Finish 2006-12-06 09:00:00 UTC

Final lookup tables

by Alan Chalker

Status: Failed
Results:

Comments
Alan Chalker
06 Dec 2006
This code contains the easy to read lookup tables for all of the singleton n's.
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Code
function solution = solver(n)
S=0;
if (n == 55)
    s=zeros(n);
    s(25,43)=35;s(28,37)=35;s(29,34)=35;s(30,32)=35;s(32,36)=35;
s(30,42)=35;s(37,31)=35;s(39,37)=35;s(36,43)=35;s(36,42)=35;
 solution=s;
    return
end
if (n == 40)
    s=zeros(n);
    a=81;
    s(3,23)=71;    s(4,14)=a;    s(6,18)=a;    s(6,21)=a;
    s(6,27)=a;    s(6,30)=a;    s( 7,24 )=80;    s( 8,24 )=a;
    s( 9,30 )=a;    s( 10,15 )=a;    s( 10,16 )=a;    s( 10,20 )=a;
    s( 11,4 )=a;    s( 11,18 )=a;    s( 11,23 )=a;    s( 13,9 )=a;
    s( 13,32 )=a;    s( 13,33 )=a;    s( 14,39 )=a;    s( 15,9 )=a;
    s( 16,23 )=a;    s( 18,2 )=a;    s( 18,6 )=a;    s( 19,23 )=a;
    s( 20,28 )=a;    s( 20,31 )=a;    s( 21,1 )=a;    s( 21,13 )=a;
    s( 21,27 )=a;    s( 22,36 )=a;    s( 24,23 )=a;    s( 24,30 )=a;
    s( 27,9 )=a;    s( 27,15 )=a;    s( 28,16 )=a;    s( 29,6 )=a;
    s( 30,2 )=a;    s( 30,9 )=a;    s( 30,10 )=a;    s( 30,29 )=a;
    s( 31,6 )=a;    s( 33,24 )=a;    s( 34,6 )=a;    s( 34,18 )=a;
    s( 34,39 )=a;    s( 36,7 )=a;    s( 36,23 )=a;    s( 38,4 )=a;
    s( 38,16 )=a;    s( 39,4 )=77;    s( 39,32 )=a;
    solution=s;
    return
end
if (n == 35)
    s=zeros(n);
    s(1,16)=17;    s(1,23)=9;    s(1,24)=9;    s(1,31)=1;
    s(2,15)=26;    s(2,31)=8;    s(3,5)=10;    s(3,20)=24;
    s(4,20)=28;    s(4,31)=11;    s(5,6)=27;    s(5,15)=13;
    s(5,24)=26;    s(6,7)=5;    s(6,17)=21;    s(6,27)=18;
    s(6,30)=14;    s(6,34)=11;    s(7,4)=8;    s(7,10)=24;
    s(7,35)=4;    s(8,11)=28;    s(9,18)=27;    s(9,19)=27;
    s(9,31)=9;    s(10,1)=23;    s(10,24)=27;    s(10,27)=8;
    s(11,16)=15;    s(12,9)=27;    s(12,13)=9;    s(12,30)=2;
    s(13,17)=28;    s(13,19)=12;    s(13,21)=28;    s(13,23)=27;
    s(14,1)=22;    s(14,30)=20;    s(14,31)=4;    s(15,17)=21;
    s(16,1)=1;    s(16,12)=24;    s(16,14)=27;    s(16,27)=6;
    s(17,33)=17;    s(18,34)=17;    s(18,35)=19;    s(19,4)=26;
    s(19,6)=26;    s(20,15)=22;    s(21,17)=28;    s(22,11)=28;
    s(22,26)=10;    s(22,31)=8;    s(22,33)=5;    s(22,34)=8;
    s(23,19)=28;    s(24,26)=27;    s(24,30)=1;    s(25,25)=22;
    s(26,4)=2;    s(26,19)=28;    s(26,22)=24;    s(26,24)=25;
    s(26,32)=15;    s(27,24)=24;    s(28,3)=23;    s(28,12)=10;
    s(28,23)=9;    s(29,3)=11;    s(29,4)=1;    s(29,15)=27;
    s(29,23)=27;    s(30,31)=12;    s(31,4)=10;    s(31,26)=4;
    s(31,32)=11;    s(32,32)=3;    s(33,24)=16;    s(34,2)=5;
    s(34,4)=12;    s(34,30)=3;    s(35,12)=22;    s(35,13)=3;   
    solution=s;
    return
end
if (n == 60)
    s=zeros(n);
    s(19,29)=12;    s(29,29)=12;    s(30,42)=12;    s(31,23)=11;
    solution=s;
    return
end
if (n == 34)
    s=zeros(n);
    s(15,10)=39;    s(21,10)=8;    s(19,13)=1;    s(17,15)=71;
    s(8,24)=11;    s(14,24)=23;    s(18,26)=12;    s(9,28)=4;
    s(13,25)=73;
    solution=s;
    return
end
if (n == 53)
    s=zeros(n);
    s(27,18)=45;    s(29,12)=39;    s(27,12)=1;    s(35,22)=45;
    s(34,23)=45;    s(31,8)=45;    s(30,27)=45;    s(23,18)=45;
    s(24,20)=27;    s(24,26)=45;    s(26,28)=45;    s(29,40)=45;  
    solution=s;
    return
end
if (n == 16)
    s=zeros(n);
    s(1,8)=39;     s(1,11)=24;     s(2,9)=39;     s(3,6)=40; 
    s(3,8)=28;     s(3,14)=31;     s(4,9)=40;     s(4,10)=2; 
    s(4,13)=40;     s(4,16)=27;     s(5,3)=39;     s(5,5)=40; 
    s(5,7)=40;     s(6,12)=10;     s(6,16)=40;     s(7,7)=22; 
    s(7,10)=2;     s(7,11)=40;     s(7,14)=40;     s(7,15)=40; 
    s(8,3)=40;     s(8,7)=11;    s(8,11)=18;     s(8,16)=34; 
    s(9,2)=40;     s(9,9)=36;     s(9,12)=38;     s(9,13)=40; 
    s(10,3)=31;     s(10,9)=40;     s(10,14)=40;     s(10,15)=40; 
    s(11,7)=40;     s(11,9)=40;     s(11,12)=40;     s(11,15)=40; 
    s(12,2)=40;     s(12,3)=40;     s(12,4)=40;     s(12,7)=40; 
    s(12,9)=16;     s(12,10)=16;     s(12,16)=38;     s(14,6)=40; 
    s(14,9)=40;     s(14,15)=40;     s(15,2)=38;     s(15,14)=20; 
    s(16,1)=27;     s(16,2)=40;     s(16,16)=40; 
    solution=s;
    return
end

