> 
1

> restart;
> Meilleur:=proc(t,N)
> local grand,i;
> grand:=t[0];
> for i from 1 to N-1 do
>          if t[i]>grand then
>                   grand:=t[i]
>          fi;
> od;
> return grand;
> end;

  Meilleur := proc(t, N)
local grand, i;
    grand := t[0];
    for i to N - 1 do
        if grand < t[i] then grand := t[i] end if
    end do;
    return grand
end proc

> t:=array(0..3,[1,4,4,3]);

  t := array(0 .. 3, [

        (0) = 1

        (1) = 4

        (2) = 4

        (3) = 3

        ])

> Meilleur(t,4);

                                  4

> DeuxMeilleursDistincts:=proc(t,N)
> local grand,i;
> grand:=array(0..1);
> grand[0]:=t[0];
> grand[1]:=0;
> for i from 1 to N-1 do
>          if t[i]>grand[0] then
>                   grand[1]:=grand[0];
>                   grand[0]:=t[i]
>          elif t[i]>grand[1] and t[i]<grand[0] then
>                   grand[1]:=t[i]
>          fi;
> od;
> return grand;
> end;

  DeuxMeilleursDistincts := proc(t, N)
local grand, i;
    grand := array(0 .. 1);
    grand[0] := t[0];
    grand[1] := 0;
    for i to N - 1 do
        if grand[0] < t[i] then
            grand[1] := grand[0]; grand[0] := t[i]
        elif grand[1] < t[i] and t[i] < grand[0] then
            grand[1] := t[i]
        end if
    end do;
    return grand
end proc

> print(DeuxMeilleursDistincts(t,4));

  array(0 .. 1, [

        (0) = 4

        (1) = 3

        ])

> 
2

> restart;
> DecomposerBase:=proc(N,k)
> local a,kclone,i;
> a:=array(0..N-1);
> kclone:=k;
> for i from 0 to N-1 do
>       a[i]:=irem(kclone,N);
>       kclone:=iquo(kclone,N)
> od;  
> return a;
> end;

  DecomposerBase := proc(N, k)
local a, kclone, i;
    a := array(0 .. N - 1);
    kclone := k;
    for i from 0 to N - 1 do
        a[i] := irem(kclone, N); kclone := iquo(kclone, N)
    end do;
    return a
end proc

> print(DecomposerBase(7,446));

  array(0 .. 6, [

        (0) = 5

        (1) = 0

        (2) = 2

        (3) = 1

        (4) = 0

        (5) = 0

        (6) = 0

        ])

> CalculerNombre:=proc(N,a)
> local k,i;
> k:=a[N-1];
> for i from 2 to N do
>          k:=k*N+a[N-i]
> od;
> return k;
> end;

  CalculerNombre := proc(N, a)
local k, i;
    k := a[N - 1];
    for i from 2 to N do k := k*N + a[N - i] end do;
    return k
end proc

> a:=DecomposerBase(7,446):CalculerNombre(7,a);

                                 446

> 
3

> restart;
> nombreOccurrences:=proc(t,N,m)
> local nbre,i;
> nbre:=0;
> for i from 0 to N-1 do
>        if t[i]=m then
>                  nbre:=nbre+1
>        fi;
> od;
> return nbre;
> end;

  nombreOccurrences := proc(t, N, m)
local nbre, i;
    nbre := 0;
    for i from 0 to N - 1 do
        if t[i] = m then nbre := nbre + 1 end if
    end do;
    return nbre
end proc

> t:=array(0..8,[1,1,2,0,1,2,1,2]):m:=1:nombreOccurrences(t,8,m);

                                  4

> positionOccurrences:=proc(t,N,m)
> local p,i,j;
> p:=array(0..N-1);
> for i from 0 to N-1 do
>        p[i]:=N
> od;
> j:=0;
> for i from 0 to N-1 do
>        if t[i]=m then
>                  p[j]:=i;
>                  j:=j+1
>        fi;
> od;
> return p;
> end;

  positionOccurrences := proc(t, N, m)
local p, i, j;
    p := array(0 .. N - 1);
    for i from 0 to N - 1 do p[i] := N end do;
    j := 0;
    for i from 0 to N - 1 do
        if t[i] = m then p[j] := i; j := j + 1 end if
    end do;
    return p
end proc

> print(positionOccurrences(t,8,m));

  array(0 .. 7, [

        (0) = 0

        (1) = 1

        (2) = 4

        (3) = 6

        (4) = 8

        (5) = 8

        (6) = 8

        (7) = 8

        ])

> nombreOccurrences_bis:=proc(t,N,m)
> local nbre,long,i;
> nbre:=0;long:=0;
> for i from 0 to N-1 do
>        if t[i]=m[long] then
>                  if long=1 then
>                            nbre:=nbre+1;
>                            long:=0
>                  else
>                            long:=long+1
>                  fi;
>        fi;
> od;
> return nbre;
> end;

  nombreOccurrences_bis := proc(t, N, m)
local nbre, long, i;
    nbre := 0;
    long := 0;
    for i from 0 to N - 1 do
        if t[i] = m[long] then
            if long = 1 then nbre := nbre + 1; long := 0
            else long := long + 1
            end if
        end if
    end do;
    return nbre
end proc

> mbis:=array(0..1,[1,2]);nombreOccurrences_bis(t,8,mbis);

  mbis := array(0 .. 1, [

        (0) = 1

        (1) = 2

        ])


