While time complexity focuses on understanding how the algorithm's performance scales with the input size, space complexity indicates the maximum amount of memory that the algorithm requires to solve a problem. This measurement is important because an algorithm's memory usage can significantly impact its efficiency and practicality, particularly in environments where memory resources are limited.
The key difference between time and space complexity is what they measure: time complexity measures the computational time required by an algorithm, while space complexity measures the memory or space requirements of an algorithm.
Just like time complexity, space complexity is also expressed using Big O notation. For example, if an algorithm has a space complexity of O(N), it means that the maximum memory usage of the algorithm grows linearly with the input size. In simple terms, doubling the size of the input would result in a doubling of the memory needed. However, it's important to note that this doesn't necessarily mean that the memory usage will grow for every input, but rather it sets an upper limit on the memory consumption.
In our discussions, we will primarily focus on time complexity as it directly impacts the runtime performance of algorithms. However, we will touch upon space complexity as well, particularly when discussing trade-offs between time and space efficiency. This will involve examining scenarios where increasing space usage can lead to improved time complexity or vice versa.
In our discussions, we will sometimes use the term auxiliary space complexity. This term refers to the extra space or temporary space used by an algorithm, excluding the space needed for the input data itself. We focus on auxiliary space complexity because it helps us understand the additional memory requirements imposed by the algorithm, beyond what is necessary to store the input.
For example, if we need to split a string into an array of characters (since strings are immutable in JavaScript), this operation requires additional space. This extra space is considered auxiliary because it is the minimum additional space needed to solve the problem, given the constraints of the programming language (such as the immutability of strings). The space complexity can't be reduced further while adhering to these constraints.