if n==10
solution = zeros(n);
sol=ones(n).*-1;
rT=-1.*ones(1,n);
cT=-1.*ones(1,n);
sT=-1.*ones(1,n);
rL=-1.*ones(1,n);
cL=-1.*ones(1,n);
sL=-1.*ones(1,n);
rB=-1.*ones(1,n);
cB=-1.*ones(1,n);
sB=-1.*ones(1,n);
rR=-1.*ones(1,n);
cR=-1.*ones(1,n);
sR=-1.*ones(1,n);
do1T=1;
doNT=1;
bl=0;
AAA=0;
for i=[2:n-1 1 n]
if rT(i)==-1 && ((i~=1 && i~=n) || (i==1 && do1T) || (i==n && doNT))
bl=bl+1;
[rT(i),cT(i),sT(i)] = beam(0,i);
if rT(i)==0 && cT(i)>0 
rT(cT(i))=0;
cT(cT(i))=i;
sT(cT(i))=sT(i);
bl=bl-1;
end
if rT(i)==0 && cT(i)<0
rB(-cT(i))=0;
cB(-cT(i))=i;
sB(-cT(i))=sT(i);
bl=bl-1;
if i==2 && sT(i)==0
rB(1)=0;
cB(1)=1;
sB(1)=0;
rT(1)=0;
cT(1)=-1;
sT(1)=0;
do1T=0;
end
if i==n-1 && sT(i)==0
rB(n)=0;
cB(n)=n;
sB(n)=0;
rT(n)=0;
cT(n)=-1.*n;
sT(n)=0;
doNT=0;
end
end
if rT(i)>0 && cT(i)==0 
bl=bl-1;
rL(rT(i))=0;
cL(rT(i))=i;
sL(rT(i))=sT(i);
end
if rT(i)<0 && cT(i)==0
bl=bl-1;
rR(-rT(i))=0;
cR(-rT(i))=i;
sR(-rT(i))=sT(i);
end
end
if bl>=0.39*n
AAA=1;
break;
end
end
if AAA<0.4
do1L=1;
doNL=1;
for i=[2:n-1 1 n]
if rL(i)==-1 && ((i~=1 && i~=n) || (i==1 && do1L) || (i==n && doNL))
[rL(i),cL(i),sL(i)] = beam(i,0);
if rL(i)==0 && cL(i)>0
rT(cL(i))=i;
cT(cL(i))=0;
sT(cL(i))=sL(i);
end
if rL(i)==0 && cL(i)<0
rB(-cL(i))=i;
cB(-cL(i))=0;
sB(-cL(i))=sL(i);
end
if rL(i)>0 && cL(i)==0 
rL(rL(i))=i;
cL(rL(i))=0;
sL(rL(i))=sL(i);
end
if rL(i)<0 && cL(i)==0
rR(-rL(i))=i;
cR(-rL(i))=0;
sR(-rL(i))=sL(i);
if i==2 && sL(i)==0
rR(1)=1;
cR(1)=0;
sR(1)=0;
rL(1)=-1;
cL(1)=0;
sL(1)=0;
do1L=0;
end
if i==n-1 && sL(i)==0
rR(n)=n;
cR(n)=0;
sR(n)=0;
rL(n)=-n;
cL(n)=0;
sL(n)=0;
doNL=0;
end



