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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
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(b) Please derive the time complexity of quick sort by the method of recurrence relation for the input data size n.
其他申論題
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.
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5. Find the exponential generating function for the sequence 0!, 1!, 2!, 3!,....
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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
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7. (a) Please state the quick sort algorithm in detail.
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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?
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(a) What is the completion time of process Pi using a nonpreemptive priority (a smaller priority number implies a higher priority) scheduling?
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(b) What is the average waiting time using shortest-job-first scheduling?
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2. A machine has 64-bit virtual addresses and 32-bit physical addresses. Pages are 32 KB. How many entries are needed for the page table?
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(a) f
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(b)
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