Python 使用单链表实现多项式 (Polynomial)

#!/usr/bin/python # -*- coding: utf-8 -*-'''Created on 2015-1-26@author: beyondzhou@name: linkPolynomail.py'''# Implementation of the Polynomial ADT using a sorted linked listclass linkPolynomial:    # Create a new polynomial object    def __init__(self, degree=None, coefficient=None):        if degree is None:            self._polyHead = None        else:            self._polyHead = _PolyTermNode(degree, coefficient)        self._polyTail = self._polyHead    # Returns the degree of the polynomial    def degree(self):        if self._polyHead is None:            return -1        else:            return self._polyHead.degree    # Returns the coefficient for the term of the given degree    def __getitem__(self, degree):        assert self.degree() >= 0, \               "Operation not permitted on an empty polynomial."        curNode = self._polyHead        while curNode is not None and curNode.degree >= degree:            curNode = curNode.next        if curNode is None or curNode.degree != degree:            return 0.0        else:            return curNode.degree    # Evaluate the polynomial at the given scalar value    def evaluate(self, scalar):        assert self.degree() >= 0, \            "Only non-empty polynomials can be evaluated."        result = 0.0        curNode = self._polyHead        while curNode is not None:            result += curNode.coefficient * (scalar ** curNode.degree)            curNode = curNode.next        return result    # Polynomial addition: newPoly = self + rhsPoly    def __add__(self, rhsPoly):        assert self.degree() >= 0 and rhsPoly.degree() >= 0, \            "Addition only allowed on non-empty polynomials."        newPoly = linkPolynomial()        nodeA = self._termList        nodeB = rhsPoly._termList        # Add corresponding terms until one list is empty        while nodeA is not None and nodeB is not None:            if nodeA.degree > nodeB .degree:                degree  = nodeA.degree                value = nodeA.coefficient                nodeA = nodeA.next            elif nodeA.degree < nodeB.degree:                degree = nodeB.degree                value = nodeB.coefficient                nodeB = nodeB.next            else:                degree = nodeA.degree                value = nodeA.coefficient + nodeB.coefficient                nodeA = nodeA.next                nodeB = nodeB.next            self._appendTerm(degree, value)        # If self list contains more terms appedn them        while nodeA is not None:            self._appendTerm(nodeA.degree, nodeA.coefficient)            nodeA = nodeA.next        # Or if rhs contains more temrs append them        while nodeB is not None:            self._appendTerm(nodeB.degree, nodeB.coefficient)            nodeB = nodeB.next        return newPoly    # Polynomial subtraction: newPoly  = self - rhsPoly    def __sub__(self, rhsPoly):        assert self.degree() >= 0 and rhsPoly.degree() >= 0, \            "Subraction only allowed on non-empty polynomials."        newPoly = linkPolynomial()        nodeA = self._termList        nodeB = rhsPoly._termList        # Add corresponding terms until one list is empty        while nodeA is not None and nodeB is not None:            if nodeA.degree > nodeB .degree:                degree  = nodeA.degree                value = nodeA.coefficient                nodeA = nodeA.next            elif nodeA.degree < nodeB.degree:                degree = nodeB.degree                value = nodeB.coefficient                nodeB = nodeB.next            else:                degree = nodeA.degree                value = nodeA.coefficient - nodeB.coefficient                nodeA = nodeA.next                nodeB = nodeB.next            self._appendTerm(degree, value)        # If self list contains more terms appedn them        while nodeA is not None:            self._appendTerm(nodeA.degree, nodeA.coefficient)            nodeA = nodeA.next        # Or if rhs contains more temrs append them        while nodeB is not None:            self._appendTerm(nodeB.degree, -nodeB.coefficient)            nodeB = nodeB.next        return newPoly    # Polynomial multiplication: newPoly = self * rhsPoly    def __mul__(self, rhsPoly):        assert self.degree() >= 0 and rhsPoly.degree() >= 0, \          "Multiplication only allowed on non-empty polynomials."        # Create a new polynomial by multiplying rhsPoly by the first term        node = self._polyHead        newPoly = rhsPoly._termMultiply(node)        # Ierate through the remaining terms of the poly computing the        # product of the rhsPoly by each term        node = node.next        while node is not None:            tempPoly = rhsPoly._termMultiply(node)            newPoly = newPoly.add(tempPoly)            node = node.next        return newPoly    # Helper method for creating a new polynomial from multiplying an     # existing polynomail by another term    def _termMultiply(self, termNode):        newPoly = linkPolynomial()        # Iterate through the terms and compute the product of each term         # and the term in termNode        curr = termNode.next        while curr is not None:            # compute the product of the term            newDegree = curr.degree + termNode.degree            newCoeff = curr.coefficient * termNode.coefficient            # Append it to the new polynomial            newPoly._appendTerm(newDegree, newCoeff)            # Advance the current pointer            curr = curr.next        return newPoly            # Helper method for appending terms to the polynomial    def _appendTerm(self, degree, coefficient):        if coefficient != 0.0:            newTerm = _PolyTermNode(degree, coefficient)            if self._polyHead is None:                self._polyHead = newTerm            else:                self._polyTail.next = newTerm            self._polyTail = newTerm# Class for creating polynomial term nodes used with the linked listclass _PolyTermNode(object):    def __init__(self, degree, coefficient):        self.degree = degree        self.coefficient = coefficient        self.next = None