Ramsey's theorem: Difference between revisions
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{{trans|Python}} |
{{trans|Python}} |
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<lang 11l>V a = |
<lang 11l>V a = [[‘0’] * 17] * 17 |
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V idx = [0] * 4 |
V idx = [0] * 4 |
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Revision as of 23:53, 18 February 2021
- Task
Find a graph with 17 Nodes such that any 4 Nodes are neither totally connected nor totally unconnected, so demonstrating Ramsey's theorem.
A specially-nominated solution may be used, but if so it must be checked to see if if there are any sub-graphs that are totally connected or totally unconnected.
11l
<lang 11l>V a = [[‘0’] * 17] * 17 V idx = [0] * 4
F find_group(mark, min_n, max_n, depth = 1)
I depth == 4
V prefix = I mark == ‘1’ {‘’} E ‘un’
print(‘Fail, found totally #.connected group:’.format(prefix))
L(i) 4
print(:idx[i])
R 1B
L(i) min_n .< max_n
V n = 0
L n < depth
I :a[:idx[n]][i] != mark
L.break
n++
I n == depth
:idx[n] = i
I find_group(mark, 1, max_n, depth + 1)
R 1B
R 0B
L(i) 17
a[i][i] = ‘-’
L(k) 4
L(i) 17
V j = (i + pow(2, k)) % 17
a[i][j] = a[j][i] = ‘1’
L(row) a
print(row.join(‘ ’))
L(i) 17
idx[0] = i
I find_group(‘1’, i + 1, 17) | find_group(‘0’, i + 1, 17)
print(‘no good’)
L.break
L.was_no_break
print(‘all good’)</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - all good
360 Assembly
<lang 360asm>* Ramsey's theorem 19/03/2017 RAMSEY CSECT
USING RAMSEY,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LA R6,1 i=1
DO WHILE=(C,R6,LE,NN) do i=1 to nn
LR R1,R6 i
MH R1,=AL2(N) *n
LR R0,R6 i
AR R1,R0 i*i+i
SLA R1,1 *2
LA R0,2 2
STH R0,A-36(R1) a(i,i)=2
LA R6,1(R6) i++
ENDDO , enddo i
LA R6,1 i=1
DO WHILE=(C,R6,LE,=F'8') do while i<=8
LA R7,1 j=1
DO WHILE=(C,R7,LE,NN) do j=1 to nn
LR R8,R7 j
AR R8,R6 +i
BCTR R8,0 -1
SRDA R8,32 ~
D R8,NN /nn
LA R8,1(R8) k=((j+i-1) mod nn)+1
LR R1,R7 j
MH R1,=AL2(N) *n
LR R0,R8 k
AR R1,R0 j*n+ki
SLA R1,1 *2
LA R0,1 1
STH R0,A-36(R1) a(j,k)=1
LR R1,R8 k
MH R1,=AL2(N) *n
LR R0,R7 j
AR R1,R0 k*n+j
SLA R1,1 *2
LA R0,1 1
STH R0,A-36(R1) a(k,j)=1
LA R7,1(R7) j++
ENDDO , enddo j
AR R6,R6 i=i+i
ENDDO , enddo i
LA R6,1 i=1
DO WHILE=(C,R6,LE,NN) do i=1 to nn
LA R7,1 j=1
LA R10,PG pgi=0
DO WHILE=(C,R7,LE,NN) do j=1 to nn
LR R1,R6 i
MH R1,=AL2(N) *n
LR R0,R7 j
AR R1,R0 i*n+j
SLA R1,1 *2
LH R4,A-36(R1) a(i,j)
IF CH,R4,EQ,=H'2' THEN if a(i,j)=2 then
MVC 0(2,R10),=C' -' output '-'
ELSE , else
XDECO R4,XDEC edit a(i,j)
MVC 0(2,R10),XDEC+10 output a(i,j)
ENDIF , endif
LA R10,2(R10) pgi+=2