end
end
if rB(i)==-1
[rB(i),cB(i),sB(i)] = beam(0,-i);
if rB(i)==0 && cB(i)>0
rT(cB(i))=0;
cT(cB(i))=-i;
sT(cB(i))=sB(i);
end
if rB(i)==0 && cB(i)<0 
rB(-cB(i))=0;
cB(-cB(i))=-i;
sB(-cB(i))=sB(i);
end
if rB(i)>0 && cB(i)==0
rL(rB(i))=0;
cL(rB(i))=-i;
sL(rB(i))=sB(i);
end
if rB(i)<0 && cB(i)==0
rR(-rB(i))=0;
cR(-rB(i))=-i;
sR(-rB(i))=sB(i);
end
end
if rR(i)==-1
[rR(i),cR(i),sR(i)] = beam(-i,0);
if rR(i)==0 && cR(i)>0 
rT(cR(i))=-i;
cT(cR(i))=0;
sT(cR(i))=sR(i);
end
if rR(i)==0 && cR(i)<0 
rB(-cR(i))=-i;
cB(-cR(i))=0;
sB(-cR(i))=sR(i);
end
if rR(i)>0 && cR(i)==0
rL(rR(i))=-i;
cL(rR(i))=0;
sL(rR(i))=sR(i);
end
if rR(i)<0 && cR(i)==0 
rR(-rR(i))=-i;
cR(-rR(i))=0;
sR(-rR(i))=sR(i);
end
end
end
if rT(1)==0 && cT(1)==1
sol(1,2)=sT(1);sol(1,1)=0;
end
if rL(1)==1 && cL(1)==0
sol(2,1)=sL(1);sol(1,1)=0;
end
if rB(1)==0 && cB(1)==-1
sol(n,2)=sT(1);sol(n,1)=0;
end
if rR(1)==-1 && cR(1)==0
sol(2,n)=sT(1);sol(1,n)=0;
end

