Big O Notation Explained: Measuring Algorithm Speed by Growth Rate, Not Clock Time

Comparing programs by raw runtime is unreliable because hardware, input size, and test conditions all vary. Time complexity instead counts basic operations as a function of input size n, giving a machine-independent measure of efficiency. Big O notation expresses the upper bound on that growth, with rules that drop constants and lower-order terms so only the dominant behavior matters. Common classes range from constant and logarithmic to quadratic and exponential, and the gap between them grows dramatically as inputs increase. The same framework applies to space complexity, which measures how much extra memory an algorithm requires as input grows.