Complexity analysis is an important aspect of data structures and algorithms that measures the time and space resources required to run an algorithm. The two primary measures of algorithm complexity are time complexity and space complexity.
Time Complexity:
Time complexity is a measure of how long an algorithm takes to run, as a function of the size of its input. It is typically expressed using big O notation, which provides an upper bound on the worst-case running time of an algorithm. For example, if the time complexity of an algorithm is O(n^2), it means that the worst-case running time of the algorithm is proportional to the square of the size of its input.
Space Complexity:
Space complexity is a measure of how much memory an algorithm uses, as a function of the size of its input. It is also typically expressed using big O notation, which provides an upper bound on the worst-case space usage of an algorithm. For example, if the space complexity of an algorithm is O(n), it means that the worst-case space usage of the algorithm is proportional to the size of its input.
In general, algorithms with better time and space complexities are preferred over those with worse complexities, because they are more efficient and can handle larger input sizes.
Some common time complexities include:
- O(1) - constant time complexity, where the running time is independent of the input size
- O(log n) - logarithmic time complexity, where the running time increases logarithmically with the input size
- O(n) - linear time complexity, where the running time increases linearly with the input size
- O(n^2) - quadratic time complexity, where the running time increases quadratically with the input size
- O(2^n) - exponential time complexity, where the running time grows exponentially with the input size
Similarly, some common space complexities include:
- O(1) - constant space complexity, where the space usage is independent of the input size
- O(log n) - logarithmic space complexity, where the space usage increases logarithmically with the input size
- O(n) - linear space complexity, where the space usage increases linearly with the input size
