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Chapter 16: Problem 11

One algorithm needs 100n basic operations to process an input of size n, and another algorithm needs 25n basic operations to process the same input. Which of the two algorithms is more efficient?

Short Answer

Expert verified
Answer: The second algorithm, which requires 25n basic operations, is more efficient than the first algorithm, which requires 100n basic operations.

Step by step solution

01

Understand the problem

To determine which of the two algorithms is more efficient, we need to compare the number of basic operations required by each algorithm to process an input of size n. The algorithm that requires fewer basic operations will be considered more efficient.
02

Calculate basic operations for the first algorithm

The first algorithm needs 100n basic operations to process an input of size n. Let's denote this as A1(n) = 100n.
03

Calculate basic operations for the second algorithm

The second algorithm needs 25n basic operations to process the same input. Let's denote this as A2(n) = 25n.
04

Compare the basic operations

To determine which algorithm is more efficient, we need to compare A1(n) and A2(n). If A1(n) < A2(n), then the first algorithm is more efficient; if A1(n) > A2(n), then the second algorithm is more efficient; if A1(n) = A2(n), then both algorithms are equally efficient.
05

Conclusion

Comparing A1(n) = 100n and A2(n) = 25n, we can see that A1(n) > A2(n) for any positive value of n. This means the second algorithm, which requires only 25n basic operations, is more efficient than the first algorithm, which requires 100n basic operations.

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Most popular questions from this chapter

With an array of 20,000 elements, what is the maximum number of comparisons the binary search will perform?

What does it mean to say that \(f(n)\) is in \(\mathrm{O}(g(n)) ?\)

Let \(a[]\) and \(b[]\) be two integer arrays of size \(n\). Following the examples of this section, give a formal description of the problem of determining if every element of \(a[]\) is also an element of \(b[] .\) The output of the algorithm should be one of the words "true" or "false."

Describe the difference between the sequential search and the binary search.

On average, with an array of 20,000 elements, how many comparisons will the sequential search perform? (Assume the items being searched have equal probability of being found at any of the positions in the array.)
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