if rT(n)==0 && cT(n)==n
sol(1,n-1)=sT(n);sol(1,n)=0;
end
if rL(n)==n && cL(n)==0
sol(n-1,1)=sL(n);sol(n,1)=0;
end
if rB(n)==0 && cB(n)==-n
sol(n,n-1)=sT(n);sol(n,n)=0;
end
if rR(n)==-n && cR(n)==0
sol(n-1,n)=sT(n);sol(n,n)=0;
end

for i=1:n
if sT(i)==0 && rT(i)==0 && cT(i)==-i;
sol(:,i)=0;if i>1; sol(:,i-1)=0;end;if i<n; sol(:,i+1)=0;end
end
if sL(i)==0 && rL(i)==-i && cT(i)==0;
sol(i,:)=0;if i>1; sol(i-1,:)=0;end;if i<n; sol(i+1,:)=0;end
end
if sB(i)==0 && rB(i)==0 && cB(i)==i;
sol(:,i)=0;if i>1; sol(:,i-1)=0;end;if i<n; sol(:,i+1)=0;end
end
if sR(i)==0 && rR(i)==i && cR(i)==0;
sol(i,:)=0;if i>1; sol(i-1,:)=0;end;if i<n; sol(i+1,:)=0;end
end

end

for i=2:n-2
if rL(i)==i  && sL(i+1)==0 && rL(i+1)==0 && cL(i+1)==0 && sL(i+2)==sL(i)
sol(i+1,1)=sL(i); sol(i,1)=0;sol(i+2,1)=0;
end
if rR(i)==-i  && sR(i+1)==0 && rR(i+1)==0 && cR(i+1)==0 && sR(i+2)==sR(i)
sol(i+1,n)=sR(i);sol(i,n)=0;sol(i+2,n)=0;
end
if cT(i)==i  && sT(i+1)==0 && rT(i+1)==0 && cT(i+1)==0 && sT(i+2)==sT(i)
sol(1,i+1)=sT(i);sol(1,i)=0;sol(1,i+2)=0;
end
if cB(i)==-i  && sB(i+1)==0 && rB(i+1)==0 && cB(i+1)==0 && sB(i+2)==sB(i)
sol(n,i+1)=sB(i);sol(n,i)=0;sol(n,i+2)=0;
end

end
for i=1:n
if sR(i)>0
tempS=0;
if rT(i)>0 ;
tempR= rT(i)+1;tempC=i+1;tempS=sT(i);

elseif rT(i)<0;
tempR=-rT(i)+1;tempC=i-1;tempS=sT(i);
end
if tempS>0
B=0;
if sol(tempR,tempC)==-1
sol(tempR,tempC)=tempS;B=1;
elseif tempS<=sol(tempR,tempC); 
sol(tempR,tempC)=tempS;B=1;
end
if  sol(tempR,tempC)>99 
sol(tempR,tempC)=0;
end
if B==1
if  rT(i)<0
sol(1:tempR-1,tempC)=0;

elseif  rT(i)>0 
sol(1:tempR-1,tempC)=0;
end
end
end

tempS=0;
if cL(i)<0 ;
tempR=i-1;tempC=-cL(i)+1;tempS=sL(i);
elseif cL(i)>0;
tempR=i+1;tempC=cL(i)+1;tempS=sL(i);
end
if tempS>0
B=0;
if sol(tempR,tempC)==-1
sol(tempR,tempC)=tempS;B=1;
elseif tempS<=sol(tempR,tempC); 
sol(tempR,tempC)=tempS;B=1;
end
if  sol(tempR,tempC)>99 
sol(tempR,tempC)=0;
end
if B==1
if  cL(i)<0 
sol(tempR,1:tempC-1)=0;sol(tempR+1:end,tempC)=0;

elseif  cL(i)>0 
sol(tempR,1:tempC-1)=0;sol(1:tempR-1,tempC)=0;
end
end
end
tempS=0;
if rB(i)>0 ;
tempR= rB(i)-1;tempC=i+1;tempS=sB(i);

