DM2 Lab2

m = Input["Vnesi redici m="]
n = Input["Vnesi redici n="]
A = Table[Input["A[[i,j]]="], {i, m}, {j, n}];
B = Table[Input["B[[i,j]]="], {i, m}, {j, n}];
Print["A+B = ", MatrixForm[A + B]];

Print["A-B = " MatrixForm[A - B]];

Bt = Transpose[B];
Print["Transponirana mat. B: ", MatrixForm[Bt]];

Print["Zbirot na elementite po dijagonala na dvete matrici e: ",
 Tr[A] + Tr[B]]



n = Input["Vnesi red na matricata (nxn) n="]
M = Table[Input["M[[i,j]]="], {i, n}, {j, n}];
M // MatrixForm
suma = 0;
For[i = 1, i <= n, i++,
 For[j = 1, j <= n, j++,
  If[Mod[M[[i, j]], 2] == 0, suma += M[[i, j]]]
  ]
 ]
Print["Zbirot na site parni elementi od matricata M e: ", suma];





n = Input["Vnesi go redot na matricata M nxn n="]
M = ConstantArray[0, {n, n}];
M // MatrixForm

poz = Round[n/2]
brDzv = 1;
For[i = 2, i <= n, i++,
 For[j = 1, j <= n, j++,
  If[j == poz, For[k = 1, k <= brDzv, k++, M[[i, j]] = "*"; j++],]
  ];
 poz--;
 brDzv += 2;
 ]
M // MatrixForm






(*4*)
(*Да се реши системот равенки со Гаусов метод:
 4x+y-z = 3,
    2x+7y+z = 19,
    x-3y+12z = 31.
*)
 (*Прво од системот ја пишуваме матрицата А*)
A = {{4, 1, -1}, {2, 7, 1}, {1, -3, 12}};
A // MatrixForm

RHS = {3, 19, 31};
RHS // MatrixForm

B = Transpose[
   Append[Transpose[A],
    RHS]];(*Се додава векторот со решенија RHS на матрицата А*)

GausovMetod[B_] := Module[{n, k, i, j, A1 = {}, RHS1 = {}},
  n = Length[B] - 1; (*n е должината на матрицата А*)


  Print["B = ", MatrixForm[B]];
  Print["Pocetok", MatrixForm[B]]; Print[" "];



(*Се генерира горнотриаголна матрица*)
For[k = 1, k <= n - 1, k++,
  For[i = k + 1, i <= n, i++,
   multiplier =
    N[B[[i, k]]/
      B[[k, k]]]; (*Функцијата N враќа нумеричка вредност на изразот*)


   For[j = k, j <= n + 1, j++,
    B[[i, j]] = B[[i, j]] - multiplier*B[[k, j]]
    ]
   ];
  (*Печатење на секој чекор*)
  Print["Cekor=", k, MatrixForm[B]]; Print[" "]
  ];
Print["Matricata B = ", MatrixForm[B]];
Print["Resenijata so RowReduce: ", MatrixForm[RowReduce[B]]];


(*---------------------*)
A1 = Take[B, {1, n}, {1, n}];
MatrixForm[A1];

RHS1 = Take[B, {1, n}, {n + 1, n + 1}];
MatrixForm[RHS1];
Print["Resenija na sistemot se: ", LinearSolve[A1, RHS1]];


Print["Proverka so Solve: ",
  Solve[{ 4*x + y - z , 2*x + 7*y + z, x - 3*y + 12*z } == {3, 19,
     31}]];
Print["Proverka so LinearSolve: ", LinearSolve[A, RHS]];









(*5*)
A = {{4, 3, 4, 2}, {1, 2, 1, 3}, {3, 2, 2, 1}, {1, 1, 2, 1}}
B = {{5, 6, 4, 3}, {3, 6, 4, 2}, {1, 6, 1, 1}, {3, 6, 4, 2}}
Print["A = ", MatrixForm[A]];
Print["B = ", MatrixForm[B]];

Apom = Take[A, -3];
Print["Apom = ", MatrixForm[Apom]];

Bpom = Take[B, 3];
Print["Bpom = ", MatrixForm[Bpom]];

If[Dimensions[Apom] == Dimensions[Bpom], Bt = Transpose[Bpom];
 Print["B transponirana = ", MatrixForm[Bt]];
 proiz = Apom.Bt;
 Print["Proizvodot na prvata i transponirana od vtorata matrica e: ",
  MatrixForm[proiz]]
 ]

(*Zamena na el. od 1vata matrica*)
pom = {};
A2 = Apom;
pom = A2[[2]];
A2[[2]] = A2[[3]];
A2[[3]] = pom;
Print["Matricata, ", MatrixForm[Apom],
  " so zameneti 2-ra i 3-ta redica: ", MatrixForm[A2]];

B2 = Bpom;
For[i = 1, i <= 3, i++,
 For[j = 1, j <= 4, j++,
  B2[[i, j]] *= 2;
  ]
 ]
Print["Matricata, ", MatrixForm[Bpom],
  " so pomnozen sekoj element so 2: ", MatrixForm[B2]];

Join[A2, B2] // MatrixForm










(*6*)
A = {};
n = Input["Vnesete red nxn, n="]

