MathematicaV97

			(*>>> Лабораториски вежби ДМ2 - Комбинаторика  <<<*) (*Martin \
Tashkoski*)

(*Zadaca 1*)
Faktoriel[n_] :=
  Module[{n0 = n, fakt = 1, i}, For[i = 1, i <= n0, i++, fakt *= i];
   Return[fakt]];
Print["n!=", Faktoriel[5]];
Print["Proverka: ", 5!];

n!=120

Proverka: 120




(*Zadaca 2*)
BinomenKoeficient[n_, m_] :=
  Module[{rez, n0 = n, m0 = m},
   rez = Faktoriel[n0]/(Faktoriel[m0]*(Faktoriel[n0 - m0])); rez];
Print["(\*GridBox[{
{n},
{m}
}]) = ", BinomenKoeficient[5, 3]];
Print["Proverka: ", Binomial[5, 3]];

(n
m

) = 10

Proverka: 10




(*Zadaca 3*)
PaskalovTriagolnik[n_] :=
  Module[{i, j, A = {}, B = {}},
   For[i = 0, i < n, i++, B = {};
    For[j = 0, j <= i, j++, AppendTo[B, BinomenKoeficient[i, j]]];
    AppendTo[A, B]; Print[B]]];
PaskalovTriagolnik[5];

{1}

{1,1}

{1,2,1}

{1,3,3,1}

{1,4,6,4,1}




(*Zadaca 4*)
BrPermutaciiBezPov[n_, k_] := Module[{br = 1}, br = n!/(n - k)!; br];
Print["Brojot na permutacii BEZ povtoruvanje od n elementi i klasa k \
e: ", BrPermutaciiBezPov[5, 2]];

Brojot na permutacii BEZ povtoruvanje od n elementi i klasa k e: 20




(*Zadaca 5*)
PermutaciiBezPov[n_, k_] :=
  Module[{Permutacii = {}, Pom = {}, i},
   For[i = 1, i <= n, i++, AppendTo[Pom, i]];
   AppendTo[Permutacii, Permutations[Pom, {k}]]; Permutacii];
Print["Site mozni permutacii BEZ povtoruvanje od n elementi, klasa k: \
", PermutaciiBezPov[5, 2]];

Site mozni permutacii BEZ povtoruvanje od n elementi, klasa k: {{{1,2},{1,3},{1,4},{1,5},{2,1},{2,3},{2,4},{2,5},{3,1},{3,2},{3,4},{3,5},{4,1},{4,2},{4,3},{4,5},{5,1},{5,2},{5,3},{5,4}}}




(*Zadaca 6*)
BrKombinaciiBezPov[n_, k_] :=
  Module[{br = 0}, br = Binomial[n, k]; br];
Print["Brojot na kombinacii BEZ povtoruvanje e: ",
  BrKombinaciiBezPov[4, 2]];

Brojot na kombinacii BEZ povtoruvanje e: 6




(*Zadaca 7*)
KombinaciiBezPov[n_, k_] :=
  Module[{Kombinacii = {}, Pom = {}, i},
   For[i = 1, i <= n, i++, AppendTo[Pom, i]];
   AppendTo[Kombinacii, Subsets[Pom, {k}]]; Kombinacii];
Print["Site mozni kombinacii BEZ povtoruvanje od n elementi, klasa k: \
", KombinaciiBezPov[4, 2]];

Site mozni kombinacii BEZ povtoruvanje od n elementi, klasa k: {{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}}




(*Zadaca 8*)
BrPermutaciiSoPov[n_, k_] := Module[{br}, br = n^k; br];
Print["Brojot na permutacii SO povtoruvanje od n elementi i klasa k \
e: ", BrPermutaciiSoPov[3, 2]];

Brojot na permutacii SO povtoruvanje od n elementi i klasa k e: 9




(*Zadaca 9*)
PermutaciiSoPov[n_, k_] :=
  Module[{Permutacii = {}, Pom = {}, i},
   For[i = 1, i <= n, i++, AppendTo[Pom, i]];
   AppendTo[Permutacii, Tuples[Pom, k]]; Permutacii];
Print["Site mozni permutacii SO povtoruvanje od n elementi, klasa k: \
", PermutaciiSoPov[3, 2]];

Site mozni permutacii SO povtoruvanje od n elementi, klasa k: {{{1,1},{1,2},{1,3},{2,1},{2,2},{2,3},{3,1},{3,2},{3,3}}}




(*Zadaca 10*)
BrKombinaciiSoPov[n_, k_] :=
  Module[{br = 0}, br = Binomial[n + k - 1, k]; br];
Print["Brojot na kombinacii SO povtoruvanje e: ",
  BrKombinaciiSoPov[3, 4]];

Brojot na kombinacii SO povtoruvanje e: 15




(*Zadaca 11*)
KombinaciiSoPov[n_, k_] :=
  Module[{Kombinacii = {}, Pom = {}, i},
   For[i = 1, i <= n, i++, AppendTo[Pom, i]];
   AppendTo[Kombinacii, Select[Tuples[Pom, {k}], OrderedQ]];
   Kombinacii];
Print["Site mozni kombinacii SO povtoruvanje od n elementi, klasa k: \
", KombinaciiSoPov[3, 4]];

Site mozni kombinacii SO povtoruvanje od n elementi, klasa k: {{{1,1,1,1},{1,1,1,2},{1,1,1,3},{1,1,2,2},{1,1,2,3},{1,1,3,3},{1,2,2,2},{1,2,2,3},{1,2,3,3},{1,3,3,3},{2,2,2,2},{2,2,2,3},{2,2,3,3},{2,3,3,3},{3,3,3,3}}}


(*---------------------------------*)