LA R7,1(R7) j++
ENDDO , enddo j
XPRNT PG,L'PG print buffer
LA R6,1(R6) i++
ENDDO , enddo i
LA R6,1 i=1
DO WHILE=(C,R6,LE,NN) do i=1 to nn
SR R0,R0 0
STH R0,BH bh=0
STH R0,BV bv=0
LA R7,1 j=1
DO WHILE=(C,R7,LE,NN) do j=1 to nn
LR R1,R6 i
MH R1,=AL2(N) *n
LR R0,R7 j
AR R1,R0 i*n+j
SLA R1,1 *2
LH R2,A-36(R1) a(i,j)
IF CH,R2,EQ,=H'1' THEN if a(i,j)=1 then
LH R2,BH bh
LA R2,1(R2) +1
STH R2,BH bh=bh+1
ENDIF , endif
LR R1,R7 j
MH R1,=AL2(N) *n
LR R0,R6 i
AR R1,R0 j*n+i
SLA R1,1 *2
LH R2,A-36(R1) a(j,i)
IF CH,R2,EQ,=H'1' THEN if a(j,i)=1 then
LH R2,BV bv
LA R2,1(R2) +1
STH R2,BV bv=bv+1
ENDIF , endif
LA R7,1(R7) j++
ENDDO , enddo j
L R2,NN nn
SRA R2,1 /2
MVI XX,X'01' xx=true
IF CH,R2,NE,BH THEN if bh<>nn/2 then
MVI XX,X'00' xx=false
ENDIF , endif
NC OKH,XX okh=okh and (bh=nn/2)
L R2,NN nn
SRA R2,1 /2
MVI XX,X'01' xx=true
IF CH,R2,NE,BV THEN if bv<>nn/2 then
MVI XX,X'00' xx=false
ENDIF , endif
NC OKV,XX okv=okv and (bv=nn/2)
LA R6,1(R6) i++
ENDDO , enddo i
MVC XX,OKH xx=okh
NC XX(1),OKV xx=okh and okv
IF CLI,XX,EQ,X'01' THEN if okh and okv then
MVC WOK,=CL4'yes' wok='yes'
ELSE , else
MVC WOK,=CL4'no' wok='no'
ENDIF , endif
MVC PG,=CL80'check=' output 'check='
MVC PG+6(L'WOK),WOK output wok
XPRNT PG,L'PG print buffer
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 return_code=0
BR R14 exit
N EQU 17 n=17 NN DC A(N) nn=n A DC (N*N)H'0' table a(n,n) halfword init 0 BH DS H count horizontal BV DS H count vertical OKH DC X'01' check horizontal OKV DC X'01' check vertical WOK DS CL4 temp ok XX DS X temp logical PG DC CL80' ' buffer XDEC DS CL12 temp xdeco
YREGS
END RAMSEY</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - check=yes
AWK
<lang AWK>
- syntax: GAWK -f RAMSEYS_THEOREM.AWK
- converted from Ring
BEGIN {
for (i=1; i<=17; i++) {
arr[i,i] = -1
}
k = 1
while (k <= 8) {
for (i=1; i<=17; i++) {
j = (i + k) % 17
if (j != 0) {
arr[i,j] = 1
arr[j,i] = 1
}
}
k = k * 2
}
for (i=1; i<=17; i++) {
for (j=1; j<=17; j++) {
printf("%s",arr[i,j]+0)
}
printf("\n")
}
exit(0)
} </lang>
- Output:
-11101000110001011 1-1110100011000101 11-111010001100010 011-11101000110001 1011-1110100011000 01011-111010001100 001011-11101000110 0001011-1110100011 10001011-111010000 110001011-11101000 0110001011-1110100 00110001011-111010 000110001011-11100 1000110001011-1110 01000110001011-110 101000110001011-10 1101000100000000-1
C
For 17 nodes, (4,4) happens to have a special solution: arrange nodes on a circle, and connect all pairs with distances 1, 2, 4, and 8. It's easier to prove it on paper and just show the result than let a computer find it (you can call it optimization).
