What is an algorithm?

Question

Accepted Answer

An **algorithm** is a finite, well-defined sequence of steps that transforms input into the desired output. We judge it on two axes: **correctness** (does it always produce the right answer?) and **efficiency** (how much time and memory does it use?).

## The idea

A valid algorithm must be *unambiguous* (each step is clear), *finite* (it terminates), and produce the *correct* result for every valid input.

## Example

```python
# Find the maximum value in a list
def find_max(nums):
    if not nums:
        return None          # handle empty input
    largest = nums[0]        # assume first is the max
    for n in nums[1:]:       # scan the rest
        if n > largest:
            largest = n      # update when we see something bigger
    return largest

find_max([3, 9, 2, 7])       # -> 9
```

This visits each element once.

## Complexity

- **Time:** O(n) — one pass over n elements.
- **Space:** O(1) — just one extra variable.

## When it matters / pitfalls

Same problem, many algorithms with different costs. Always check edge cases (empty input, single element, duplicates) — that is where correctness usually breaks.

## Why it matters

Algorithms are the core of problem solving in software.

Two programs can produce the same answer while one is thousands of times faster.

Thinking in terms of correctness *and* efficiency is what separates code that works on a test case from code that works at scale.

It is also the shared language of technical interviews and system design discussions.