complexity is crucial for analyzing and comparing the efficiency of different algorithms for solving a given problem. By considering the computational complexity, we can determine which algorithm is more suitable for large inputs and identify bottlenecks that might affect the performance of an algorithm.
For example, let's say we have two sorting algorithms: Bubble Sort and Quick Sort. Bubble Sort has a time complexity of O(n^2), while Quick Sort has a time complexity of O(n log n). This means that as the input size grows larger, Quick Sort will be more efficient in terms of running time compared to Bubble Sort. Thus, Quick Sort would be a better choice for sorting large datasets.
In summary, computational complexity is the study of how the efficiency of algorithms and computational problems is affected by the size of the input. It involves analyzing the time and space requirements of algorithms to determine their performance characteristics.