For[i = 1, i <= n, i++,
 pom = {};
 For[j = 1, j <= n, j++,
  AppendTo[pom, Input["A[i,j]="]]
  ];
 AppendTo[A, pom];
 ]
Print["A = ", MatrixForm[A]];

If[MatrixQ[A], B = MatrixPower[A, 5]; Print["Minori: ", Minors[B]],];

MatrixForm[UpperTriangularize[A]]
MatrixForm[LowerTriangularize[A]]








(*grafovi 1*)

n = 7
a = MakeGraph[Range[n], (Mod[#1, #2] == 1) &]
ShowGraph[a]
n = 10
b = MakeGraph[Range[n], (Mod[#1, #2] < 3) &]
ShowGraph[b]
n = 12
c = MakeGraph[Range[n], (Floor[#1/#2] > 5 || Floor[#1/#2] < 3) &]
ShowGraph[c]
n = 20
d = MakeGraph[Range[n], (#1^2 + #1 > #2^3 - #2) &]
ShowGraph[d]
n = 15
e = MakeGraph[
  Range[2, n + 1], (#1 - IntegerPart[Sqrt[#1]] >= Mod[#2, (#2 - 1)]) &]
ShowGraph[e]






(*2*)
<< DiscreteMath`Combinatorica`

n = Input["Vnesi N"]
m = Input["Vnesi M"]
i = Input["Vnesi I"]
j = Input["Vnesi J"]
completegraph = CompleteGraph[n]
ShowGraph[
 SetGraphOptions[
  AddVertex[
   completegraph, {i, j}], {{1, 2, VertexColor -> Blue,
    VertexStyle -> Disk[Large]}, {n, VertexColor -> Red}},
  EdgeColor -> Green]]
stargraph = Star[m]
ShowGraph[DeleteEdge[stargraph, {i, j}]]




(*3*)
<< DiscreteMath`Combinatorica`


n = Input["Vnesi N"]
m = Input["Vnesi M"]
t = Input["Vnesi T"]
loopgraph1 = MakeGraph[Range[n], (#1 == #2) &]
loopgraph2 = MakeGraph[Range[m], (#1 == #2) &]
For[i = 1, i < n, i++, loopgraph1 = AddEdge[loopgraph1, {i, i + 1}];
 loopgraph2 = DeleteVertex[loopgraph2, i];]
For[i = 0, i < m, i++, loopgraph1 = AddVertex[loopgraph1];
 loopgraph2 = DeleteEdge[loopgraph2, {i, i}];]
ShowGraph[loopgraph1]
ShowGraph[loopgraph2]
uniongraph = GraphUnion[loopgraph1, loopgraph2]
ShowGraph[uniongraph]
ShowGraph[InduceSubgraph[uniongraph, RandomSubset[Range[t]]]]







(*4*)
While[1 == 1, opcija = Input["Izberi Opcija"];
 If[opcija == 0, Break[]];
 If[opcija == 1, n = Input["vnesi n"];
  graph = CompleteGraph[n];];
 If[opcija == 2, n = Input["vnesi n"];
  graph = Star[n];];
 If[opcija == 3, graph = AddVertex[graph]];
 If[opcija == 4, index = Input["Vnesi indeks"];
  graph = DeleteVertex[graph, index]];
 If[opcija == 5, 19 teme1 = Input["Vnesi prvo teme"];
  teme2 = Input["Vnesi vtoro teme"];
  graph = AddEdge[opcija, {teme1, teme2}]];
 If[opcija == 6, teme1 = Input["Vnesi prvo teme"];
  teme2 = Input["Vnesi vtoro teme"];
  graph = DeleteEdge[graph, {teme1, teme2}]]]
ShowGraph[graph]






(*5*)
<< DiscreteMath`Combinatorica`

graf1 = MakeGraph[Range[5], (#1 == #2 || #1 < #2) &];
graf2 = MakeGraph[Range[5], (#1 == #2 || #1 > #2) &];
Isomorphism[graf1, graf2, All]
graf3 = CompleteGraph[5]
graf4 = CompleteGraph[5]
Isomorphism[graf3, graf4, All]






(*6*)
<< DiscreteMath`Combinatorica`

n = Input["Vnesi vrednost za n:"]
graf = CompleteGraph[n]
table = TableForm[ToAdjacencyMatrix[graf]]
Vertices[graf]
brojac = 0;
suma = 0;
For[i = 1, i <= n, i++, 20 brojac = 0;
 For[j = 1, j <= n, j++,
  If[table[[1, i, j]] == 1 || table[[1, j, i]] == 1, brojac++];];
 suma += brojac;]
Print[suma]
rebra = suma/2
Print[rebra]






(*7*)
<< DiscreteMath`Combinatorica`

n = 5
(*graph=MakeGraph[Range[4],(True)&]*)
graph = OrientGraph[RandomGraph[n, 0.85]]
ShowGraph[graph]
tabela = TableForm[ToAdjacencyMatrix[graph]]
izleg = 0
vleg = 0
For[i = 1, i <= n, i++,
 For[j = 1, j <= n, j++, If[tabela[[1, i, j]] == 1, izleg++];
  If[tabela[[1, j, i]] == 1, vleg++];]]
rebra = izleg
Print[rebra]