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What is Big-O notation?

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01

Understand the problem

Explain time and space complexity.

complexitybig-o
02

Attempt it yourself

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Nudge consolestandby

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03

Study the solution

Big-O describes how an algorithm's running time or space grows relative to input size n in the worst case, ignoring constants — e.g. O(1) constant, O(log n) logarithmic, O(n) linear, O(n log n), O(n²) quadratic. It lets you compare algorithms independent of hardware.

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04

Read the code

Constant vs linear vs quadratic
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def constant(nums):        # O(1) - one access, size-independent
    return nums[0] if nums else None

def linear(nums, target):  # O(n) - touches each element once
    for x in nums:
        if x == target:
            return True
    return False

def quadratic(nums):       # O(n^2) - every pair
    pairs = []
    for i in range(len(nums)):
        for j in range(i + 1, len(nums)):
            pairs.append((nums[i], nums[j]))
    return pairs


# --- demo ---
print(constant([10, 20, 30]))       # 10
print(linear([10, 20, 30], 20))     # True
print(quadratic([1, 2, 3]))         # [(1, 2), (1, 3), (2, 3)]
05

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