Why Analysis of Algorithms Matters

Have you ever written code that works perfectly… but becomes slow when data grows? That’s where analysis of algorithms comes in. Real Problem Imagine you have two ways to sort or search data. Both give correct results But one takes seconds, the other takes hours So which one should you choose? Why Do We Analyze Algorithms? We analyze algorithms to answer: How fast does it run? How much memory does it use? Will it scale for large data? Which algorithm is best? Example: Linear Search vs Binary Search Linear Search (Slow) for (int i = 0; i < arr.length; i++) { if (arr[i] == target) return i; } Checks each element one by one Binary Search (Fast) 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; } Divides the search space into half each time Key Insight For small data → difference is small For large data → difference is HUGE Binary Search becomes exponentia