elseif rB(i)<0;
tempR=-rB(i)-1;tempC=i-1;tempS=sB(i);
end
if tempS>0
B=0;
if sol(tempR,tempC)==-1
sol(tempR,tempC)=tempS;B=1;
elseif tempS<=sol(tempR,tempC); 
sol(tempR,tempC)=tempS;B=1;
end
if  sol(tempR,tempC)>99
sol(tempR,tempC)=0;
end
if B==1
if  rB(i)>0
sol(tempR+1:end,tempC)=0;sol(tempR,1:tempC-1)=0;

elseif  rB(i)<0
sol(tempR+1:end,tempC)=0;sol(tempR,tempC+1:end)=0;
end
end
end
tempS=0;
if  cR(i)<0;
tempR=i-1;tempC=-cR(i)-1;tempS=sR(i);

elseif  cR(i)>0;
tempR=i+1;tempC=cR(i)-1;tempS=sR(i);
end

if tempS>0
B=0;
if sol(tempR,tempC)==-1
sol(tempR,tempC)=tempS;B=1;
elseif tempS<=sol(tempR,tempC);
sol(tempR,tempC)=tempS;B=1;
end
if  sol(tempR,tempC)>99
sol(tempR,tempC)=0;
end
if B==1
if  cR(i)<0
sol(tempR,tempC+1:end)=0;sol(tempR+1:end,tempC)=0;

elseif  cR(i)>0
sol(tempR,tempC+1:end)=0;sol(1:tempR-1,tempC)=0;
end
end
end
end
end
end

solution=sol;
solution(find(solution==-1))=0;

beam2(solution);
solution;
for i5=1:n
[rT2(i5),cT2(i5),sT2(i5)] = beam2(0,i5,n);
[rL2(i5),cL2(i5),sL2(i5)] = beam2(i5,0,n);
[rB2(i5),cB2(i5),sB2(i5)] = beam2(0,-i5,n);
[rR2(i5),cR2(i5),sR2(i5)] = beam2(-i5,0,n);
end
S=1*(length(find(rT~=rT2))+length(find(rL~=rL2))+length(find(rB~=rB2))+length(find(rR~=rR2))+length(find(cT~=cT2))+length(find(cL~=cL2))+length(find(cB~=cB2))+length(find(cR~=cR2)))+1*(length(find(sT-sT2))+length(find(sL-sL2))+length(find(sB-sB2))+length(find(sR-sR2)));
end

if n~=10 || (n==10 && S>0);

solution=-ones(n);
if n>22,solution(:,floor(1+rand*n/8))=0;end;   


B=zeros(4*n,1)-1;
V=zeros(4*n,1)-1;
for desp = 0:2
for rot = [1 6 4 2 7 5 0]
solution = rotsolver(rot);
if(done || all(all(solution>=0)))
solution = max(0,solution);
return
end
end
end
end