No issue with the code or the output, there seems to be a bug with Rosettacode's tag handlers. - aamrun <lang c>#include <stdio.h>
int a[17][17], idx[4];
int find_group(int type, int min_n, int max_n, int depth) { int i, n; if (depth == 4) { printf("totally %sconnected group:", type ? "" : "un"); for (i = 0; i < 4; i++) printf(" %d", idx[i]); putchar('\n'); return 1; }
for (i = min_n; i < max_n; i++) { for (n = 0; n < depth; n++) if (a[idx[n]][i] != type) break;
if (n == depth) { idx[n] = i; if (find_group(type, 1, max_n, depth + 1)) return 1; } } return 0; }
int main() { int i, j, k; const char *mark = "01-";
for (i = 0; i < 17; i++) a[i][i] = 2;
for (k = 1; k <= 8; k <<= 1) { for (i = 0; i < 17; i++) { j = (i + k) % 17; a[i][j] = a[j][i] = 1; } }
for (i = 0; i < 17; i++) { for (j = 0; j < 17; j++) printf("%c ", mark[a[i][j]]); putchar('\n'); }
// testcase breakage // a[2][1] = a[1][2] = 0;
// it's symmetric, so only need to test groups containing node 0 for (i = 0; i < 17; i++) { idx[0] = i; if (find_group(1, i+1, 17, 1) || find_group(0, i+1, 17, 1)) { puts("no good"); return 0; } } puts("all good"); return 0; }</lang>
- Output:
(17 x 17 connectivity matrix)
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - all good
D
<lang d>import std.stdio, std.string, std.algorithm, std.range;
/// Generate the connectivity matrix. immutable(char)[][] generateMatrix() {
immutable r = format("-%b", 53643);
return r.length.iota.map!(i => r[$-i .. $] ~ r[0 .. $-i]).array;
}
/**Check that every clique of four has at least one pair connected and one pair unconnected. It requires a symmetric matrix.*/ string ramseyCheck(in char[][] mat) pure @safe in {
foreach (immutable r, const row; mat) {
assert(row.length == mat.length);
foreach (immutable c, immutable x; row)
assert(x == mat[c][r]);
}
} body {
immutable N = mat.length; char[6] connectivity = '-';
foreach (immutable a; 0 .. N) {
foreach (immutable b; 0 .. N) {
if (a == b) continue;
connectivity[0] = mat[a][b];
foreach (immutable c; 0 .. N) {
if (a == c || b == c) continue;
connectivity[1] = mat[a][c];
connectivity[2] = mat[b][c];
foreach (immutable d; 0 .. N) {
if (a == d || b == d || c == d) continue;
connectivity[3] = mat[a][d];
connectivity[4] = mat[b][d];
connectivity[5] = mat[c][d];
// We've extracted a meaningful subgraph,
// check its connectivity.
if (!connectivity[].canFind('0'))
return format("Fail, found wholly connected: ",
a, " ", b," ", c, " ", d);
else if (!connectivity[].canFind('1'))
return format("Fail, found wholly " ~
"unconnected: ",
a, " ", b," ", c, " ", d);
}
}
}
}
return "Satisfies Ramsey condition.";
}
void main() {
const mat = generateMatrix;
writefln("%-(%(%c %)\n%)", mat);
mat.ramseyCheck.writeln;
}</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - Satisfies Ramsey condition.
Elixir
<lang elixir>defmodule Ramsey do
def main(n\\17) do
vertices = Enum.to_list(0 .. n-1)
g = create_graph(n,vertices)
edges = for v1 <- :digraph.vertices(g), v2 <- :digraph.out_neighbours(g, v1), do: {v1,v2}
print_graph(vertices,edges)
case ramsey_check(vertices,edges) do
true -> "Satisfies Ramsey condition."
{false,reason} -> "Not satisfies Ramsey condition:\n#{inspect reason}"
end
|> IO.puts
end
def create_graph(n,vertices) do
g = :digraph.new([:cyclic])
for v <- vertices, do: :digraph.add_vertex(g,v)
for i <- vertices, k <- [1,2,4,8] do
j = rem(i + k, n)
:digraph.add_edge(g, i, j)
:digraph.add_edge(g, j, i)
end
g
end
def print_graph(vertices,edges) do
Enum.each(vertices, fn j ->
Enum.map_join(vertices, " ", fn i ->
cond do
i==j -> "-"
{i,j} in edges -> "1"
true -> "0"
end
end)
|> IO.puts
end)
end
def ramsey_check(vertices,edges) do
listconditions =
for v1 <- vertices, v2 <- vertices, v3 <- vertices, v4 <- vertices,
v1 != v2, v1 != v3, v1 != v4, v2 != v3, v2 != v4, v3 != v4
do
all_cases = [ {v1,v2} in edges, {v1,v3} in edges, {v1,v4} in edges,
{v2,v3} in edges, {v2,v4} in edges, {v3,v4} in edges ]
{v1, v2, v3, v4, Enum.any?(all_cases), not(Enum.all?(all_cases))}
end
if Enum.all?(listconditions, fn {_,_,_,_,c1,c2} -> c1 and c2 end) do
true
else
{false, (for {v1,v2,v3,v4,false,_} <- listconditions, do: {:wholly_unconnected,v1,v2,v3,v4})
++ (for {v1,v2,v3,v4,_,false} <- listconditions, do: {:wholly_connected,v1,v2,v3,v4}) }
end
end
end
Ramsey.main</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - Satisfies Ramsey condition.
