Algorithm Efficiency and Big O Basics

When solving a problem, there are often many possible algorithms. But how do you decide which one is best? Algorithm efficiency is the study of how much time and space (memory) an algorithm requires as the size of the input grows.

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Why Efficiency Matters

Consider searching for a name in a phone book with 1,000,000 entries:

• Linear search might check up to 1,000,000 entries
• Binary search would check at most 20 entries

Both solve the same problem, but binary search is vastly more efficient. For real-world applications processing millions of records, choosing the right algorithm can mean the difference between a result appearing in milliseconds or taking hours.

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Measuring Efficiency: Time Complexity

We measure the efficiency of an algorithm by counting the number of basic operations (comparisons, swaps, assignments, etc.) it performs relative to the input size, n.

We focus on how the number of operations grows as n increases, rather than the exact count.

Common Growth Rates