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中山◆資工◆離散數學與演算法
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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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3. How many positive integers n divide 99373n + 342246?
其他申論題
8.4 What types of dependencies can occur during out-of-order execution?
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(a) ≥ 1,1 ≤ i ≤ 4.
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(b)x1,x2,X1＞2,0＜X4≤14.
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2. If p, q are primes, prove that pla if and only if p = q.
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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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(b) Please derive the time complexity of quick sort by the method of recurrence relation for the input data size n.
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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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