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

科目：中山◆資工◆離散數學與演算法 | 年份：109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) ≥ 1,1 ≤ i ≤ 4.

(b)x₁,x₂,X₁＞2,0＜X₄≤14.

2. If p, q are primes, prove that pla if and only if p = q.

3. How many positive integers n divide 99373n + 342246?

4. Let f,g:R → R, where g(x) = 1 - x + x² and f = ax + b. If (g。f)(x) = 9x² -9x +3, determine a, b.

5. Find the exponential generating function for the sequence 0!, 1!, 2!, 3!,....

6. If as = 0, a₁ = 2, a₂ = 6, and a₂ = 56 satisfy the recurrence relation = 0, where n ≥ 0 and b, c are constants, determine b, c and solve for an

7. (a) Please state the quick sort algorithm in detail.

(b) Please derive the time complexity of quick sort by the method of recurrence relation for the input data size n.

8. Let T = (V,E) be a complete m-ary tree of height h. This tree is called a full m-ary tree if all of its leaves are at level h. If T is a full m-ary tree with height 7 and 279,936 leaves, how many internal vertices are there in T?