Why Analysis of Algorithms?
You have two ways to sort a list: Bubble Sort and Quick Sort. Both work, but one may finish in seconds while the other takes hours. Analysis of algorithms helps us compare algorithms based on their efficiency – not just that they work, but how well they work as input grows.
We analyze algorithms to answer questions like:
- How fast does this algorithm run?
- How much memory does it use?
- Will it scale when data becomes huge?
- Which algorithm should I choose for my problem?
Consider two algorithms to find a number in a sorted array:
// Linear Search (checks one by one)
for (int i = 0; i < arr.length; i++) {
if (arr[i] == target) return i;
}
// Binary Search (jump to middle)
int low = 0, high = arr.length - 1;
while (low <= high) {
int mid = (low + high) / 2;
if (arr[mid] == target) return mid;
else if (arr[mid] < target) low = mid + 1;
else high = mid - 1;
}
Two Minute Drill
- Analysis compares algorithms based on time and memory.
- Helps choose the best algorithm for a given problem.
- Ensures scalability with large input sizes.
- Two main metrics: time complexity and space complexity.
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