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首頁 > 中山◆電機◆資料結構 > 102年 - 102 國立中山大學_碩士班招生考試_電機系(丙組)：資料結構#110205 > 申論題

題組內容

4. The array A shown below is used to represent the complete binary tree.
Please answer the following three questions:

(1) [5 points] Draw the corresponding binary tree T.

相關申論題

(a) [5 points] Given the size n of the input data, where n is a positive integer, we assume that the running time of a program is O(f(n). State the formal definition of O(f(n)).

(b) [5 points] Let . Tell us the value of Note that you will et o points if you just povide the ansver. In other words, you must show your reasons.

(c) [5 points] Given the size n of the input data, where n is a positive integer, we assume that a program requires the running time T1(n) = O( f(n). Derive the function f(n) .

(d) [5 points] Let n be the radius of a circle C and A(n) be the area of C. Let T2(n)=|sinθ|xlog A(n)= O(f(n) . Derive the function f(n).

2. [5 points] Consider the following function F written in a C-like pseudo-code, which takes an array A of n positive integers and an initially-empty stack S as input parameters: What is the output (returned value) of the function F for the array A= [2, 14, 4, 7, 11, 18, 10, 15, 6, 23, 12, 8]?

(1) [10 points] Please find the vertex sequence derived by DFS and BFS respectively. Note that we assume that node A is the root.

(2) [10 points] Please apply Kruskal's algorithm to drive the minimum cost spanning tree. Note that you must show your actions step by step.

(2) [5 points] Is T a max heap? Is T a min heap? Explain your reasons.

(3) [15 points] Perform the following three heap operations sequentially: INSERT (18), INSERT (27) , DELETE on T. Draw the resultant tree after each operation.

(a) [5 points] Given an unsorted integer array of size n, does the binary search algorithm outperform the sequential search algorithm? Use the big-O notation to justify your answer.

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