                                  3

> positionOccurrences_bis:=proc(t,N,m)
> local p,long,i,j;
> p:=array(0..N-1);
> for i from 0 to N-1 do
>        p[i]:=N
> od;
> j:=0;
> long:=0;
> for i from 0 to N-1 do
>        if t[i]=m[long] then
>                  if long=1 then
>                            p[j]:=i-1;
>                            j:=j+1;
>                            long:=0
>                  else
>                            long:=long+1
>                  fi;
>        fi;
> od;
> return p;
> end;

  positionOccurrences_bis := proc(t, N, m)
local p, long, i, j;
    p := array(0 .. N - 1);
    for i from 0 to N - 1 do p[i] := N end do;
    j := 0;
    long := 0;
    for i from 0 to N - 1 do
        if t[i] = m[long] then
            if long = 1 then
                p[j] := i - 1; j := j + 1; long := 0
            else long := long + 1
            end if
        end if
    end do;
    return p
end proc

> print(positionOccurrences_bis(t,8,mbis));

  array(0 .. 7, [

        (0) = 1

        (1) = 4

        (2) = 6

        (3) = 8

        (4) = 8

        (5) = 8

        (6) = 8

        (7) = 8

        ])

> 
4

> restart;
> Scinder:=proc(u,p)
> local ts,i;
> ts:=array(0..1);
> ts[0]:=array(0..2^(p-1)-1);
> ts[1]:=array(0..2^(p-1)-1);
> for i from 0 to 2^(p-1)-1 do
>       ts[0][i]:=u[i];
>       ts[1][i]:=u[i+2^(p-1)]
> od;
> return ts;
> end;

  Scinder := proc(u, p)
local ts, i;
    ts := array(0 .. 1);
    ts[0] := array(0 .. 2^(p - 1) - 1);
    ts[1] := array(0 .. 2^(p - 1) - 1);
    for i from 0 to 2^(p - 1) - 1 do
        ts[0][i] := u[i]; ts[1][i] := u[i + 2^(p - 1)]
    end do;
    return ts
end proc

> u:=array(0..7,[25,4,0,12,9,4,8,0]):print(Scinder(u,3));

  array(0 .. 1, [

        (0) = array(0 .. 3, [

        (0) = 25

        (1) = 4

        (2) = 0

        (3) = 12

        ])

        (1) = array(0 .. 3, [

        (0) = 9

        (1) = 4

        (2) = 8

        (3) = 0

        ])

        ])

> Fusionner:=proc(t,s,p)
> local u,it,is,iu,j;
> u:=array(0..2^(p+1)-1);
> it:=0;
> is:=0;
> iu:=0;
> while it<2^p and is<2^p do
>         if t[it]<s[is] then
>                    u[iu]:=t[it];
>                    it:=it+1
>         else
>                    u[iu]:=s[is];
>                    is:=is+1
>         fi;
>         iu:=iu+1;
> od;
> if it=2^p and iu<2^(p+1) then
>         for j from iu to 2^(p+1)-1 do
>                    u[j]:=s[is+j-iu]
>         od;
> elif is=2^p and iu<2^(p+1) then
>         for j from iu to 2^(p+1)-1 do
>                    u[j]:=t[it+j-iu]
>         od;
> fi;        
> return u;
> end;

  Fusionner := proc(t, s, p)
local u, it, is, iu, j;
    u := array(0 .. 2^(p + 1) - 1);
    it := 0;
    is := 0;
    iu := 0;
    while it < 2^p and is < 2^p do
        if t[it] < s[is] then u[iu] := t[it]; it := it + 1
        else u[iu] := s[is]; is := is + 1
        end if;
        iu := iu + 1
    end do;
    if it = 2^p and iu < 2^(p + 1) then for j from iu to
        2^(p + 1) - 1 do u[j] := s[is + j - iu]
        end do
    elif is = 2^p and iu < 2^(p + 1) then for j from iu to
        2^(p + 1) - 1 do u[j] := t[it + j - iu]
        end do
    end if;
    return u
end proc

> a:=array(0..3,[2,4,4,9]);b:=array(0..3,[1,1,4,10]);
> print(Fusionner(a,b,2));

  a := array(0 .. 3, [

        (0) = 2

        (1) = 4

        (2) = 4

        (3) = 9

        ])


  b := array(0 .. 3, [

        (0) = 1

        (1) = 1

        (2) = 4

        (3) = 10

        ])


  array(0 .. 7, [

        (0) = 1

        (1) = 1

        (2) = 2

        (3) = 4

        (4) = 4

        (5) = 4

        (6) = 9

        (7) = 10

        ])

> triFusion:=proc(t,p)
> local tscinde,a,b;
> if p=0 then
>       return t
> else
>       tscinde:=Scinder(t,p);
>       a:=triFusion(tscinde[0],p-1);
>       b:=triFusion(tscinde[1],p-1);
>       return Fusionner(a,b,p-1)
> fi;
> end;

  triFusion := proc(t, p)
local tscinde, a, b;
    if p = 0 then return t
    else
        tscinde := Scinder(t, p);
        a := triFusion(tscinde[0], p - 1);
        b := triFusion(tscinde[1], p - 1);
        return Fusionner(a, b, p - 1)
    end if
end proc

> print(triFusion(u,3));

  array(0 .. 7, [

        (0) = 0

        (1) = 0

        (2) = 4

        (3) = 4

        (4) = 8

        (5) = 9

        (6) = 12

        (7) = 25

        ])

>