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设 D 为5行5列的方阵, 其元素表示为D(I,J), 每个D(I,J)皆是0--9中的某个数字,D(1,1)=r为已知. 试求满足以下条件的全部方阵 D:
(1) D 的每行,每列,每条对角线均为一个五位素数.
(2) 由键盘输入S, 上述各素数的各位数字之和均等于S.
program lxw005; {素数矩阵}
const s:array [1..4] of integer= (1,3,7,9);
type arr2=array [0..50000] of boolean;
e5=array [1..5] of shortint;
var x: array [1..2] of ^arr2;
limit,k,k1,t,ss,tt,r,sum1:longint;
a1:array[1..1000] of e5;
d1:array[1..5] of e5;
g1,temp:e5;
procedure p2;forward;
procedure p3;forward;
procedure p4;forward;
procedure p5;forward;
procedure p6;forward;
procedure look(p, w:integer;st:e5;var tr:boolean);
{p=1:处理行,w:行号. p=2:处理列w:列号. 不处理对角线 }
label 10;
var i:integer;
j,k:shortint;
begin
tr:=false;
for i:=1 to tt do
begin
for j:=1 to 5 do if a1[i,j]<>st[j] then goto 10;
case p of
1: for k:=1 to 5 do d1[w,k]:=st[k];
2: for k:=1 to 5 do d1[k,w]:=st[k];
end;
tr:=true; exit;
10:
end;
end;
function plac(ad:longint;i:integer):integer;
var
pl2,sta:integer;
ad2:string[5];
ad3:string[1];
begin
str(ad:5,ad2); ad3:=copy(ad2,i,1);
val(ad3,pl2,sta); plac:=pl2;
end;
procedure assign_g(a1,a2,a3,a4,a5:shortint);
begin
g1[1]:=a1; g1[2]:=a2; g1[3]:=a3; g1[4]:=a4; g1[5]:=a5;
end;
procedure prim1;
{ 求 100000 以内的素数及取定和的五位素数 }
var i,j,t,t1,t2,t3,pr,ii:longint;
pl:e5;
begin{1}
limit:=50000;
for j:=1 to 2 do getmem(x[j],sizeof(x[j]^));
for i:=1 to limit do x[1]^[i]:=true;
x[2]^:=x[1]^; x[1]^[1]:=false;
for i:=1 to round(sqrt(limit)) do
if x[1]^[i] then
begin{2}
t:=i;
t2:=limit div t;
for j:=2 to t2 do x[1]^[t*j]:=false;
t3:=2*limit div t;
for j:=t2+1 to t3 do x[2]^[j*t-limit]:=false;
end;{2}
tt:=0;
for j:=1 to 2 do
begin {3}
t:=10000;
if j=2 then t:=1;
for i:=t to limit do
if x[j]^[i] then
begin
ii:=i+(j-1)*limit;
for k:=1 to 5 do pl[k]:=plac(ii,k);
if pl[1]+pl[2]+pl[3]+pl[4]+pl[5]=sum1 then
begin inc(tt); a1[tt]:=pl; end;
end;
end; {3}
writeln("tt=",tt);
for j:=1 to 2 do freemem(x[j],sizeof(x[j]^));
end;{1}
procedure p1; { 第 1 行 }
var i,j:integer;
begin{3}
d1[1,1]:=r;
for j:=1 to tt do
if (a1[j,1]=r) then
begin{5}
temp:=a1[j];
d1[1,2]:=temp[2]; d1[1,3]:=temp[3];
d1[1,4]:=temp[4]; d1[1,5]:=temp[5];
p2;
end;{5}
end;{3}
procedure p2; {第 5 列}
var i1,i2,i3,i4:integer;
tr2:boolean;
begin
for i1:=1 to 4 do
for i2:=1 to 4 do
for i3:=1 to 4 do
for i4:=1 to 4 do
if (d1[1,5]+s[i1]+s[i2]+s[i3]+s[i4])=sum1 then
begin
assign_g(d1[1,5],s[i1],s[i2],s[i3],s[i4]);
look(2,5,g1,tr2);
if tr2 then p3;
end;
end;
procedure p3; {主对角线}
