4948363
Descrição
Quiz por kanghsien92, atualizado more than 1 year ago
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Criado por kanghsien92
aproximadamente 8 anos atrás
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Questão 1
Questão
Tick the answer(s). There can be more than one answers
In order to recursively define an entity, we need
Responda
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A number of base cases - describes simple instances of the entity
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A number of step cases - describes complicated instances of the entity
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Define the operations should do for each base cases
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Define the operations should do for each step cases
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Come out with the algorithm first
Questão 2
Questão
[40, 20, 3] = [blank_start]40 : [20, 3][blank_end]
= [blank_start]40 : 20 : [3][blank_end]
= [blank_start]40 : 20 : 3 : [ ][blank_end]
Responda
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40 : [20, 3]
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40 : 20 : [3]
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40 : 20 : 3 : [ ]
Questão 3
Questão
Is the mathematical recursive definition related to programming?
Responda
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Yes
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No
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I am not very sure. But since recursion is used in programming, they should be related?
Questão 4
Questão
add[2, 4, 10] = [blank_start]add( 2 : [4, 10] )[blank_end]
= 2 + [blank_start]add[4, 10][blank_end]
= 2 + [blank_start]add( 4 : [10] )[blank_end]
= 2 + 4 + [blank_start]add[10][blank_end]
= 2 + 4 + [blank_start]add( 10 : [ ] )[blank_end]
= [blank_start]2 + 4 + 10 + add[ ][blank_end]
= 2 + 4 + 10
= 16
Responda
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add( 2 : [4, 10] )
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2 + 4 + 10 + add[ ]
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add( 10 : [ ] )
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add[4, 10]
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add( 4 : [10] )
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add[10]
Questão 5
Questão
[99, 9] ++ [23, 1] = [blank_start](99 : [9]) ++ [23, 1][blank_end]
= 99 : [blank_start]([9] ++ [23, 1])[blank_end]
= 99 : [blank_start]((9 : [ ]) ++ [23, 1])[blank_end]
= 99 : [blank_start](9 : ([ ] ++ [23, 1]))[blank_end]
= 99 : [blank_start](9 : ([23, 1]))[blank_end]
= 99 : 9 : [23, 1]
= [99, 9, 23, 1]
Responda
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(99 : [9]) ++ [23, 1]
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([9] ++ [23, 1])
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((9 : [ ]) ++ [23, 1])
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(9 : ([ ] ++ [23, 1]))
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(9 : ([23, 1]))
Questão 6
Questão
Can we prove the property by induction?
Responda
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Why do we need to prove? Its already proven!
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Yes we need to prove this
Questão 7
Questão
What are the orders to prove them?
1) Replace the statement with [blank_start]the base case of Lists[blank_end]
2) Prove the replaced statement using [blank_start]the properties given[blank_end]
3) Replace the statement with [blank_start]the step case of Lists[blank_end]
4) Prove the replaced statement using [blank_start]the properties given[blank_end]
5) Make us of [blank_start]the induction hypothesis[blank_end]
Responda
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the base case of Lists
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the properties given
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the step case of Lists
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the property given
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the induction hypothesis
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