Write a test program that uses BMat objects to do specified Boolean matrix calculations. The starting version of your program should be the sample file P4Test.java. Instance BMat objects for the matrices A, B, C, D, E, F, and G that are defined in P4Test . Using BMat methods, have your program calculate the following (X is an integer variable, and W is a work matrix):

a. W = (C' (A B)) B' (M' = complement of M)

b. W = (B^T B) (C C^T)

c. W = C¹⁸ = C C ... C (18 C's)

d. W = (D E)^T (D^T E^T)

e. W = D¹ D² D³ D⁴

f. X = maximum out-degree of all nodes in D

g. W = symmetric closure of D. Is D symmetric?

h. W = transitive closure of E. Is E transitive?

i. Show that matrix F represents a tree (has a candidate root node and has no cycles).

j. Show that matrix G does not represent a tree.

*** This is the Bmat.java given***

// Boolean Matrix Class public class BMat { // Instance variables public int M[][]; public int SIZE;

// Boolean matrix constructors

public BMat(int s) { SIZE = s; M = new int[SIZE][SIZE]; // Fill M with zeros for(int r = 0; r < SIZE; r++){ for(int c = 0; c < SIZE; c++){ M[r][c] = 0; } } }

public BMat(int[][] B) { SIZE = B.length; M = new int[SIZE][SIZE]; // Copy matrix B values into M for(int r = 0; r < SIZE; r++){ for(int c = 0; c < SIZE; c++){ if(B[r][c] == 0) M[r][c] = 0; else M[r][c] = 1; } } }

// Boolean matrix methods

public void show() { // Display matrix for(int r = 0; r < SIZE; r++){ for(int c = 0; c < SIZE; c++){ System.out.print(" " + M[r][c]); } System.out.println(); } return; }

public boolean isEqual(BMat M2) { // Check if current matrix equals matrix M2 for(int r = 0; r < SIZE; r++){ for(int c = 0; c < SIZE; c++){ if(this.M[r][c] != M2.M[r][c]) return false; } } return true; }

public int trace() { // Sum of main diagonal values int diag = 0; for(int r = 0; r < SIZE; r++) diag = diag + M[r][r]; return diag; }

public int arrows() { // No. of 1's in matrix int narrows = 0; for(int r = 0; r < SIZE; r++){ for(int c = 0; c < SIZE; c++){ narrows = narrows + M[r][c]; } } return narrows; }

public int indegree(int K) { // Number of arrows INTO node K of digraph // Nodes are numbered 0,1,2,...,SIZE-1 int colsum = 0; for(int r = 0; r < SIZE; r++) colsum = colsum + M[r][K]; return colsum; }

public BMat complement() { // Logical NOT of current matrix BMat W1 = new BMat(SIZE); for(int r = 0; r < SIZE; r++){ for(int c = 0; c < SIZE; c++){ if(this.M[r][c] == 0) W1.M[r][c] = 1; else W1.M[r][c] = 0; } } return W1; }

public BMat join(BMat M2) { // Logical OR of current matrix with matrix M2 BMat W1 = new BMat(SIZE); for(int r = 0; r < SIZE; r++){ for(int c = 0; c < SIZE; c++){ W1.M[r][c] = this.M[r][c] | M2.M[r][c]; } } return W1; }

public BMat power(int N) { // Raise current matrix to Boolean Nth power (N> = 1) BMat W1 = new BMat(this.M); BMat W2 = new BMat(this.M); for(int k = 2; k <= N; k++){ W1 = W1.product(W2); } return W1; }

public BMat rclosure() { // Reflexive closure of current matrix BMat W1 = new BMat(this.M); // Put 1's on main diagonal for(int r = 0; r < SIZE; r++) W1.M[r][r] = 1; return W1; }

public BMat sclosure() { // Symmetric closure of current matrix BMat W1 = new BMat(this.M); BMat W2 = W1.transpose(); W1 = W1.join(W2); return W1; }

// ********************************* // Project #4 functions to add // *********************************

public int outdegree(int K) { int add = 0; for(int i= 0; i < SIZE; i++) { add = add + M[K][i]; } return add; }

public BMat meet(BMat M2) { BMat W1 = new BMat(SIZE); for(int i = 0; i < SIZE; i++) { for(int x = 0; x< SIZE; x++) { W1.M[i][x] = this.M[i][x] & M2.M[i][x]; } } return W1; }

public BMat transpose() { for(int i = 0; i < SIZE; i++) { for(int x = 0; x < SIZE; x++) { if(i == x) continue; this.M[i][x] = this.M[i][x]; } } return this;

}

public BMat product(BMat M2) { BMat W1 = new BMat(SIZE); for (int i = 0; i < SIZE; i++) { for (int x = 0; x< SIZE; x++) { for (int k = 0; k < SIZE; k++) { W1.M[i][x] = W1.M[i][x] + this.M[i][k] * M2.M[k][x]; } } } return W1;

}

public BMat tclosure() { for (int i = 0; i < SIZE; i++) { for (int x = 0; x < SIZE; x++) { if (this.M[x][i]==1) for (int k = 0; k < SIZE; k++) if (this.M[x][i]==1 && this.M[i][k]==1) this.M[x][k] = 1; else this.M[x][k]=0; } } return this; }

public int rootnode() { int norn=0; int node=-1; for (int i = 0; i < SIZE; i++) { int count=0; for (int j = 0; j< SIZE; j++) { if (this.M[j][i]==0) count=count+1; } if (count==SIZE) { norn=norn+1; node=i; } } if (norn==1) return node+1; return -1; }

} // end class

***This is the P4Test.java that the code will be written in***

// Project #4 test program public class P4Test { public static void main(String[] args) { // Boolean matrix definitions

int A[][] = new int[][] {{1, 1, 0, 0, 1}, {1, 0, 1, 0, 0}, {0, 0, 0, 0, 0}, {1, 0, 0, 0, 0}, {0, 0, 1, 0, 1}};

int B[][] = new int[][] {{0, 1, 0, 0, 1}, {0, 1, 1, 0, 0}, {1, 0, 1, 0, 0}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 1}};

int C[][] = new int[][] {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {1, 0, 0, 0, 1}, {0, 1, 0, 0, 0}};

int D[][] = new int[][] {{1, 1, 0, 0, 0, 0}, {1, 1, 1, 0, 0, 0}, {0, 1, 1, 1, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1}};

int E[][] = new int[][] {{0, 1, 1, 0, 0, 1}, {0, 1, 1, 0, 0, 1}, {0, 0, 1, 0, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, 0}};

int F[][] = new int[][] {{0, 0, 0, 0, 1, 0, 1, 0, 0}, {1, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}};

int G[][] = new int[][] {{0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}};

BMat BMA = new BMat(A); // Put code here...

} // end main

} // end class