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# Name:Treasa Bency Biju Jose
# Date: 10-22-2020
# Assignment #14
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1. 
CountRuns := proc(L, k) local i, m, t; 
t := 0; 
m := nops(L) - k + 1; 
for i to m do 
  if L[i] = L[i + k - 1] then 
    t := t + 1; 
  end if; 
end do; 
t; 
end proc;

CountRuns([1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2], 3);
                               4
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2. 
AvePathRuns := proc(m, n, k, N) local i, t, avg, L, var, j, s;
t := 0; 
L := []; 
for i to N do 
  t := CountRuns(RPath(m, n), k); 
  L := [op(L), t]; 
end do; 
avg := evalf(add(L)/N); 
s := add(seq((L[i] - avg)^2, i = 1 .. nops(L))); 
var := evalf(sqrt(s/N)); 
avg, var; 
end proc;

seq([AvePathRuns(200, 200, 5, 3000)], i = 1 .. 10);
[197.4600000, 9.834619125], [197.2693333, 9.902834022],
                  
  [197.6666667, 9.933422465], [197.4583333, 9.874559685],

  [197.3006667, 9.977955674], [197.5610000, 9.887884743],

   [197.3633333, 1[04506419], [197.6166667, 9.886845557],

    [197.7953333, 9.721185754], [197.6186667, 9.985017516]
                 

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3.
AveGPathRuns := proc(m, n, k, N) local i, t, avg, L, var, j, s; 
t := 0; 
L := []; 
for i to N do 
  t := CountRuns(RGPath(m, n), k); 
  L := [op(L), t]; 
end do; 
avg := evalf(add(L)/N); 
s := add(seq((L[i] - avg)^2, i = 1 .. nops(L))); 
var := evalf(sqrt(s/N)); 
avg, var; 
end proc;

seq([AveGPathRuns(200, 200, 5, 3000)], i = 1 .. 10);
[197.7820000, 9.870923231], [198.1173333, 9.897418815], [198.3470000, 

  10.05335360], [198.1630000, 9.902850717], [197.9370000, 

  9.762464752], [[198.4343333, 9.882223790], [198.2893333, 

  10.14253140], [197.9983333, 9.937823202], [198.1573333, 

  9.904641417], [198.0300000, 9.950365153]

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4. 
CountMaximalRuns := proc(L, k) local i, m, t; t := 0; 
m := nops(L) - k + 1; 
for i to m do 
 if L[i] = L[i + k - 1] and L[i] <> 1 and i + k <= m then 
  if L[i - 1] <> L[i] and L[i + k] <> L[i] then 
   t := t + 1; 
  end if; 
 end if; 
end do; 
t; 
end proc;


AvePathMaximalRuns := proc(m, n, k, N) local i, t, avg, L, var, j, s; 
t := 0; 
L := []; 
for i to N do 
 t := CountMaximalRuns(RPath(m, n), k); 
 L := [op(L), t]; 
end do; 
avg := evalf(add(L)/N); 
s := add(seq((L[i] - avg)^2, i = 1 .. nops(L))); 
var := evalf(sqrt(s/N)); 
avg, var; 
end proc;


AveGPathMaximalRuns := proc(m, n, k, N) local i, t, avg, L, var, j, s; 
t := 0; 
L := []; 
for i to N do 
 t := CountMaximalRuns(RGPath(m, n), k); 
 L := [op(L), t]; 
end do; 
avg := evalf(add(L)/N); 
s := add(seq((L[i] - avg)^2, i = 1 .. nops(L))); 
var := evalf(sqrt(s/N)); 
avg, var; 
end proc;

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5. 
GoodBrother := proc(L) local s, i, p, n, q; 
p := 0; q := 0; 
s := add(seq(L[i]), i = 1 .. nops(L)); 
if type(nops(L), odd) and s = 1 then 
 n := 1/2*nops(L) - 1/2; 
 for i to nops(L) do 
  if L[i] = 1 then 
   p := p + 1; 
  elif L[i] = -1 then 
   q := q + 1; 
  else 
   0; 
  end if; 
 end do; 
 if 2*n + 1 = p + q then 
  CycShi(L)[nops(L) - 1]; 
 end if; 
end if; 
end proc;

GoodBrother([1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1]);
             [1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1]

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