(*Zadaca 12*)
BrPermutaciiBezPov2[n_, m_] :=
  Module[{br, i, k},
   For[i = 1, i <= m, i++, k = i; br = n!/(n - k)!; Print[br]]];
BrPermutaciiBezPov2[5, 4];

5

20

60

120




(*Zadaca 13*)
BrKombinaciiBezPov2[n_, m_] :=
  Module[{br, i, k},
   For[i = 1, i <= m, i++, k = i; br = Binomial[n, k]; Print[br]]];
BrKombinaciiBezPov2[4, 3];

4

6

4




(*Zadaca 14*)
BrPermutaciiSoPov2[n_, m_] :=
  Module[{br, i, k},
   For[i = 1, i <= m, i++, k = i; br = n^k; Print[br]]];
BrPermutaciiSoPov2[4, 3];

4

16

64




(*Zadaca 15*)
BrKombinaciiSoPov2[n_, m_] :=
  Module[{br, i, k},
   For[i = 1, i <= m, i++, k = i; br = Binomial[n + k - 1, k];
    Print[br]]];
BrKombinaciiSoPov2[3, 4];

3

6

10

15


(*---------------------------------*)


(*Zadaca 16 & Zadaca 17*)
A = {a, b, c};
B = {1, 2, 3, 4};
SiteMozniPermutacii[mnoz_, k_] :=
  Module[{pom = {}, i, j, p},
   For[i = 1, i <= Length[mnoz], i++,
    For[j = 1, j <= k, j++, AppendTo[pom, mnoz[[i]]]]];
   p = Permutations[pom];
   Print["Brojot na site mozni permutacii nad mnozestvoto ", pom,
    " e: ", Length[p]];
   Print["Site mozni permutacii nad mnozestvoto ", pom, " se:", p]];
SiteMozniPermutacii[A, 2];
Print[];
SiteMozniPermutacii[B, 1];

Brojot na site mozni permutacii nad mnozestvoto {a,a,b,b,c,c} e: 90

Site mozni permutacii nad mnozestvoto {a,a,b,b,c,c} se:{{a,a,b,b,c,c},{a,a,b,c,b,c},{a,a,b,c,c,b},{a,a,c,b,b,c},{a,a,c,b,c,b},{a,a,c,c,b,b},{a,b,a,b,c,c},{a,b,a,c,b,c},{a,b,a,c,c,b},{a,b,b,a,c,c},{a,b,b,c,a,c},{a,b,b,c,c,a},{a,b,c,a,b,c},{a,b,c,a,c,b},{a,b,c,b,a,c},{a,b,c,b,c,a},{a,b,c,c,a,b},{a,b,c,c,b,a},{a,c,a,b,b,c},{a,c,a,b,c,b},{a,c,a,c,b,b},{a,c,b,a,b,c},{a,c,b,a,c,b},{a,c,b,b,a,c},{a,c,b,b,c,a},{a,c,b,c,a,b},{a,c,b,c,b,a},{a,c,c,a,b,b},{a,c,c,b,a,b},{a,c,c,b,b,a},{b,a,a,b,c,c},{b,a,a,c,b,c},{b,a,a,c,c,b},{b,a,b,a,c,c},{b,a,b,c,a,c},{b,a,b,c,c,a},{b,a,c,a,b,c},{b,a,c,a,c,b},{b,a,c,b,a,c},{b,a,c,b,c,a},{b,a,c,c,a,b},{b,a,c,c,b,a},{b,b,a,a,c,c},{b,b,a,c,a,c},{b,b,a,c,c,a},{b,b,c,a,a,c},{b,b,c,a,c,a},{b,b,c,c,a,a},{b,c,a,a,b,c},{b,c,a,a,c,b},{b,c,a,b,a,c},{b,c,a,b,c,a},{b,c,a,c,a,b},{b,c,a,c,b,a},{b,c,b,a,a,c},{b,c,b,a,c,a},{b,c,b,c,a,a},{b,c,c,a,a,b},{b,c,c,a,b,a},{b,c,c,b,a,a},{c,a,a,b,b,c},{c,a,a,b,c,b},{c,a,a,c,b,b},{c,a,b,a,b,c},{c,a,b,a,c,b},{c,a,b,b,a,c},{c,a,b,b,c,a},{c,a,b,c,a,b},{c,a,b,c,b,a},{c,a,c,a,b,b},{c,a,c,b,a,b},{c,a,c,b,b,a},{c,b,a,a,b,c},{c,b,a,a,c,b},{c,b,a,b,a,c},{c,b,a,b,c,a},{c,b,a,c,a,b},{c,b,a,c,b,a},{c,b,b,a,a,c},{c,b,b,a,c,a},{c,b,b,c,a,a},{c,b,c,a,a,b},{c,b,c,a,b,a},{c,b,c,b,a,a},{c,c,a,a,b,b},{c,c,a,b,a,b},{c,c,a,b,b,a},{c,c,b,a,a,b},{c,c,b,a,b,a},{c,c,b,b,a,a}}



Brojot na site mozni permutacii nad mnozestvoto {1,2,3,4} e: 24

Site mozni permutacii nad mnozestvoto {1,2,3,4} se:{{1,2,3,4},{1,2,4,3},{1,3,2,4},{1,3,4,2},{1,4,2,3},{1,4,3,2},{2,1,3,4},{2,1,4,3},{2,3,1,4},{2,3,4,1},{2,4,1,3},{2,4,3,1},{3,1,2,4},{3,1,4,2},{3,2,1,4},{3,2,4,1},{3,4,1,2},{3,4,2,1},{4,1,2,3},{4,1,3,2},{4,2,1,3},{4,2,3,1},{4,3,1,2},{4,3,2,1}}