Help with MatrixChain.cpp Dynamic Programming: Optimal Matrix Chain Multipli- ca
ID: 3598495 • Letter: H
Question
Help with MatrixChain.cpp
Dynamic Programming: Optimal Matrix Chain Multipli- cation Order In this assignment you are asked to implement a dynamic programming algorithm: matrix chain multiplication (chapter 15.2), where the goal is to find the most computationally efficient matrix order when multiplying an arbitrary number of matrices in a row. You can assume that the entire input will be given as integers that can be stored using the standard C++ int type and that matrix sizes will be at least 1. You will use Grade06" to grade your code. Your execution file name must be "MatrixChain.exe". Refer to the previous lab assignments for instructions on how to use the grading tool. The input has the following format. The first number, n > 1, in the test case will tell you how many matrices are in the sequence. The first number will be then followed by n+1 numbers indicating the size of the dimensions of the matrices. Recall that the given information is enouglh to fully specify the dimensions of the matrices to be multiplied. First, you need to output the minimum number of scalar multiplications needed to multiply the given matrices. Then, print the matrix multiplication sequence, via parentheses, that minimizes the total nurnber of multiplications. Each matrix should be named A, where # is the matrix number starting at 0 (zero) and ending at n - 1. See the examples below. Examples of input and output Input 1 2 2 3 5 Output 1 30 (A0A1)Explanation / Answer
package com;
import java.util.ArrayList;
public class ArrayWithExponentAsIndexPolynomial implements PolynomialInterface
{
int polynomial[];
int highExp;
ArrayWithExponentAsIndexPolynomial()
{
polynomial=new int[200];
}
ArrayWithExponentAsIndexPolynomial(String pol)
{
polynomial=new int[200];
highExp=0;
int co=0;//Coefficient
int exp=0;//exponent
//Convert the polynomial string into linked list of polynomial terms
for(int i=0;i<pol.length();i++)
{
co=0;
exp=0;
//Find coefficient
while(pol.charAt(i)!='x' && pol.charAt(i)!='X' )
{
if(pol.charAt(i)=='-')
{
i++;
while(i<pol.length())
{
if(pol.charAt(i)!='x' && pol.charAt(i)!='X' )
{
String sub=pol.substring(i,i+1);
co=co*10+Integer.parseInt(sub);
}
else
break;
i++;
}
co=co*-1;
}
else if (pol.charAt(i)=='+')
{
i++;
}
else
{
String sub=pol.substring(i,i+1);
co=co*10+Integer.parseInt(sub);
i++;
}
if(i>=pol.length())
break;
}
i++;//skip x
if(i==pol.length())
{
if(pol.charAt(i-1)=='x' || pol.charAt(i-1)=='X')
exp=1;
}
i++;//skip ^
if(i<pol.length())
while(pol.charAt(i)!='-' && pol.charAt(i)!='+' )
{
String sub=pol.substring(i,i+1);
exp=exp*10+Integer.parseInt(sub);
i++;
if(i>=pol.length())
break;
}
if(highExp<exp)
highExp=exp;
addATerm(exp,co);
i--;
}
}
// stores the coefficient at index(exp)
void addATerm(int exp,int co)
{
// store the coefficient at index(exp)
polynomial[exp]=co;
}
int getHigh()
{
return highExp;
}
@Override
//Adds two polynomials and returns the resultant polynomial
public PolynomialInterface add(PolynomialInterface other)
{
int high;
ArrayWithExponentAsIndexPolynomial temp=new ArrayWithExponentAsIndexPolynomial();
ArrayWithExponentAsIndexPolynomial otherPoly=(ArrayWithExponentAsIndexPolynomial)other;
if(this.getHigh()<otherPoly.getHigh())
{
high=otherPoly.getHigh();
temp.highExp=otherPoly.getHigh();
}
else
{
high=this.getHigh();
temp.highExp=this.getHigh();
}
for(int i=0;i<=high;i++)
{
if(this.polynomial[i]!=0 && otherPoly.polynomial[i]!=0)
{
temp.polynomial[i]=this.polynomial[i]+otherPoly.polynomial[i];
}
else if (this.polynomial[i]==0 && otherPoly.polynomial[i]!=0)
{
temp.polynomial[i]=otherPoly.polynomial[i];
}
else if (this.polynomial[i]!=0 && otherPoly.polynomial[i]==0)
{
temp.polynomial[i]=this.polynomial[i];
}
}
return temp;
}
@Override
//Substracts one polynomial from another and returns the resultant polynomial
public PolynomialInterface subtract(PolynomialInterface other)
{
int high;
ArrayWithExponentAsIndexPolynomial temp=new ArrayWithExponentAsIndexPolynomial();
ArrayWithExponentAsIndexPolynomial otherPoly=(ArrayWithExponentAsIndexPolynomial)other;
if(this.getHigh()<otherPoly.getHigh())
{
high=otherPoly.getHigh();
temp.highExp=otherPoly.getHigh();
}
else
{
high=this.getHigh();
temp.highExp=this.getHigh();
}
for(int i=0;i<=high;i++)
{
if(this.polynomial[i]!=0 && otherPoly.polynomial[i]!=0)
{
temp.polynomial[i]=this.polynomial[i]-otherPoly.polynomial[i];
}
else if (this.polynomial[i]==0 && otherPoly.polynomial[i]!=0)
{
temp.polynomial[i]=0-otherPoly.polynomial[i];
}
else if (this.polynomial[i]!=0 && otherPoly.polynomial[i]==0)
{
temp.polynomial[i]=this.polynomial[i];
}
}
return temp;
}
public String toString()
{
String poly="";
//Convert the linked list into polynomial string
for(int i=this.getHigh();i>=0;i--)
{
if(polynomial[i]!=0)
{
if(i==1)
{
if(polynomial[i]<0)
poly=poly+"-"+polynomial[i]*-1+"x";
else
poly=poly+polynomial[i]+"x";
}
else if(i!=0)
{
if(polynomial[i]<0)
poly=poly+"-"+polynomial[i]*-1+"x^"+i;
else
{
if(i!=this.getHigh())
poly=poly+"+"+polynomial[i]+"x^"+i;
else
poly=poly+polynomial[i]+"x^"+i;
}
}
else
{
if(polynomial[i]<0)
poly=poly+"-"+polynomial[i]*-1;
else
poly=poly+"+"+polynomial[i];
}
}
}
return poly;
}
}
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