Running Time Examples

Let’s look at common examples of running times starting from the least.

**1)**

`O(1)`

Some Examples of

`O(1)`

:`""" O(1) """ # Any assignments x = 1 # O(1) x += 1 # O(1) # If statement structure # Condition and code inside not always O(1) if 1 == 1: # O(1) print(1) # O(1) else: # O(1) print(2) # O(1) # Some list operations x = [1, 2, 4, 213] x.append(14) # O(1) x[0] = 11 # O(1) # Many, many more`

`O(1)`

is also known as constant running time, as the running time is unaffected by the input size. To clarify, even if a list is size one million, appending something at the end is still going to take the same time as it would appending something to the end of a list size five.**2)**

`O(n)`

Example:

`""" O(n) """ # "Most" for loops are O(n) for number in [123, 4, 21, 312, 41]: # O(n) print(number) # O(1)`

`O(n)`

is also known as linear running time, as the number of operations to run the code when the input is size n is a constant times n. To clarify, if a list is size one million and we are looping through and printing all of them, it would take two million operations.**3)**

`O(n^2)`

, `O(n^3)`

, and so onExample:

`""" O(n^2), O(n^3), etc. """ # "Most" of the time, every extra for loop # increases running time by a factor of n example_list = [12, 3, 214, 5, 12] for num1 in example_list: # O(n) for num2 in example_list: # O(n) print(num1, num2) # O(1)`

MOST of the time, every extra nested for loop increases the running time by a factor of n. So 2 for loops is

`O(n^2)`

, 3 for loops is `O(n^3)`

, and so on. Suppose a list is size one million. For `O(n^2)`

, the number of operations is a constant times one million squared. For `O(n^3)`

, the number of operations is a constant times one million cubed.**4)**Many others

There are many running times not covered like logarithmic, exponential, multiple variables (not just n). The ones covered so far are most of the easier running times.

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