Please I need help with the question I couldn\'t understand very well.. A) use i
ID: 3597647 • Letter: P
Question
Please I need help with the question I couldn't understand very well.. A) use it in matlab or octave to solve a) 2X2 system b) 4x4 system c) 6x6 system B) Compare the solutions you find using the gelim function with the solutions calculated by Matlab using the backslash operator (i.e. x=a if a is the coefficient matrix and b is the constant vector). function [x. flag] gelima, b) %The purpose ofthis funtion is to solve a linear system a x-b using % Gaussian elimination with partial pivotmg. The calling procedure is [x, flag]-gelim(ab) % where: %a-coefficient matrix for the system(must be square) % b-constant vector for the system; % x computed solution (if found); %flag-oifasolution is found, or flag-0 ifthere is no unique solution. lag-0 ifm--n disp( the input matrix must be a square matrix) end for i-1:m-1 % Find the pivot element and check to make sure the pivot element is nonzero. amax.pl-max(absani if amax lag-i end p=p+i-1; % Interchange rows if necessary temp-a(1,1:n); emp-bi) bir bip) end % Apply the elementary row operations to zero the subdiagonal entries in column i for j-i-1 :n end end if a(n,n) end % Do the backward substitution. or i-n-I:-1 endExplanation / Answer
public class mColoringProblem {
final int V = 4;
int color[];
/* A utility function to check if the current
color assignment is safe for vertex v */
boolean isSafe(int v, int graph[][], int color[],
int c)
{
for (int i = 0; i < V; i++)
if (graph[v][i] == 1 && c == color[i])
return false;
return true;
}
/* A recursive utility function to solve m
coloring problem */
boolean graphColoringUtil(int graph[][], int m,
int color[], int v)
{
/* base case: If all vertices are assigned
a color then return true */
if (v == V)
return true;
/* Consider this vertex v and try different
colors */
for (int c = 1; c <= m; c++)
{
/* Check if assignment of color c to v
is fine*/
if (isSafe(v, graph, color, c))
{
color[v] = c;
/* recur to assign colors to rest
of the vertices */
if (graphColoringUtil(graph, m,
color, v + 1))
return true;
/* If assigning color c doesn't lead
to a solution then remove it */
color[v] = 0;
}
}
/* If no color can be assigned to this vertex
then return false */
return false;
}
/* This function solves the m Coloring problem using
Backtracking. It mainly uses graphColoringUtil()
to solve the problem. It returns false if the m
colors cannot be assigned, otherwise return true
and prints assignments of colors to all vertices.
Please note that there may be more than one
solutions, this function prints one of the
feasible solutions.*/
boolean graphColoring(int graph[][], int m)
{
// Initialize all color values as 0. This
// initialization is needed correct functioning
// of isSafe()
color = new int[V];
for (int i = 0; i < V; i++)
color[i] = 0;
// Call graphColoringUtil() for vertex 0
if (!graphColoringUtil(graph, m, color, 0))
{
System.out.println("Solution does not exist");
return false;
}
// Print the solution
printSolution(color);
return true;
}
/* A utility function to print solution */
void printSolution(int color[])
{
System.out.println("Solution Exists: Following" +
" are the assigned colors");
for (int i = 0; i < V; i++)
System.out.print(" " + color[i] + " ");
System.out.println();
}
// driver program to test above function
public static void main(String args[])
{
mColoringProblem Coloring = new mColoringProblem();
/* Create following graph and test whether it is
3 colorable
(3)---(2)
| / |
| / |
| / |
(0)---(1)
*/
int graph[][] = {{0, 1, 1, 1},
{1, 0, 1, 0},
{1, 1, 0, 1},
{1, 0, 1, 0},
};
int m = 3; // Number of colors
Coloring.graphColoring(graph, m);
}
}