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題組內容

1.Prove each of the following for all n≥ 1 by the Principle of Mathematical Induction.

(b)[10%]

相關申論題

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.

1. Find the general solutions of y1 and y2 (10 分)

2. The tank in Fig. 1 contains 80 Ib of salt dissolved in 500 gal of water. The inflow per minute is 20 1b of salt dissolved in 20 gal of water. The outflow is 20 gal/min of the uniform mixture. Find the time when the salt content y(t) in the tank reaches 95% of its limiting value (as t→ ∞). (10 分)

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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

110年 · #104300

109年 - 109 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#105755

109年 · #105755

108年 - 108 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#105778

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