Algorithms and recursive functions by A.I. Mal'cev

By A.I. Mal'cev

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G. for, while) to repeat a process until a condition is met. Each step in a loop is called an iteration. It’s great for running through an input and applying the same operations on every part of it. For example: 35 | C E CIE CE I ILL You’re given a list of saltwater fish and a list of freshwater fish, both in alphabetical order. How do you create a list featuring all the fish in alphabetical order? FISH REUNION We can iteratively compare the top items of the two lists as follows: Cod Herring Marlin Asp Carp Ide Trout Asp Carp Cod Herring Ide Marlin Asp Carp Cod Asp Carp Asp Ide Trout Cod Herring Marlin Carp Ide Trout Asp Carp Cod Herring Ide Marlin Marlin Cod Herring Marlin Asp Carp Cod Herring Ide Trout Asp Carp Cod Herring Ide Marlin Trout Herring Marlin Ide Trout Asp Carp Cod Herring Ide Marlin Trout Trout Trout Fig63e .

When n is a million, n2 is a trillion, whereas n log n is just a few million. Years running a quadratic algorithm on a large input could be equivalent to minutes if a O(n log n) algorithm was used. That’s why you need time complexity analysis when you design systems that handle very large inputs. When designing a computational system, it’s important to anticipate the most frequent operations. , “that sorting algorithm is oh-n-squared”. energy/bigo. 4 Complexity | most algorithms only work with specific input structures.

Next, we’ll see how to analyze a worst case scenario, hands on. Fig63e . com. | Complexity . Co6n5ing Time We find the time complexity of an algorithm by counting the number of basic operations it requires for a hypothetical input of size n. We’ll demonstrate it with Selection Sort, a sorting algorithm that uses a nested loop. swap_items current, smallest Let’s see what happens with a list of n items, assuming the worst case. The outer loop runs n − 1 times and does two operations per run (one assignment and one swap) totaling 2n − 2 operations.

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