Virtual Labs

1. In a linked-list representation of a polynomial, which information is normally stored in each term node?

a: Coefficient and exponent Explanation

Explanation

b: Only coefficient Explanation

Explanation

c: Only exponent Explanation

Explanation

d: Coefficient and node position Explanation

Explanation

2. In a linked-list representation, how is the constant term

7

represented as a coefficient-exponent pair?

(0,7)

Explanation

(7,0)

Explanation

(7,1)

Explanation

(1,7)

Explanation

3. When adding two polynomial linked lists, what should be done when the current terms have the same exponent?

a: Multiply their coefficients Explanation

Explanation

b: Compare their node addresses Explanation

Explanation

c: Add their coefficients Explanation

Explanation

d: Add their exponents Explanation

Explanation

4. Suppose a polynomial is represented by nodes ordered by decreasing exponent. Which node should be encountered first for

5x^3 + 2x + 1

a: The node for

1

Explanation

b: The node for

2x

Explanation

c: Any node, because order does not matter Explanation

Explanation

d: The node for

5x^3

Explanation

5. If two polynomial linked lists contain

m

and

n

terms respectively and both are traversed once to perform addition, what is the time complexity?

O(1)

Explanation

O(\log(m+n))

Explanation

O(m+n)

Explanation

O(mn)

Explanation

6. During polynomial addition, the current exponents are

4

and

2

. What should the algorithm do when the lists are maintained in decreasing exponent order?

a: Add the coefficients and advance both lists Explanation

Explanation

b: Discard both terms Explanation

Explanation

c: Multiply the two coefficients Explanation

Explanation

d: Advance the list whose current exponent is smaller Explanation

Explanation

7. What is the main advantage of using a linked list for a sparse polynomial?

a: It stores only the nonzero terms that are present Explanation

Explanation

b: It guarantees constant-time access to every term Explanation

Explanation

c: It automatically sorts terms without any comparisons Explanation

Explanation

d: It removes the need to store coefficients Explanation

Explanation

8. If two terms

3x^4

and

5x^4

are encountered while adding two polynomial linked lists, what term should be placed in the result?

8x^8

Explanation

15x^4

Explanation

8x^4

Explanation

2x^4

Explanation

9. If a polynomial has

m

terms and another polynomial has

n

terms, what is the worst-case number of nodes that an addition algorithm may need to process?

mn

Explanation

m+n

Explanation

m-n

Explanation

\log(m+n)

Explanation

Polynomial Arithmetic