In general, while working on competitive programming issues on multiple sites, the most difficult task is developing the code at the appropriate complexity level; otherwise, the programme will receive a TLE ( Time Limit Exceeded ). A simplistic answer is nearly never acceptable. So, how do you determine what level of complexity is acceptable?
The answer is directly connected to the amount of operations that may be performed within a second. Most sites now allow 10^8 operations per second, with only a few exceptions still allowing 107 operations. After determining the amount of operations that may be executed, look at the restrictions in the problem to determine the appropriate complexity.
Algorithm Time Complexity
We may compare two algorithms by the amount of time it takes to execute (particularly on greater input), which is known as an algorithm's time complexity, and the amount of space it uses, which is known as an algorithm's space complexity.
The execution time of an algorithm is referred to as the growth of time with regard to input; hence, for two algorithms, the running time may differ initially on the lower value, and may differ as the input grows; this increase of time complexity is exponential.
Algorithm Space Complexity
The space or memory required for an algorithm to operate or execute is referred to as its space complexity. The scale of the challenge is determined by the amount of the incoming data.
The asymptotic complexity of an algorithm indicates which method can tackle a given issue of a certain size. We may naturally raise the size of the problem if we improve the processing speed of the computer, but for a particular size of the problem, an algorithm's speed is measured to reach a conclusion. Let us look at an example to better grasp the characteristics of various algorithms.
The time it takes for certain algorithms to run varies greatly depending on the amount of the input. Some algorithms may operate on massive amounts of data in seconds or minutes, but others might take days to finish.
Time complications that are common
Let n be the problem's primary variable.
• If n ≤ 12, the time complexity can be O(n!).
• If n ≤ 25, the time complexity can be O(2n).
• If n ≤ 100, the time complexity can be O(n4).
• If n ≤ 500, the time complexity can be O(n3).
• If n ≤ 10 ^ 4, the time complexity can be O(n2).
• If n ≤ 10 ^ 6, the time complexity can be O(n log n).
• If n ≤ 10 ^ 8, the time complexity can be O(n).
• If n > 10 ^ 8, the time complexity can be O(log n) or O(1).