polynomials
TRANSCRIPT
Polynomials
Steve Paks
Polynomials
• Representing Polynomials as Singly Linked Lists
A(x) = am-1xem-1+…+a0xe0
ai = nonzero coefficientei = nonnegative integer exponents, such that em-1 > em-2 > … > e0 ≥ 0
class PolyNode{int doef;int expon;
}
PolyNode a, b, d;
coef expon link
Polynomials(Cont’d)
• Representing Polynomials as Singly Linked Lists(Cont’d)a = 3x14 + 2x8 + 1b = 8x14 – 3x10 + 10x6
3 14 2 8 1 0 null
8 14 -3 10 10 6 nulla
b
Polynomials(Cont’d)
• Adding Polynomials
3 14 2 8 1 0 null
8 14 -3 10 10 6 nulla
b11 14
d(a) a.expon == b.expon
Polynomials(Cont’d)
• Adding Polynomials(Cont’d)
3 14 2 8 1 0 null
8 14 -3 10 10 6 nulla
b11 14
d(b) a.expon < b.expon
-3 10
Polynomials(Cont’d)
• Adding Polynomials(Cont’d)
3 14 2 8 1 0 null
8 14 -3 10 10 6 nulla
b11 14
d(c) a.expon > b.expon
-3 10 2 8
Polynomials(Cont’d)• Erasing Polynomials
void erase(Polynomials ptr){Polynomials temp;while(ptr != null){
temp = ptr; ∙∙∙ (a)ptr = ptr.link; ∙∙∙ (b)
}}
nullptr
temp
(a)
nullptr
temp
(b)
ptr
Polynomials(Cont’d)
• Representing Polynomials as Circular Linked Lists
– Reusing the nodes that they are no longer in use– Maintaining these nodes that have been “freed”– These nodes are reused if they are not emptied.– Using getNode(), retNode()
• getNode()– getting a node
• retNode()– adding a node to the node lists
– The avail list• collection of Polynomials
3 14 2 8 1 0
a a = 3x14 + 2x8 + 1
Polynomials(Cont’d)
• Representing Polynomials as Circular Linked Lists(Cont’d)– getNode()
null
avail
(a)
null
avail
(b)
avail
node
node
Polynomials(Cont’d)
• Representing Polynomials as Circular Linked Lists(Cont’d)– retNode()
ptr
avail
(a)
ptr
avail
Polynomials(Cont’d)
• Representing Polynomials as Circular Linked Lists(Cont’d)– retNode()
(b)
ptr
avail
avail
Polynomials(Cont’d)
• Representing Polynomials as Circular Linked Lists(Cont’d)– Erasing a circular list
…
null…ptr
avail
…
null…
ptr
avail
temp
Polynomials(Cont’d)
• Representing Polynomials as Circular Linked Lists(Cont’d)– Erasing a circular list(Cont’d)
…
null…
ptr
avail
temp
…
null…
ptravailtemp
Polynomials(Cont’d)
• Representing Polynomials as Circular Linked Lists(Cont’d)– Erasing a circular list(Cont’d)
null null …
null…
ptravailtemp
Polynomials(Cont’d)
• Representing Polynomials as Circular Linked Lists(Cont’d)– Erasing a circular list(Cont’d)
temp
null
ptr avail
null
null null
tempptr avail