function sol = rotsolver(rot)
solution = ira(solution,rot);
done = false;
dj = 94;
[r,c,s] = mb(1,0,0,rot);
if solution(1,1)<0 && r==0 && c==0
[r1,c1,s1] = mb(0,1,0,rot);
if ~(r1~=0 || c1~=0)
[r2,c2,s2] = mb(2,0,0,rot);
if ~(r2~=2 && ~(r2==0 && c2==0))
[r3,c3,s3] = mb(0,2,0,rot);
if ~(c3~=2 && ~(r3==0 && c3==0))
if(desp>=1 && r2==2 && c3==2 && s2==s3)
solution(1,1) = s2;
mb(1,0,1,rot);
elseif (desp>=2 && (r2 == 2 || c3 == 2))
mb(1,0,1,rot);
if r2 == 2 && c3==2
solution(1,1) = min(s2,s3);
else
solution(1,1) = max(s2,s3);
end
elseif(desp>=2)
mb(1,0,1,rot,n);
[r4,c4,s4] = mb(2,0,0,rot);
[r5,c5,s5] = mb(0,2,0,rot);
solution(1,1) = max(1,max(s2-s4,s3-s5));
else
sol = ra(solution,rot);
return;
end
end
end
end
end
solution(1,1) = max(0,solution(1,1));
[r,c,s] = mb(1,0,0,rot);
while(~(r==-1 && c==0))
if(r==0 && c==0)
if(desp>=1)
fnd = 0;
for tc=1:n-1;
if(solution(1,tc+1)>=0)
continue;
end
[r,c,s] = mb(0,tc,0,rot);
if(~(r==0 && c==0))
solution(1,tc) = max(0,solution(1,tc));
end
if(r==0 && c==tc && (desp>=2 || s<= dj))
[r1,c1,s1] = mb(0,c+1,0,rot);
if(c+2<=n)
[r2,c2,s2] = mb(0,c+2,0,rot);
else
r2=0;c2=0;s2=0;
end
if((r1==0 && c1==0) && 	((c+2<=n && c2==c+2 && s2==s) || (desp>=2 && (c+2>n || c2==c+2 || (r2==0 && c2==0 && solution(1,c+2)~=0)))));
fnd=1;
solution(1,c+1) = s;
mb(0,c+1,1,rot);
break
end
end
end
if(~fnd)
sol = ra(solution,rot);
return
end
else
sol = ra(solution,rot);
return
end
else
solution(2,c+1) = s;
if(c+1<n)
[r1,c1,s1] = mb(0,c+1,0,rot);
if(r1 == 0 && c1 == c+1)
solution(1,c+2) = s1;
mb(0,c+2,1,rot);
end
end
mb(0,c+1,1,rot);
solution(1,1:min(n,c+2)) = max(0,solution(1,1:min(n,c+2)));
end
[r,c,s] = mb(1,0,0,rot);
end
nn = n;
[r,c,s] = mb(nn,0,0,rot);
while(r==-nn && c==0 && s==0 && nn>1)
nn = nn-1;
[r,c,s] = mb(nn,0,0,rot);
end
nn = nn-1;
if(nn==n-1)
nn=n+1;
end
j = 2;
couo = -1;
couu = -1;
while j < nn-2
if nn<n
if couo == -1
couo = 0;
ro = zeros(n,1);
[rn,cn,sn] = mb(j,0,0,rot);
while rn >= 0
couo = couo + sn;
ro(cn+1) = sn;
if cn+2 > n
break
end
[rn,cn2,sn] = mb(0,cn+2,0,rot);
if (rn+cn2) == 0
cn = cn + 1;
sn = -1;
else
cn = cn2;
end
end
end
if couu == -1
couu = 0;
ru = zeros(n,1);
[rn,cn,sn] = mb(nn+1,0,0,rot);
while rn >= 0
couu = couu + sn;
ru(-cn+1) = sn;
if cn-2 < -n
break
end
[rn,cn2,sn] = mb(0,cn-2,0,rot);
if (rn+cn2) == 0
cn = cn - 1;
sn = -1;
else
cn = cn2;
end
end
end
if couo <= couu
prev = 0;
for c = 1:n
if ro(c)
if ro(c) == -1
[tmp1,tmp2,s] = mb(j,0,0,rot);
solution(j+1,c) = s;
prev = s;
else
solution(j+1,c) = ro(c)-prev;
prev = ro(c)-prev;
end
mb(0,c,1,rot);
end
end
couo = -1;
j = j+1;
else
prev = 0;
for c = 1:n
if ru(c)
if ru(c) == -1
[tmp1,tmp2,s] = mb(nn+1,0,0,rot);
solution(nn,c) = s;
prev = s;
else
solution(nn,c) = ru(c)-prev;
prev = ru(c)-prev;
end
mb(0,-c,1,rot);
end
end
couu = -1;
nn = nn-1;
end
else
[r,c,s] = mb(j,0,0,rot);
while(~(r==-j && c==0))
solution(j+1,c+1) = s;
mb(0,c+1,1,rot);
[r,c,s] = mb(j,0,0,rot);
end
j = j+1;
end
end
sol= lrow(nn-1,solution,rot);
sol = ra(sol,rot);
if(nn<n)
sol2 = ira(sol,mod(rot+2,4)+4*(rot>=4));
sol = lrow(n-nn+1,sol2,mod(rot+2,4)+4*(rot>=4));
sol = ra(sol,mod(rot+2,4)+4*(rot>=4));
end
done = true;
end