Erlang
<lang erlang>-module(ramsey_theorem). -export([main/0]).
main() -> Vertices = lists:seq(0,16), G = create_graph(Vertices), String_ramsey = case ramsey_check(G,Vertices) of true -> "Satisfies Ramsey condition."; {false,Reason} -> "Not satisfies Ramsey condition:\n" ++ io_lib:format("~p\n",[Reason]) end, io:format("~s\n~s\n",[print_graph(G,Vertices),String_ramsey]).
create_graph(Vertices) -> G = digraph:new([cyclic]), [digraph:add_vertex(G,V) || V <- Vertices], [begin J = ((I + K) rem 17), digraph:add_edge(G, I, J), digraph:add_edge(G, J, I) end || I <- Vertices, K <- [1,2,4,8]], G.
print_graph(G,Vertices) -> Edges = [{V1,V2} || V1 <- digraph:vertices(G), V2 <- digraph:out_neighbours(G, V1)], lists:flatten( [[ [case I of J -> $-; _ -> case lists:member({I,J},Edges) of true -> $1; false -> $0 end end,$ ] || I <- Vertices] ++ [$\n] || J <- Vertices]).
ramsey_check(G,Vertices) -> Edges = [{V1,V2} || V1 <- digraph:vertices(G), V2 <- digraph:out_neighbours(G, V1)], ListConditions = [begin All_cases = [lists:member({V1,V2},Edges), lists:member({V1,V3},Edges), lists:member({V1,V4},Edges), lists:member({V2,V3},Edges), lists:member({V2,V4},Edges), lists:member({V3,V4},Edges)], {V1,V2,V3,V4, lists:any(fun(X) -> X end, All_cases), not(lists:all(fun(X) -> X end, All_cases))} end || V1 <- Vertices, V2 <- Vertices, V3 <- Vertices, V4 <- Vertices, V1/=V2,V1/=V3,V1/=V4,V2/=V3,V2/=V4,V3/=V4], case lists:all(fun({_,_,_,_,C1,C2}) -> C1 and C2 end,ListConditions) of true -> true; false -> {false, [{wholly_unconnected,V1,V2,V3,V4} || {V1,V2,V3,V4,false,_} <- ListConditions] ++ [{wholly_connected,V1,V2,V3,V4} || {V1,V2,V3,V4,_,false} <- ListConditions]} end.</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - Satisfies Ramsey condition.
FreeBASIC
<lang freebasic> Dim Shared As Integer i, j, k = 1 Dim Shared As Integer a(17,17), idx(4) For i = 0 To 17
a(i,i) = 2
Next i
Function EncontrarGrupo(tipo As Integer, min As Integer, max As Integer, fondo As Integer) As Boolean
If fondo = 0 Then
Dim As String c = ""
If tipo = 0 Then c = "des"
Print Using "Grupo totalmente &conectado:"; c
For i = 0 To 4
Print " " & idx(i)
Next i
Print
Return true
End If
For i = min To max
k = 0
For j = k To fondo
If a(idx(k),i) <> tipo Then Exit For
Next j
If k = fondo Then
idx(k) = i
If EncontrarGrupo(tipo, 1, max, fondo+1) Then Return true
End If
Next i
Return false
End Function
While k <= 8
For i = 1 To 17
j = (i + k) Mod 17
If j <> 0 Then
a(i,j) = 1 : a(j,i) = 1
End If
Next i
k *= 2
Wend For i = 1 To 17
For j = 1 To 17
If a(i,j) = 2 Then
Print "- ";
Else
Print a(i,j) & " ";
End If
Next j
Print
Next i
' Es simétrico, por lo que solo necesita probar grupos que contengan el nodo 0. For i = 0 To 17
idx(0) = i
If EncontrarGrupo(1, i+1, 17, 1) Or EncontrarGrupo(0, i+1, 17, 1) Then
Print Chr(10) & "No satisfecho."
