The following algorithmtakes a sorted array A[1..n] of characters and outputs, in reverse order, all 2-letter words νω such that ν≤ω. for all i=n down to 1 do for all j=n down to i do print "A[i]A[j]" end for end forCount the number of primitive operations (evaluating an expression, indexing into an array).

Question

The following algorithmtakes a sorted array A[1..n] of characters and outputs, in reverse order, all 2-letter words νω such that ν≤ω. for all i=n down to 1 do for all j=n down to i do print "A[i]A[j]" end for end forCount the number of primitive operations (evaluating an expression, indexing into an array).

BlackTom AI · Accepted Answer

We start by restating the problem to ensure we understand what's being counted and when the counts occur.
Question: An algorithm processes a sorted array A[1..n] and, for all i from n down to 1, and for all j from n down to i, prints the string formed by A[i]A[j]. The task is to count primitive operations, defined as evaluating an expression or indexing into an array.
Option given: a. 2n^2 + 5n + 1 primitive operations.

Now, analyze the loop structure and what happens inside the inner loop.
- The outer loop runs i from n down to 1, which yields n iterations.
- For a fixed i, the inner loop runs j from n down to i, which yields (n - i + 1) iterations.
- Therefore, the total number of iterations of the inner body (i.e., the print statement) across all i is the sum over i = 1 to n of (n - i + 1) = 1 + 2 + ... + n = n(n + 1)/2.

Within each iteration of the inner loop, what primitive operations occur according to the definition given?
- Two array indexings: A[i] and A[j]. Each indexing into the array counts as one primitive operation.
- An expression evaluation to form the string from A[i] and A[j] before printing. This counts as one primitive operation (evaluating the expression that combines the two retrieved values).
Thus, per inner-loop iteration, we incur 2 (indexings) + 1 (expression evaluation) = 3 primitive operations.

Total primitive operations = (number of inner-loop iterations) × (cost per iteration) = [n(n + 1)/2] × 3 = (3/2)(n^2 + n) = 1.5n^2 + 1.5n.

Now compare this result to the provided option 2n^2 + 5n + 1.
- The exact count under the stated definitions yields 1.5n^2 + 1.5n, not 2n^2 + 5n + 1. The discrepancy is significant in the quadratic and linear coefficients.
- You might wonder if additional costs were overlooked, such as loop control costs (comparisons, increments/decrements) or the cost of the print operation itself. If we were to include typical loop-control overhead (comparisons and decrements) as primitive operations, the overall count would increase, but it would still depend on precisely which operations are included and how many times they execute, and it would no longer match a simple 2n^2 + 5n + 1 form without a clearly specified accounting scheme.
- Since the problem statement explicitly labels primitive operations as evaluating an expression or indexing into an array, and the only such operations in the inner body are the two indexings plus the expression evaluation, the derived count 1.5n^2 + 1.5n is the appropriate result under that definition.

In light of this, the provided option does not align with the counted quantity under the given definition of primitive operations. If the assignment intended to include loop-control costs, one would need to state that clearly and provide the exact counting rules to derive a corresponding polynomial.

COMP9024-Data Structures and Algorithms - 2025 T1

查看解析

登录即可查看完整答案

类似问题

Which of the following statements is true with reference to an algorithm’s runtime?

How many times is the diamond (◊) operation performed in the following algorithm? Algorithm mystery(A) Input an array A of n integers Output ???1 value <- A[0] ◊ A[n-1]2 for i <- 1 to n-1 do3 A[i] <- A[i] ◊ 2 4 for i <- 0 up to 316 do5 A[i] <- 3 ◊ A[i] 6 return A[0]

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单