Complexity Analysis

Why Code Efficiency Matters

Efficient code distinguishes novice developers from experts by optimizing time and space.

Time and Space Optimization

Time Optimization:

Example: Brute Force solving a Rubik's cube takes 1.4 trillion years. Efficient algorithms drastically reduce this time.

Takeaway: Saves significant time.

Space Optimization:

Example: Using seats for luggage on a bus requires more buses, illustrating inefficient space usage.

Takeaway: Efficient memory usage is critical.

Measuring Code Efficiency

Execution Time: Measure start and end times; varies with hardware.

Theoretical Estimation: Time Complexity counts operations; Space Complexity measures memory usage.

Time and Space Complexity

Time Complexity: Operations increase with input size.

Example: Calculating the average of numbers from 1 to N involves 2N + 3 operations.

Nested Loops: Complexity increases, e.g., N² for double loops.

Space Complexity: Memory usage based on input size.

Example: An array of N elements has a space complexity of O(N).

Big-O Notation

Describes the upper bound of running time.

Common notations: O(1), O(log n), O(n), O(n log n), O(n²), O(2ⁿ), O(n!).

Simplify by focusing on the highest degree term.

Growth of Complexity

Algorithms have varying complexities affecting performance.

Choosing the right algorithm is essential.

Choosing the operation based on operation frequency and available resources is very important. For more detailed information, refer to the Notion link:

Complexity Analysis⁠

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