When evaluating algorithms, two main factors come into play:

• How long they take to run (time complexity)
• How much memory they use (space complexity).

Understanding these helps us make better choices when designing solutions.

Time vs. Space Complexity

Algorithms can be thought of as instructions that consume both time and memory. Measuring efficiency means considering both, but they often trade off against each other. Here’s a look at what each one involves:

Time Complexity

Time complexity measures the number of steps an algorithm takes as the input size grows. It helps predict how long a program will run.

• Why It Matters: Faster algorithms improve user experience. No one wants to wait several seconds for a simple task.
• Example: A loop that runs n times will take longer as n gets larger. If you search through a list of 1,000 names, it takes about 1,000 steps. Searching through 10,000 names takes around 10,000 steps.

Space Complexity

Space complexity measures the amount of memory an algorithm needs relative to the input size. This is crucial when working with memory-limited environments like mobile devices.

• Why It Matters: Using less memory prevents programs from crashing on devices with limited resources.
• Example: If a program creates an array with n elements, the memory required increases as n increases. A list with 1,000 elements takes less space than a list with 10,000 elements.