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110年 - 110 國立高雄大學_碩士班招生考試_資訊工程學系：離散數學與資料結構#102139
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2. (15%) Define a relation R on Z by x R y if x - y is even.
(c) Describe the equivalence classes of the relation R.
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(a) at least one ball is selected for each color?
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(b) no more than four balls are selected for each color?
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(c) odd number of red balls, odd number of green balls, even number of white balls, and even number of black balls are selected?
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(a) Describe each of the four properties: (i) reflexivity, (ii) symmetry, (iii) transitivity, and (iv) antisymmetry.
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(b) Show that R is an equivalence relation.
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3. (10%) For the B-tree below, show the new B-tree that would result from inserting 21.
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(a) (10%) Use Heapsort to sort the array and show the array a[ ] after the complete max heap is constructed (i.e., after phase 1 of Heapsort is done).
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(b) (5%) What is the time complexity of Heapsort?
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5. (5%) Consider the five keys on the left side of the figure below. Also as shown in the figure, a hash function is applied to these five keys where two keys are hashed to the same integer. Discuss how to solve this collision.
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(a) (20%) Discuss how to find the intersection nodes of the two lists (the intersection nodes refer to the nodes appear in both of the two lists), and what is the corresponding time complexity.
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相關試卷
110年 - 110 國立臺灣科技大學_碩士班招生試題_工業工程系：統計學#111373
110年 · #111373
110年 - 110 國立高雄大學_碩士班招生考試_資訊工程學系：離散數學與資料結構#102139
110年 · #102139
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