110年 - 110 國立中山大學_碩士班招生考試_資工系(資安)：離散數學與演算法#104300

科目：中山◆資工◆離散數學與演算法 | 年份：110年 | 選擇題數：0 | 申論題數：10

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所屬科目：中山◆資工◆離散數學與演算法

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申論題 (10)

(a)[10%].

(b)[10%]

2. [10%] Prove that there are infinitely many primes.

(a)[10%] Show that if any 19 integers are selected from the set S = {1, 2, …, 35｝, there are at least two whose sum is 36.

(b)[10%] Write a statement that generalizes the results of part (a).

4. [10%] Given an alphabet Σ, is there a languagewhere A* = A?

5. [10%] Find the generating function for the number of integer solutions to the equation

6. (Algorithm points) [10%] Find by Euclidean algori thm.

7. (Algorithm points) [10%] Please express quicksort algorithm and analyze its time complexity in detail.

8.(Algorithm points) [10%] Please express the construction of Huffman coding and analyze its time complexity in detail.