Question

class PNode {

//JAVA COMPLETE TODO Marked answers

// Basic node

int deg; // The degree of a term

float coeff; // The coefficient of a term

PNode next;

PNode(int d, float c) { // Constructor: builds a node with given data

next = null;

deg = d;

coeff = c;

}

PNode(int d, float c, PNode n) { // Constructor: builds a node with given reference

next = n;

deg = d;

coeff = c;

}

// Basic node operations

void scale(float k) { // scales coeff by k

coeff = coeff * k;

}

void multiplyByX(int d) { // increases the degree by d

deg = deg + d;

}

boolean simplified(PNode p) {

// PRE: p is the first node of a list of PNodes.

// POST: Returns true iff the nodes are sorted (descending) according to their

// degree field

// AND all nodes have distinct deg fields (no repeats)

// AND all nodes have a non-zero coefficient field.

PNode temp = p;

while (temp != null) {

if (temp.coeff == 0 || (temp.next != null && temp.next.deg > temp.deg))

return false;

temp = temp.next;

}

return true;

}

PNode simplify(PNode p) {

// PRE: p is the first node of a list of PNodes. All nodes in the list are

// already

// Sorted descending according to their deg field

// POST: Rearranges the list so that it is simplified but equivalent to the

// original representation,

// i.e. ensures that each node has distinct deg field (by using polynomial

// arithmetic)

// AND removes any nodes with coeff field set to 0.

// The simplified representation must be mathematically equivalent (as a

// polynomial)

// to the original representation.

// Returns the first node of the now rearranged list

while (p != null && p.coeff == 0)

p = p.next;

PNode temp = p;

while (temp != null) {

if ((temp.next != null && temp.next.coeff != 0 && temp.next.deg == temp.deg)) {

temp.coeff = temp.coeff + temp.next.coeff;

temp.next = temp.next.next;

} else if ((temp.next != null && temp.next.coeff == 0))

temp.next = temp.next.next;

temp = temp.next;

}

return p;

}

PNode priorityAdd(PNode p, int d, float c) {

// PRE: the given list p list is simplified (simplified returns TRUE);

// POST: Creates a new PNode with the given data (deg = d, coeff=c) and adds it

// to the

// current list so that the result is also simplified.

// Returns the first node of the list with the new addition

PNode newNode = new PNode(d, c);

if (p != null && p.deg <= newNode.deg) {

newNode.next = p;

p = newNode;

return simplify(p);

}

PNode temp = p;

while (temp != null) {

if (temp.next != null && (temp.next.deg <= newNode.deg)) {

newNode.next = temp.next;

temp.next = newNode;

break;

} else if (temp.next == null) {

temp.next = newNode;

break;

}

temp = temp.next;

}

return simplify(p);

}

}

class PolyList {// TODO

PNode first = null;

// Class invariant -- an instance of PolyList must always satisfy the condition:

// The list is empty OR

// (The list is not empty AND

// All nodes have distinct deg fields AND

// There are no nodes having coeff equal to 0 AND

// All nodes are ordered from first to last with decreasing deg field. )

PolyList(PNode p) { // Constructor that sets its first node to the given PNode p.

first = p;

}

int getDegree() { // TODO

// Returns the largest degree in the list representation.

return 0;

}

}

Answer 1

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