Which of the following would have a exponential Big O run-time complexity?

Question

BlackTom AI · Accepted Answer

Exponential time complexity means the running time grows proportional to a^n (e.g., O(2^n), O(3^n)) or factorial-like growth (e.g., O(n!)) where the cost doubles (or more) for each additional input element. Typical exponential algorithms enumerate many combinations or subsets (for n items there are 2^n subsets).

Step-by-step reasoning for each option:

1. Determine if a binary number is even or odd.
- Knowledge: parity of a binary integer is determined by its least significant bit.
- Work: inspect the final bit (0 => even, 1 => odd). This is a single constant-time operation.
- Complexity: O(1). Not exponential.

2. Efficiently find the definition of a given word in a dictionary.
- Knowledge: dictionaries (sorted lists) allow binary search (O(log n)); hash tables or tries give average O(1) lookup.
- Work: with an efficient method you do at most O(log n) comparisons or constant-time hashing/trie traversal proportional to word length.
- Complexity: O(log n) or O(1) (with respect to number of entries). Not exponential.

3. Find all duplicates in a list.
- Knowledge: naive pairwise check does O(n^2) comparisons (n(n−1)/2), improved method uses a hash set for a single pass.
- Work: using a hash set, check each element and record seen items → O(n) average time.
- Complexity: O(n) (efficient) or O(n^2) (naive). Neither is exponential.

4. Find the largest value in an unsorted list.
- Knowledge: one linear scan tracking the maximum.
- Work: compare each of the n elements once (n−1 comparisons).
- Complexity: O(n). Not exponential.

Why other options are incorrect: none of these operations require examining an exponential number of combinations; their known algorithms are constant, logarithmic, linear, or quadratic at worst.

Conclusion: since none of the listed tasks require exponential-time algorithms, the correct answer is "none of these," which matches the provided answer.

Which of the following would have a exponential Big O run-time complexity?单项选择题

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