Final answer:
The correct answer is 'b. none of these', as none of the listed options typically have an exponential Big O runtime complexity. Big O notation expresses algorithmic complexity, none of which applies to the options given.
Step-by-step explanation:
The question is asking which of the listed options would have an exponential Big O runtime complexity. The concept of Big O notation is used in computer science to describe the performance or complexity of an algorithm. Specifically, it is a way to express the worst-case scenario for how long an algorithm could take to complete as the size of the input data increases.
- Efficiently finding the definition of a given word in a dictionary is typically done using a hash table or binary search, both of which have better than exponential complexity.
- Finding the largest value in an unsorted list has a linear complexity, as it requires checking each element only once (O(n)).
- Determining if a binary number is even or odd can be done in constant time by checking the last digit of the number (O(1)).
- Finding all duplicates in a list can be done in O(n^2) in the worst case without extra space, or O(n) with additional space such as a hash table.
None of the options listed would typically have an exponential Big O runtime complexity, so the correct answer is 'b. none of these'.