Exit For
End If
Next i Print Chr(10) & "Satisface el teorema de Ramsey." End </lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 - Satisface el teorema de Ramsey.
Go
<lang go>package main
import "fmt"
var (
a [17][17]int idx [4]int
)
func findGroup(ctype, min, max, depth int) bool {
if depth == 4 {
cs := ""
if ctype == 0 {
cs = "un"
}
fmt.Printf("Totally %sconnected group:", cs)
for i := 0; i < 4; i++ {
fmt.Printf(" %d", idx[i])
}
fmt.Println()
return true
}
for i := min; i < max; i++ {
n := 0
for ; n < depth; n++ {
if a[idx[n]][i] != ctype {
break
}
}
if n == depth {
idx[n] = i
if findGroup(ctype, 1, max, depth+1) {
return true
}
}
}
return false
}
func main() {
const mark = "01-"
for i := 0; i < 17; i++ {
a[i][i] = 2
}
for k := 1; k <= 8; k <<= 1 {
for i := 0; i < 17; i++ {
j := (i + k) % 17
a[i][j], a[j][i] = 1, 1
}
}
for i := 0; i < 17; i++ {
for j := 0; j < 17; j++ {
fmt.Printf("%c ", mark[a[i][j]])
}
fmt.Println()
}
// Test case breakage // a[2][1] = a[1][2] = 0
// It's symmetric, so only need to test groups containing node 0.
for i := 0; i < 17; i++ {
idx[0] = i
if findGroup(1, i+1, 17, 1) || findGroup(0, i+1, 17, 1) {
fmt.Println("No good.")
return
}
}
fmt.Println("All good.")
}</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - All good.
J
Interpreting this task as "reproduce the output of all the other examples", then here's a stroll to the goal through the J interpreter: <lang j> i.@<.&.(2&^.) N =: 17 NB. Count to N by powers of 2 1 2 4 8
1 #~ 1 j. 0 _1:} i.@<.&.(2&^.) N =: 17 NB. Turn indices into bit mask
1 0 1 0 0 1 0 0 0 0 1
(, |.) 1 #~ 1 j. 0 _1:} i.@<.&.(2&^.) N =: 17 NB. Cat the bitmask with its own reflection
1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1
_1 |.^:(<N) _ , (, |.) 1 #~ 1 j. 0 _1:} <: i.@<.&.(2&^.) N=:17 NB. Then rotate N times to produce the array
_ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _
NB. Packaged up as a re-usable function ramsey =: _1&|.^:((<@])`(_ , [: (, |.) 1 #~ 1 j. 0 _1:} [: <: i.@<.&.(2&^.)@])) ramsey 17
_ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _ 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 _</lang>
To test if all combinations of 4 rows and columns contain both a 0 and a 1 <lang j>
comb=: 4 : 0 M. NB. All size x combinations of i.y
if. (x>:y)+.0=x do. i.(x<:y),x else. (0,.x comb&.<: y),1+x comb y-1 end.
)
NB. returns 1 iff the subbmatrix of y consisting of the columns and rows labelled x contains both 1 and 0
checkRow =. 4 : 0 "1 _
*./ 0 1 e. ,x{"1 x{y
)
*./ (4 comb 17) checkRow ramsey 17
1 </lang>
Java
Translation of Tcl via D
<lang java>import java.util.Arrays; import java.util.stream.IntStream;
public class RamseysTheorem {
static char[][] createMatrix() {
String r = "-" + Integer.toBinaryString(53643);
int len = r.length();
return IntStream.range(0, len)
.mapToObj(i -> r.substring(len - i) + r.substring(0, len - i))
.map(String::toCharArray)
.toArray(char[][]::new);
}
/**
* Check that every clique of four has at least one pair connected and one
* pair unconnected. It requires a symmetric matrix.
*/
static String ramseyCheck(char[][] mat) {
int len = mat.length;
char[] connectivity = "------".toCharArray();
for (int a = 0; a < len; a++) {
for (int b = 0; b < len; b++) {
if (a == b)
continue;
connectivity[0] = mat[a][b];
for (int c = 0; c < len; c++) {
if (a == c || b == c)
continue;
connectivity[1] = mat[a][c];
connectivity[2] = mat[b][c];
for (int d = 0; d < len; d++) {
if (a == d || b == d || c == d)
continue;
connectivity[3] = mat[a][d];
connectivity[4] = mat[b][d];
connectivity[5] = mat[c][d];
// We've extracted a meaningful subgraph,
// check its connectivity.
