Final answer:
Evaluation stacks grow large with deeply nested expressions or high recursion, such as calculating Fibonacci numbers without memoization. Understanding and managing stack growth is critical in programming to prevent stack overflow errors. Optimization and iterative approaches can mitigate large stack sizes.
Step-by-step explanation:
The evaluation stack, which is part of a computer program's runtime environment, can grow large when evaluating expressions that are deeply nested or have high recursion. Deeply nested expressions contain many layers of functions calls or operations within each other, while recursive functions call themselves repeatedly, each time adding a new frame to the stack. For example, evaluating an expression like ((a + (b * (c - d))) ^ e) can cause the stack to grow more because each operation may need to be pushed onto the stack before the entire expression can be evaluated. Similarly, a recursive algorithm calculating the n-th Fibonacci number without memoization will also cause the evaluation stack to grow very large, as it will perform a large number of function calls.
In programming, especially with recursive algorithms, it is crucial to understand and manage the size of the evaluation stack because stack overflow errors can cause programs to crash. This error occurs when the stack's maximum capacity is exceeded. Factoring in the use of tail-call optimization and using iterative approaches can help mitigate the risk of an excessively growing stack.