Explain Time Complexity & Space Complexity. Why are they important?

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1. Time Complexity

Time Complexity tells how much time an algorithm takes to run, or how the speed of the algorithm changes when the input size increases.

• In simple words:
  “How fast or slow an algorithm runs?”

• Time complexity is mostly represented using Big-O notation
  → O(1), O(n), O(n²), O(log n), etc.

Example:

If your algorithm's loop runs 1 time → O(1)
If the loop runs n times → O(n)
If there is a nested loop → O(n²)

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2. Space Complexity

Space Complexity tells how much memory (RAM) an algorithm needs, and how memory usage increases when the input size increases.

• In simple words:
  “How much memory does the algorithm use?”

• Memory includes:
  ✔ Variables
  ✔ Data structures (arrays, stacks, queues)
  ✔ Extra temporary memory

Example:

If the algorithm uses only 1 variable → O(1)
If the algorithm uses an array of n items → O(n)

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Why are Time & Space Complexity Important?

1. To check efficiency

Complexity helps to understand whether an algorithm is fast or slow, light or heavy.

2. To choose the best algorithm for large inputs

Small input can be handled by any algorithm,
but for big data only efficient algorithms work well.

3. Helpful for comparing performance

To find which algorithm is better —
time & space complexity helps in the decision.

4. Helps in optimization

If an algorithm is slow or uses more memory,
complexity helps to optimize and improve it.

5. Important in real-world applications

Where speed and memory are limited, such as:

• Mobile apps

• Online servers

• Gaming

• AI systems

Efficient algorithms are required in such cases.

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Short Exam-Friendly Summary

• Time Complexity → The time taken by an algorithm to run.

• Space Complexity → The memory required to run an algorithm.

• Both are important because they show how fast and memory-efficient an algorithm is.

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