Python Constant Time O(1)

O(1) means constant time: the operation takes the same number of steps whether the input has 5 elements or a million. The work does not grow at all.

This is the best complexity there is. Typical O(1) operations in Python are: reading a list element by index, reading a dictionary value by key, len(), appending one element, and simple math.

Note what O(1) does not mean: it does not mean "fast", it means "does not get slower when the input grows". One constant step can still be a slow step — but it stays one step.

A list element lives at a known position in memory, so words[2] is one jump — the computer does not walk through the elements before it. The same read costs the same in a list of one million elements.

A dictionary lookup like ages["Ben"] also takes constant time on average: the key tells the dictionary directly where the value is stored. A missing key raises a KeyError with square brackets, so lookups often use ages.get("Ben") instead — it returns the value, or None when the key is missing.

The program reads one element from a 5-element list and one from a list with a million elements. Both reads are a single step — the list length plays no role.

ages.get("Ben") finds 25 directly. The missing key "Dan" returns None, and get("Dan", 0) returns the fallback 0 instead — still in constant time.

append() adds one element at the end of a list. Most of the time that is one step. (Once in a while the list must grow and gets copied, but averaged out the cost per append stays constant.)

All the small operations — assignments, additions, comparisons, swapping two values — are O(1) too. They are the "steps" that all the other complexity classes are counted in.

append() puts "yellow" at the end. The cost does not depend on how many colors are already in the list.

a, b = b, a swaps the two values in one constant-time step — no helper variable needed.