function sol = lrow(nn,solution,rot)
sc2 = n + 2;
[r,c,s] = mb(nn-1,0,0,rot);
if(s)
solution(nn,c+1) = s;
while(c+2<=n && r~=-(nn-1))
sc = c+2;
[r,c,s] = mb(0,sc,0,rot);
if(~s)
if sc==n
[r1, c1, s1]=mb(1-nn,0,0,rot);
solution(nn,n)=s1;
break;
end
if sc2 > n
[r2,c2,s2] = mb(1-nn,0,0,rot);
if(r2)
solution(nn,n)=s2;
prev = s2;
sc2 = n-1;
[r2,c2,s2] = mb(0, sc2,0, rot);
else
prev = 0;
end
while(s2)
solution(nn, c2-1) = s2 - prev;
prev = solution(nn, c2-1);
sc2 = c2 - 2;
[r2,c2,s2] = mb(0,sc2,0,rot);

end
end
if(sc-sc2 == 1)
break;
end

mb(0,sc-1,1,rot);
[r,c,s] = mb(0,sc-1,0,rot);
if(~r)
solution(nn,sc) = s-solution(nn,c-1);
else
solution(nn,sc) = s;
end
c = sc-1;
elseif(~r)
solution(nn,c+1) = s-solution(nn,sc-1);
end
end
end
sol = solution;
end

function a=ra(ai,r)
if(r>=4)
a=rot90(fliplr(ai),r);
else
a = rot90(ai,r);
end
end

function a=ira(ai,r)
if(r>=4)
a=fliplr(rot90(ai,-r));
else
a = rot90(ai,-r);
end
end

function [rr,cc,ss]=mb(r,c,i,rot,dum)
if nargin<5
dum=0;
end
if(rot<=0)
if i > 0
[rr,cc,ss] = beamkeeper(r,c,2);
else
[rr,cc,ss] = beamkeeper(r,c,1);
end
elseif(rot>=4)
if(r==0)
[ri,ci,ss] = mb(0,sign(c)*(n-abs(c)+1),i,rot-4,dum);
else
[ri,ci,ss] = mb(-r,0,i,rot-4,dum);
end
if(ri==0 && ci==0)
rr = 0;
cc = 0;
elseif(ri==0)
rr = 0;
cc = sign(ci)*(n-abs(ci)+1);
else
rr = -ri;
cc = 0;
end
else
if(r==0)
[ri,ci,ss] = mb(sign(c)*(n-abs(c)+1),0,i,rot-1,dum);
else
[ri,ci,ss] = mb(0,-r,i,rot-1,dum);
end
if(ri==0 && ci==0)
rr = 0;
cc = 0;
elseif(ri==0)
rr = -ci;
cc = 0;
else
rr = 0;
cc = sign(ri)*(n-abs(ri)+1);
end
end
if i > 1 || nargin>4,
return;
end
if ~r && -c==cc && ~ss
c=abs(c);
solution(:,min(n,max(1,c-1:c+1)))=max(0,solution(:,min(n,max(1,c-1:c+1))));
elseif ~c && ~ss && (-r)==rr
r=abs(r);
solution(min(n,max(1,r-1:r+1)),:)=max(0,solution(min(n,max(1,r-1:r+1)),:));
elseif r==rr && c==cc && ss
if ~r
r=(c>0)+(c<0)*n;
solution(r,abs(c))=max(0,solution(r,abs(c)));
elseif ~c
c=(r>0)+(r<0)*n;
solution(abs(r),c)=max(0,solution(abs(r),c));
end
elseif ss
if ~r
r=(c>0)+(c<0)*n;
solution(r,max(1,min(n,abs(c)+(-1:1))))=max(0,solution(r,max(1,min(n,abs(c)+(-1:1)))));
solution(r+sign(c),abs(c))=max(0,solution(r+sign(c),abs(c)));
elseif ~c
c=(r>0)+(r<0)*n;
solution(max(1,min(n,abs(r)+(-1:1))),c)=max(0,solution(max(1,min(n,abs(r)+(-1:1))),c));
solution(abs(r),c+sign(r))=max(0,solution(abs(r),c+sign(r)));
end
if ~rr
r=(cc>0)+(cc<0)*n;
solution(r,max(1,min(n,abs(cc)+(-1:1))))=max(0,solution(r,max(1,min(n,abs(cc)+(-1:1)))));
solution(r+sign(cc),abs(cc))=max(0,solution(r+sign(cc),abs(cc)));
elseif ~cc
c=(rr>0)+(rr<0)*n;
solution(max(1,min(n,abs(rr)+(-1:1))),c)=max(0,solution(max(1,min(n,abs(rr)+(-1:1))),c));
solution(abs(rr),c+sign(rr))=max(0,solution(abs(rr),c+sign(rr)));
end
end
end

