Data Structures -1 st test- March 30, 2015 授課教授：李錫智.

Data Structures-1st test-

March 30, 2015

授課教授：李錫智

Question 1

• Suppose you want to open a grocery store. Please design an abstract data type (ADT) for your store. Please give at least five operations.

Solution of Q.1

Grocery

+getTotalItem(): integer

+isEmpty(): boolean

+stockItem(newEntry: ItemType): boolean

+sellItem(anEntry: ItemType): boolean

+findItem(anEntry: ItemType): ItemType

Question 2

• Suppose we use an integer variable itemcount and an array A of size 12 to implement the bag structure. Note that objects are stored in no particular order and objects may be duplicated. We would like to store integers in a bag.

Q.2-1

• We have to initialize the bag. Please show the content of itemcount and A in the initial state.

Solution of Q.2-1

itemcount = 0

Q.2-2

• Suppose we add six integers 5, 10, 5, 5, 15, and 10 successively in the bag. Please show the content of itemcount and A after these additions.

Solution of Q.2-2

• itemcount = 6

• A[] = {5, 10, 5, 5, 15, 10, , , , }

Q.2-3

• We want to delete the second 5 from the bag. How do you do it? Please describe. Also, please show the content of itemcount and A after execution.

Solution of Q.2-3

Q.2-3:

num5count = 0

For i from 0 to 12:

If A[i] == 5:

If num5count == 1:

For j from i+1 to 12:

Copy A[j] to A[j-1]

itemcount = itemcount – 1

Else:

num5count = num5count + 1

End

itemcount = 5

A[] = { 5, 10, 5, 15, 10, , , , , }

Q.2-4

• We want to see whether the bag is empty. How do you do it? Please describe.

Solution of Q.2-4

isEmpty:

If itemcount == 0:

print “The bag is empty.”

Else:

print “There is something in bag.”

End

Q.2-5

• We want to clear the bag, i.e., making the bag empty. How do you do it? Please describe.

Solution of Q.2-5

Clear:

itemcount = 0

for i from 0 to 12:

A[i] = NULL

End

Question 3

• Suppose we use a pointer variable headPtr and a chain to implement the bag structure. We would like to store integers in a bag.

Q.3-1

• We have to initialize the bag. Please show the content of headPtr and the chain in the initial state.

Solution of Q.3-1

headPtr nullptr

Q.3-2

• Suppose we add six integers 5, 10, 5, 5, 15, and 10 successively in the bag. Please show the headPtr and the chain after these additions.

Solution of Q.3-2

headPtr nextPtr5 nextPtr10 nextPtr5

nextPtr5 nextPtr15 nextPtr10 nullptr

Q.3-3

• We want to delete the second 5 from the bag. How do you do it? Please describe. Also, please show headPtr and the chain after execution.

Solution of Q.3-3

headPtr nextPtr5 nextPtr10 nextPtr5

nextPtr5 nextPtr15 nextPtr10 nullptr

Q.3-4

• We want to see whether the bag is empty. How do you do it? Please describe.

Solution of Q.3-4

• Check whether the headPtr points to nullptr.

headPtr nullptr?

Q.3-5

• We want to clear the bag, i.e., making the bag empty. How do you do it? Please describe.

Solution of Q.3-5

• Find next node and free current node from headPtr until that the next node is nullptr.

Question 4

• Suppose we have the following recursive program:

• Let’s execute the function call kkk(5,3).

1. int kkk(n, m)2. {3. cout<<"About to compute for n, m = "<< n <<" , "<< m <<endl;4. if ((n==m) or (m==0))5. return 1;6. else7. return kkk(n-1,m)+kkk(n-1,m-1);8. }

Q.4

• How many times kkk(2,1) is executed before termination? 3

• How many times kkk(1,1) is executed before termination? 3

• What messages are shown on the screen? Please show them in correct order.

• What is the final return value? 10

• Is this function efficient? Why or why not?

Solution of Q.4

Q.4-3


About to compute for n, m = 5,3About to compute for n, m = 4,3 About to compute for n, m = 3,3 About to compute for n, m = 3,2 About to compute for n, m = 2,2 About to compute for n, m = 2,1 About to compute for n, m = 1,1 About to compute for n, m = 1,0 About to compute for n, m = 4,2 About to compute for n, m = 3,2 About to compute for n, m = 2,2 About to compute for n, m = 2,1 About to compute for n, m = 1,1 About to compute for n, m = 1,0About to compute for n, m = 3,1About to compute for n, m = 2,1About to compute for n, m = 1,1About to compute for n, m = 1,0About to compute for n, m = 2,0

Q.4-5

• Is this function efficient? Why or why not?

• Usually, recursion is not efficient in terms of stack and system overhead. Think about a recursion to calculate the factorial of a number. You will have n-1 recursion calls.

Question 5

• Suppose we have a program:

• where max takes the larger of its two arguments. Let’s execute the function call aaa(A,0,6) with A = [20, 80, 30, 40, 10, 70, 50].

1. int aaa(A,i,n)2. {3. cout<<"About to compute for i, n = "<<i<<" , "<< n <<endl;4. if (n==i)5. return A[n];6. else7. return max(aaa(A,i,(n+i)/2), aaa(A,(n+i)/2+1,n));8. }

Q.5

• Please list all the base cases encountered during execution and show what values of n and i in each case.


• How many times the function max is executed? 6 Please show its two arguments each time.

• What is the final return value? 80

Solution of Q.5

Q.5-1

• Please list all the base cases encountered during execution and show what values of n and i in each case.

• aaa(A, 0, 0)、 aaa(A, 1, 1)、 aaa(A, 2, 2)

aaa(A, 3, 3)、 aaa(A, 4, 4)、 aaa(A, 5, 5)

Q.5-2

• About to compute for i, n = 0 , 6













Question 6

• Suppose we have a recursive program:

• where Swap exchanges the two values involved. Let’s execute the function call qqq(A,0,7) with A = [20, 80, 30, 40, 10, 70, 50].

1. void qqq(A,i,n) 2. {3. cout<<"About to compute for i, n = "<<i <<" , "<< n <<endl;4. if (n>1)5. cout<<"To swap the indices "<<i<<" and "<< i+n-1<<endl;6. Swap A[i] and A[i+n-1];7. qqq(A,i+1,n-2);8. cout<<"End computing for i, n = "<<i<<", "<<n<<endl;9. }

Q.6

• How many times the function qqq is called before termination, including qqq(A,0,7) itself? 4


• How many times the Swap operation is performed? 3

• What is the content of A after execution?

• [50, 70, 10, 40, 30, 80, 20]

Solution of Q.6

• 0, 7 06

• 1, 5 15

• 2, 3 24

• 3, 1 End

Q.6-2



To swap the indices 0 and 6

About to compute for i, n = 1 , 5





End computing for i, n = 3 , 1

Data Structures -1 st test- March 30, 2015 授課教授：李錫智.

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