Definition

Time complexity measures how the runtime of an algorithm changes as the size of the input grows. It is crucial for evaluating the efficiency of algorithms.

Big O Notation (O)

• Describes the upper bound of an algorithm's time complexity.
• Represents the worst-case scenario.
• Example: Binary Search has a time complexity of O(log n).

Big Ω Notation (Ω)

• Describes the lower bound of an algorithm's time complexity.
• Represents the best-case scenario.
• Example: Linear Search has a time complexity of Ω(1) in the best case.

Big Θ Notation (Θ)

• Describes the tight bound, providing both upper and lower bounds.
• Represents the average case or a guarantee of behavior.
• Example: Bubble Sort has a time complexity of Θ(n²).

Common Time Complexities

• O(1): Constant time
• O(log n): Logarithmic time
• O(n): Linear time
• O(n log n): Log-linear time
• O(n²): Quadratic time

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