> restart;
Question1 
> n:=6:E:=array(0..n-1,[seq(i,i=0..n-1)]):
> i:=2:j:=4:E[j]:=i:print(E);

  array(0 .. 5, [

        (0) = 0

        (1) = 1

        (2) = 2

        (3) = 3

        (4) = 2

        (5) = 5

        ])
 
Question 2
> representant:=proc(E,i)
> local r;
> r:=i;
> while E[r]<>r do 
>             r:=E[r] 
>             od;
> return r;
> end:
> E:=array(0..6,[0,1,1,6,5,5,2]):
> representant(E,0);

                                  0
 
Question 3
> sontAmis:=proc(E,i,j)
> local r,s;
> s:=representant(E,j);
> r:=representant(E,i);
> if r=s then return true 
>        else return false 
> fi;
> end:

> sontAmis(E,0,4);sontAmis(E,3,1);

                                false
 

                                 true
 
Question 4
> ajout:=proc(E,i,j)
> local F,r,s;
> F:=E;
> if sontAmis(E,i,j)=false then r:=representant(E,i);
>                               s:=representant(E,j);
>                               F[r]:=s;
> fi;
> return F;
> end:

> print(ajout(E,3,4));

  array(0 .. 6, [

        (0) = 0

        (1) = 5

        (2) = 1

        (3) = 6

        (4) = 5

        (5) = 5

        (6) = 2

        ])
 
Question 6
> couleurNO:=proc(T,i,j)
> if i*j=0 then return 0 
>          else return T[i-1,j-1] 
> fi;
> end:
> couleurN:=proc(T,i,j)
> if i=0 then return 0 
>        else return T[i-1,j] 
> fi;
> end:
> couleurO:=proc(T,i,j)
> if j=0 then return 0 
>        else return T[i,j-1] 
> fi;
> end:
> R:=6:T:=array(0..R-1,0..R-1,[[0,1,1,0,1,0],[0,1,1,0,1,0],[1,0,0,0,1,0],[1,0,0,0,1,0],[1,0,0,0,1,1],[1,1,1,1,1,0]]):
> couleurN(T,0,3);couleurN(T,2,2);

                                  0
 

                                  1
 

Question 7
> C:=7:E:=array(0..C,[seq(i,i=0..C)]):
> marquage:=proc(T)
> local S,i,j,cno,cn,co;
> global nc;
> nc:=0;
> S:=T;
> for i from 0 to R-1 do
>                    for j from 0 to R-1 do 
>                                        if T[i,j]=0 then S[i,j]:=0
>                                                   else cno:=couleurNO(T,i,j);
>                                                cn:=couleurN(T,i,j);
>                                              co:=couleurO(T,i,j);
>                                                   if cno<>0 then S[i,j]:=cno
>                                                           elif co<>0 and cn=0 then S[i,j]:=co
>                                                           elif cn<>0 and co=0 then S[i,j]:=cn
>                                                           elif cn=0 and co=0 then nc:=nc+1;S[i,j]:=nc
>                                                           elif cn=co and cn<>0 then S[i,j]:=cn
>                                                           elif cn<>co and cn<>0 and co<>0 then S[i,j]:=cn;
>                                                                                    ajout(E,cn,co)
>                                                           else 
>                                              fi;
>                                        fi;
>                 od;
> od;
> return S;
> end:
> 
> print(marquage(T));

  array(0 .. 5, 0 .. 5, [

        (0, 0) = 0

        (0, 1) = 1

        (0, 2) = 1

        (0, 3) = 0

        (0, 4) = 2

        (0, 5) = 0

        (1, 0) = 0

        (1, 1) = 1

        (1, 2) = 1

        (1, 3) = 0

        (1, 4) = 2

        (1, 5) = 0

        (2, 0) = 3

        (2, 1) = 0

        (2, 2) = 0

        (2, 3) = 0

        (2, 4) = 2

        (2, 5) = 0

        (3, 0) = 3

        (3, 1) = 0

        (3, 2) = 0

        (3, 3) = 0

        (3, 4) = 2

        (3, 5) = 0

        (4, 0) = 3

        (4, 1) = 0

        (4, 2) = 0

        (4, 3) = 0

        (4, 4) = 2

        (4, 5) = 2

        (5, 0) = 3

        (5, 1) = 3

        (5, 2) = 3

        (5, 3) = 3

        (5, 4) = 2

        (5, 5) = 0

        ])
 

Question 8
> diffusion :=proc(T)
> local S,i,j;
> S:=T;
> for i from 0 to R-1 do
>                     for j from 0 to R-1 do
>                                         S[i,j]:=representant(E,T[i,j]) 
>                     od;
> od;
> return S;
> end:
> colorier:=proc(T)
> global C;
> local E;
> E:=array(0..C,[seq(i,i=0..C)]);
> marquage(T);
> diffusion(T);
> end:
> print(colorier(T));

  array(0 .. 5, 0 .. 5, [

        (0, 0) = 0

        (0, 1) = 1

        (0, 2) = 1

        (0, 3) = 0

        (0, 4) = 3

        (0, 5) = 0

        (1, 0) = 0

        (1, 1) = 1

        (1, 2) = 1

        (1, 3) = 0

        (1, 4) = 3

        (1, 5) = 0

        (2, 0) = 3

        (2, 1) = 0

        (2, 2) = 0

        (2, 3) = 0

        (2, 4) = 3

        (2, 5) = 0

        (3, 0) = 3

        (3, 1) = 0

        (3, 2) = 0

        (3, 3) = 0

        (3, 4) = 3

        (3, 5) = 0

        (4, 0) = 3

        (4, 1) = 0

        (4, 2) = 0

        (4, 3) = 0

        (4, 4) = 3

        (4, 5) = 3

        (5, 0) = 3

        (5, 1) = 3

        (5, 2) = 3

        (5, 3) = 3

        (5, 4) = 3

        (5, 5) = 0

        ])