var temp1,temp2:shortint;
j:integer;
begin{3}
temp1:=d1[1,1]; temp2:=d1[5,5];
for j:=1 to tt do
begin{5}
temp:=a1[j];
if (temp[1]=temp1)and(temp[5]=temp2) then
begin
d1[2,2]:=temp[2]; d1[3,3]:=temp[3]; d1[4,4]:=temp[4];
p4;
end;
end;{5}
end;{3}
procedure p4; {第 5 行 }
var i1,i2,i3,i4:integer;
tr4:boolean;
begin
for i1:=1 to 4 do
for i2:=1 to 4 do
for i3:=1 to 4 do
for i4:=1 to 4 do
if (s[i1]+s[i2]+s[i3]+s[i4]+d1[5,5])=sum1 then
begin
assign_g(s[i1],s[i2],s[i3],s[i4],d1[5,5]);
look(1,5,g1,tr4);
if tr4 then p5;
end;
end;
procedure p5; {次对角线及第 4 列,第 2 列,第 3 行}
label 50;
var temp1,temp2,temp3,t31,t32,t34,t5:shortint;
tr5,tr52,tr53:boolean;
j:integer;
begin
temp1:=d1[5,1]; temp2:=d1[3,3]; temp3:=d1[1,5];
for j:=1 to tt do
begin
temp:=a1[j];
if (temp[1]=temp1) and (temp[3]=temp2)
and (temp[5]=temp3) then
begin {p5.3}
d1[4,2]:=temp[2];
d1[2,4]:=temp[4];
t34:=sum1-(d1[1,4]+d1[2,4]+d1[4,4]+d1[5,4]);
if (t34<0)or(t34>9) then goto 50;
assign_g(d1[1,4],d1[2,4],t34,d1[4,4],d1[5,4]);
look(2,4,g1,tr5);
if tr5=false then goto 50;
t32:=sum1-(d1[1,2]+d1[2,2]+d1[4,2]+d1[5,2]);
if (t32<0)or(t32>9) then goto 50;
assign_g(d1[1,2],d1[2,2],t32,d1[4,2],d1[5,2]);
look(2,2,g1,tr52);
if tr52=false then goto 50;
t31:=sum1-(d1[3,2]+d1[3,3]+d1[3,4]+d1[3,5]);
if (t31<=0)or(t31>9) then goto 50;
assign_g(t31,d1[3,2],d1[3,3],d1[3,4],d1[3,5]);
look(1,3,g1,tr53);
if tr53 then p6;
end;{p5.3}
50:
end;
end;
procedure p6; { 第 1 列, 第 2,4 行, 第 3 列 }
label 60;
var i1,i2,i3,i4:integer;
t23,t43:shortint;
tr6:boolean;
begin
for i1:=1 to 9 do
for i2:=1 to 9 do
begin
assign_g(d1[1,1],i1,d1[3,1],i2,d1[5,1]);
look(2,1,g1,tr6);
if tr6=false then goto 60;
t23:=sum1-(d1[2,1]+d1[2,2]+d1[2,4]+d1[2,5]);
if (t23<0)or(t23>=9) then goto 60;
assign_g(d1[2,1],d1[2,2],t23,d1[2,4],d1[2,5]);
look(1,2,g1,tr6);
if tr6=false then goto 60;
t43:=sum1-(d1[4,1]+d1[4,2]+d1[4,4]+d1[4,5]);
if (t43<0)or(t43>9) then goto 60;
assign_g(d1[4,1],d1[4,2],t43,d1[4,4],d1[4,5]);
look(1,4,g1,tr6);
if tr6=false then goto 60;
if (d1[1,3]+d1[2,3]+d1[3,3]+d1[4,3]+d1[5,3])<>sum1
then goto 60;
for i3:=1 to 5 do g1[i3]:=d1[i3,3];
look(2,3,g1,tr6);
if tr6=false then goto 60;
inc(ss); writeln("No.",ss);
for i3:=1 to 5 do
begin for i4:=1 to 5 do write(d1[i3,i4]:2); writeln; end;
60:;
end;
end;
begin
write("d[1,1]="); readln(r);
write("sum of row="); readln(sum1);
ss:=0; prim1; p1;
if ss=0 then writeln("No Solution!");
end. |
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