#C22.txt, April 15, 2019, Dr,Z.'s ExpMath class

Help:=proc(): print(` PSB(m,n), IP(m,n), RHM(S,B), Moves(S,B) , RG(S,B) ,`):
print(`  Cont(L,B) , AllGramesK(S,B,K), PlotPos(S) , EF(S,B) `):
print(`SmartOne(S,B), SmartGame(S,B)  , BestRand(S,B,K),  BestRandStory(S,B,K) `):
print(`RectBoard(m,n), RectBoardIP(m,n) `):
end:

PSB:=proc(m,n) local i,j:
{
seq(seq([i,j],i=m+1..m+2*n-1),j=1..m),
seq(seq([i,j],i=1..2*m+2*n-1),j=m+1..m+2*n-1),
seq(seq([i,j],i=m+1..m+2*n-1),j=m+n+1..2*m+2*n-1)}
end:

IP:=proc(m,n): PSB(m,n) minus {[m+n,m+n]}: end:

#RHM(S,B): Given a position S in a peg-solitaire with board B, all the right horizontal moves in Peg Solitaire
RHM:=proc(S,B) local mo,s:

mo:={}:

for s in S do
 if member(s+[1,0],S) and  (not member(s+[2,0],S)) and member(s+[2,0],B) then
  mo:=mo union {S minus {s,s+[1,0]} union {s+[2,0]}}:
 fi:
od:

mo:

end:



#LHM(S,B): Given a position S in a peg-solitaire with board B, all the left  horizontal moves in Peg Solitaire
LHM:=proc(S,B) local mo,s:

mo:={}:

for s in S do
 if member(s-[1,0],S) and  (not member(s-[2,0],S)) and member(s-[2,0],B) then
  mo:=mo union {S minus {s,s-[1,0]} union {s-[2,0]}}:
 fi:
od:

mo:

end:



#UVM(S,B): Given a position S in a peg-solitaire with board B, all the up vertical  moves in Peg Solitaire
UVM:=proc(S,B) local mo,s:

mo:={}:

for s in S do
 if member(s+[0,1],S) and  (not member(s+[0,2],S)) and member(s+[0,2],B) then
  mo:=mo union {S minus {s,s+[0,1]} union {s+[0,2]}}:
 fi:
od:

mo:

end:


#DVM(S,B): Given a position S in a peg-solitaire with board B, all the down vertical  moves in Peg Solitaire
DVM:=proc(S,B) local mo,s:

mo:={}:

for s in S do
 if member(s-[0,1],S) and  (not member(s-[0,2],S)) and member(s-[0,2],B) then
  mo:=mo union {S minus {s,s-[0,1]} union {s-[0,2]}}:
 fi:
od:

mo:

end:

Moves:=proc(S,B):RHM(S,B) union LHM(S,B) union UVM(S,B) union DVM(S,B): end:


#RG(S,B): a random game
RG:=proc(S,B) local L,S1,mo:
L:=[S];

S1:=S:

while Moves(S1,B)<>{} do
 mo:=Moves(S1,B):
 S1:=mo[rand(1..nops(mo))()]:
 L:=[op(L),S1]:
od:

L:

end:

Cont:=proc(L,B) local la,gu,gu1:
 la:=L[-1]:
 gu:=Moves(la,B):
 {seq([op(L),gu1],gu1 in gu)}
end:


#AllGamesK(S,B,K) of length K
AllGamesK:=proc(S,B,K) local gu,gu1:
option remember:
if K=0 then
 RETURN({[S]}):
fi:

gu:=AllGamesK(S,B,K-1):

{seq(op(Cont(gu1,B)), gu1 in gu)}:

end:

with(plots):

PlotPos:=proc(S) plot(S,style=point,axes=none): end:

#PlotGame(G): plots all the intermediate positions of the game
#pausing for s seconds
PlotGame:=proc(G) local i:

for i from 1 to nops(G) do
  PlotPos(G[i]):
  #Threads[Sleep](s):
od:

end:

#EF1(S,B): the number of moves available at position S with Peg Solitaire with board B
EF1:=proc(S,B) : nops(Moves(S,B)): end:

#SmartOne(S,B,f): the best move from S using Quentin D.'s evaluation function
#(the position with most options)
SmartOne:=proc(S,B,f) local mo,rec,cha,i:
mo:=Moves(S,B):

if mo={} then
  RETURN(S):
fi:

cha:=mo[1]:
rec:=f(cha,B):
for i from 2 to nops(mo) do
 
  if EF(mo[i],B)>rec then
    cha:=mo[i]:
     rec:=f(cha,B):
  fi:
od:
cha:
end:


#SmartGame(S,B,f)
SmartGame:=proc(S,B,f) local L,S1,S2:
S1:=S:
L:=[S1]:
S2:=SmartOne(S1,B,f):
while S1<>S2 do
L:=[op(L),S2]:
S1:=S2:
S2:=SmartOne(S1,B,f):
od:
L:
end:


#EF2(S,B,k): the best move according to QD's but looking k moves ahead
EF2:=proc(S,B,k)

end:


#BestRand(S,B,K): the best of K random game
BestRand:=proc(S,B,K) local i,rec,cha,hope:

cha:=RG(S,B):
rec:=nops(cha[-1]):

for i from 1 to K do

 hope:=RG(S,B):
 
if nops(hope[-1])< rec then
   cha:=hope:
   rec:=nops(hope[-1]):
fi:

od:
cha:

end:


#BestRandStory(S,B,K): the best of K random game
BestRandStory:=proc(S,B,K) local i,rec,cha,hope:

cha:=RG(S,B):
rec:=nops(cha[-1]):

for i from 1 to K do

 hope:=RG(S,B):
 

if nops(hope[-1])< rec then
   cha:=hope:
   rec:=nops(hope[-1]):
print(`The current record is`, rec):
print(`The current champion is`):
lprint(cha):
fi:

od:
cha:

end:


#RectBoard(m,n): a rectangular m by n Peg Solitaire Board
RectBoard:=proc(m,n) local i,j:
{seq(seq([i,j],i=1..n),j=1..m)}:
end:

#RectBoardIP(m,n): the inital position of a rectangular m by n Peg Solitaire Board
RectBoardIP:=proc(m,n) :
 RectBoard(m,n) minus {[1,1]}:
end: