Memoizing
When running a function over and over, avoiding the cost to call that function can greatly speed up the resulting code.
Think of a for loop or a recursive function that maybe has to call that function dozens of times. If instead of calling it, it could preserve the known results of a previous call to the function, it could make code much faster.
The most common example for is the Fibonacci sequence. The sequence is computed by adding the first two numbers, then the second number is added to the result, and so on.
This means that in the sequence 1, 1, 2, 3, 5, computing 5 required us to compute 3 + 2, which required us to compute 2 + 1, which required us to compute 1 + 1.
Doing the Fibonacci sequence in a recursive manner is the most obvious approach as it leads to 5 = fib(n3) + fib(n2), which was made of 3 = fib(n2) + fib(n1), so you can easily see that we had to compute fib(n2) twice. Memoizing the result of fib(n2) would allow us to perform such computation only once and then reuse...
