Question

Find an optimal parenthesisation of a matrix chain product whose sequene of dimensions given by {4,6,30,8,9}

Answer 1

import java.io.*; public class Main public static int[][] m; public static int[][] s; public static void main(String[] args) int[] p -getMatrixsizes (args); int n p.length-1; if (n <2 |I n > 15) System.out.println("Wrong input"); System.exit(e); system . out.println("######Using a recursive non Dyn. Prog. method:"); int mm-RMC(p, 1, n); System.out.println("Min number of multiplications:"mm+ System . out.println("######Using bottom-top Dyn. Prog. method:" MCO (p); System.out.println("Table of m[i][j]:"); System.out.print("j\lil"); for (int 1-1; i<-n; i+) System.out.printf("X5d ", і); System.out.print("n-"); for (int i-1; i<-6 n-1; i++) System.out.print("-") System.out.println(); for (int j-n; j-1; j-- System.out.print("" i+"|")

31 for (int 1-1; i-i+) 2 System.out.printf("%5d ", m[i][j]); 33 System.out.println) 5 System.out.println("Min number of multiplications:"m[1][n] 6 System.out.println("Table of s[i][j]:"); 37 System.out.print( j\lil"); 38 for (int i-1; i<-n; i++) 39 System.out.printf("%2d ", i); 40 System.out.print( n"); 41 for (int i-1; i<-3*n-1; i++) 42 System.out.print("- "); 43 System.out.println(); 4 for (int j-n; j>-2; j--) 46 System.out.print(" "+j""); 47 for (int i-1; i<-j-1; i++) 48 System.out.printf( "%2d ", s[i][j]); 49 System.out.println); 50 51 System.out.print("Optimal multiplication order:"); 52 MCM(s, 1, n); 53 System.out.println("\n"); 54 system . out.println("######Using top-bottom Dyn. Prog. method;" 55 mm-MMC (p); 6 System.out.println("Min number of multiplications:" mm); 57 8 public static int RMC (int[] p, int i, int j) 59 60 if (i--j) return(e); 61 int m_ij- Integer.MAX_VALUE;

62 for (int k-i; k<j; k++) 64 int q RNC ( p, i, k) + RMC (p, k+1, j) + p[1]*p(k)"plj]; 65 if (q<m_ij) 66 m_ij-q; 67 68 return(m_ij); 69 70 public static void MCO (int[] p) 71 72 int n p.length-1; // # of matrices in the product 73 mnew int[n+1 [n+1]; I/ create and automatically initialize array m 74 S-new int[n+1] [n+1]; 75 for (int 1-2; 1<-n; 1+) 76 77 for (int i-1; i<-n-1+1; i++) 78 79 int j-i+1-1; 80 mi][j] - Integer.MAX_VALUE; 81 for (int k-i; k<-j-1; k++) 82 83 int qm[i][k] m[k+1j]p[i-1] p[k] p[j]: 84 if (q <m[i][j]) 85 87 s[i][j] =k; 89 90 91 92

93 public static void MCM(int[][] s, int i, int j) 94 95 if (i-j) system . out.print("A" İ); + 96 else 97 ▼ 98 System.out.print("("); 99 MCM(s, i, s[i][j]) 100 MCM(s, s[1][j]+1,j); 101 System.out.print(")"); 102 103 104 public static int MMC (int[] p) 105 106 int n p.length-1; 107 mnew int n+11[n+1]; 108 for (int i-0; i<-n; i++) 109 for (int j=i; j<=n; j++) 110 m[i][j] Integer.MAX_VALUE; 111 return(LC(p, 1, n)); 112 113 public static int LC(int[] p, int i, int j) 114 115 İf (m[1][j] < Integer.MAX-VALUE) return(m[i][j]); 116 if (i-j) m[i][j]- e; 117 else 118 119 for (int k-i; k<j; k++) 120▼ { 121 int q LE(p, і, k) + LC (p, k+1, j) + p[1]*p(k)"plj, 122 123 if (q <m[i][j]) 124 m[i]] q; 125

126 127 return(m[i][j]); 128 129 public static intl getMatrixSizes(Stringl ss) 130 131 int k -ss.length; 132 if (ke) 133 134 System.out.println( "No matrix dimensions entered"); 135 System.exit(e); 136 137 int] p-new intkl: 138 for (int i-e; ick; i++) 139 ▼ 140 try 141 142 p[i]Integer.parseInt (ss[i]); 143 if (P[i] <-) 144 145 System.out.println( "Illegal input number "+ k); 146 System.exit(0); 147 148 149 catch(NumberFormatException e) 150 151 System.out.println("Illegal input token " Ss[i]); 152 System.exit(e); 153 154 155 return(p); 156 157

Command Prompt C:\Users Appirio-13522\Desktop java Main 5 4 6 30 8 9 ######Using a recursive non Dyn. Prog . method: Min number of multiplications:2064 ######Using bottom-top Dyn. Prog. method: Table of m[i][j]: ji 1 2345 51 2100 1920 1872 2160 41 1792 1632 1440 0 3 120 72 e 2 120 e Min number of multiplications:2100 Table of s[i][jj: jli 1 2 3 4 5 4|1 2 3 Optimal multiplication order: (A 1( (A 2 (A 3A_4))A5)) ######Using Min number of multiplications:2064 top-bottom Dyn. Prog. method: C:\Users\Appirio-13522\Desktop>