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When using most algorithms structures to build a search feature, the normal behavior is more data means slower search in most cases. Except for one special category of algorithm. Imagine an operation that takes exactly the same amount of time to search through 10 contacts on your phone or 10 million records in a government database.

What O(1) really means

O(1) is not about speed, it is about sameness.

When an algorithm runs in O(1) time, we are making a mathematical promise. The time it takes to complete an operation will not change as the dataset grows. The 1 does not mean one operation or one second, it represents a constant factor that will not change no matter the size of inputs

O(1) database access works like GPS coordinates 
home_address = address_database["742_Evergreen_Terrace"]
Not: search through all addresses for '742 Evergreen...  
But: go directly to the '742_Evergreen_Terrace' entry

What makes it so fast

Direct addressing

Arrays gives us the original O(1) operation. Your computer calculates memory_address = start_address + (index x element_size) and jump directly to that location. No searching, no iteration, just mathematics and physics.
Hash Tables

Hash tables feel like magic because they use a simple system, convert any data to a number then use that number as an array index.
Example: Trying to findDaniel Okoro in a database of 100 million people? Convert Daniel Okoro to a number (say 42,876), jump to that location, and that’s the data.
Hardware level

Your computer memory, CPU Cache and Registry access are all O(1) operations. When you write x = 5, the computer will not search for x in memory instead, it calculates exactly where x lives and goes there.

Why O(1) is important

Let me use X's like feature as an example. When a user taps the heart icon to like a tweet, X need to increase the counter. If this were O(n) when a post is going viral, the system would break or get very slow to respond. A tweet with 10 million likes would take longer time to like than one with 100 likes. With O(1) your likes take the same time whether you are the first or the millionth person to engage.

Other examples

Google Search autocomplete: Trie lookups are O(1) for prefix matching.

Load balancers: Consistent hashing for O(1) request routing.

Blockchain addresses: Direct wallet lookups in massive ledgers.

When not to use O(1)

Sometime O(n) and O(log n) is better.

When data changes constantly
When memory is extremely limited (hash table use extra space)
When you need sorted data (most O(1) operations do not maintain order)

Conclusion