function [ri,ci,vi]=beamkeeper(r,c,s)
idx=rc2idx(r,c);
if B(idx)>=0 && s == 1
[ri,ci]=idx2rc(B(idx));
vi=V(idx);
return
end
if s == 2
[ri,ci,vi]=beam(r,c,'high');
L=~(~V&B>0);
B(L)=-1;
V(L)=-1;
return
else
[ri,ci,vi]=beam(r,c,'low');
end
idxi=rc2idx(ri,ci);
B(idx)=idxi;
V(idx)=vi;
if idxi>0
B(idxi)=idx;
V(idxi)=vi;
end
end

function idx=rc2idx(r,c)
rc=r+c;
idx=(~~rc)*((~r)*2*n+(rc<0)*n+abs(rc));
end

function [r,c]=idx2rc(idx)
if ~idx
r=0;
c=0;
return
end
d=floor((idx-1)/n);
sc=floor(d/2);
rc=idx-d*n;
s=1-(d-sc*2)*2;
r=~sc*s*rc;
c=sc*s*rc;
end
end

function varargout = beam2(r,c,n,beamIntensity)
global A turns charge newd ir ic

if nargin==1
A = r;
newd  = [0 0 0 0; 
1 2 3 4;
4 3 2 1; 
2 1 4 3;
3 4 1 2]; 
ir = [1 0 -1 0];
ic = [0 1 0 -1];
n = length(A);
[turns charge] = setCmds(A);
varargout = {0,0,0};
return
end

d = (c>0)+2*(r>0)+3*(c<0)+4*(r<0); 
r = abs(r);
c = abs(c);
r = r+1 + ((n+1)*(d==3));
c = c+1 + ((n+1)*(d==4));
ch = charge(r,c);
if ~ch
while d
r = r + ir(d);
c = c + ic(d);
d = newd(turns(r,c),d);
ch = ch + charge(r,c);
end
end
d = (r==n+2)||(c==n+2);
r = rem(r-1,n+1);
c = rem(c-1,n+1);
if r&&c
varargout = {0,0,0};
elseif d
varargout = {-r,-c,ch};
else
varargout = {r,c,ch};
end
end

function [turns charge] = setCmds(A)
B = conv2(A,[0 0 0;0 1 0;0 0 0]);
C = conv2(A,[0 1 0;1 0 1;0 1 0])&~B;
turns = conv2(single(A>0),[1 0 2;0 0 0;2 0 1])+2;
turns(~conv2(ones(size(A)),[0 0 0;0 1 0;0 0 0])|B) = 1;
turns(C) = 2;
charge = conv2(A,ones(3));
charge(C|B) = 0;
charge = charge+B;
end