String conn = new String(connectivity);
if (conn.indexOf('0') == -1)
return String.format("Fail, found wholly connected: "
+ "%d %d %d %d", a, b, c, d);
else if (conn.indexOf('1') == -1)
return String.format("Fail, found wholly unconnected: "
+ "%d %d %d %d", a, b, c, d);
}
}
}
}
return "Satisfies Ramsey condition.";
}
public static void main(String[] a) {
char[][] mat = createMatrix();
for (char[] s : mat)
System.out.println(Arrays.toString(s));
System.out.println(ramseyCheck(mat));
}
}</lang>
[-, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1] [1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1] [1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0] [0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1] [1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0] [0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0] [0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0] [0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1, 1] [1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0, 1] [1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0, 0] [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0, 0] [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1, 0] [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0, 1] [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1, 0] [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1, 1] [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -, 1] [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, -] Satisfies Ramsey condition.
Julia
<lang julia>const a, idx = zeros(Int, 17, 17), zeros(Int, 4)
function findgroup(typ, nmin, nmax, depth)
if depth == 4
print("Totally ", typ > 0 ? "" : "un", "connected group:")
for i in 1:4
print(" ", idx[i], i == 4 ? "\n" : "")
end
return true
end
for i in nmin:nmax-1
for i in nmin:nmax-1
m = 0
for n in 0:depth-1
if a[idx[n + 1] + 1, i + 1] != typ
break
end
m = n +1
end
if m == depth
idx[m + 1] = i
if findgroup(typ, 1, nmax, depth + 1)
return true
end
end
end
end
return false
end
function testnodes()
mark = "01-"
for i in 1:17
a[i, i] = 2
end
for k in [1, 2, 4, 8], i in 0:16
j = (i + k) % 17
a[i + 1, j + 1] = a[j + 1, i + 1] = 1
end
for i in 1:17, j in 1:17
print(mark[a[i, j] + 1], j == 17 ? "\n" : " ")
end
# testcase breakage
# a[2][1] = a[1][2] = 0
# it's symmetric, so only need to test groups containing node 0
for i in 1:17
idx[1] = i
if findgroup(1, i + 1, 17, 1) || findgroup(0, i + 1, 17, 1)
println("Test with $i is no good.")
return
end
end
println("All tests are OK.")
end
testnodes()
</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - All tests are OK.
Kotlin
<lang scala>// version 1.1.0
val a = Array(17) { IntArray(17) } val idx = IntArray(4)
fun findGroup(type: Int, minN: Int, maxN: Int, depth: Int): Boolean {
if (depth == 4) {
print("\nTotally ${if (type != 0) "" else "un"}connected group:")
for (i in 0 until 4) print(" ${idx[i]}")
println()
return true
}
for (i in minN until maxN) {
var n = depth
for (m in 0 until depth) if (a[idx[m]][i] != type) {
n = m
break
}
if (n == depth) {
idx[n] = i
if (findGroup(type, 1, maxN, depth + 1)) return true
}
}
return false
}
fun main(args: Array<String>) {
for (i in 0 until 17) a[i][i] = 2
var j: Int
var k = 1
while (k <= 8) {
for (i in 0 until 17) {
j = (i + k) % 17
a[i][j] = 1
a[j][i] = 1
}
k = k shl 1
}
val mark = "01-"
for (i in 0 until 17) {
for (m in 0 until 17) print("${mark[a[i][m]]} ")
println()
}
for (i in 0 until 17) {
idx[0] = i
if (findGroup(1, i + 1, 17, 1) || findGroup(0, i + 1, 17, 1)) {
println("\nRamsey condition not satisfied.")
return
}
}
println("\nRamsey condition satisfied.")
}</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - Ramsey condition satisfied.
Mathematica
<lang mathematica>CirculantGraph[17, {1, 2, 4, 8}]</lang>
Mathprog
<lang>/*Ramsey 4 4 17
This model finds a graph with 17 Nodes such that no clique of 4 Nodes is either fully connected, nor fully disconnected Nigel_Galloway January 18th., 2012
- /
param Nodes := 17; var Arc{1..Nodes, 1..Nodes}, binary;
clique{a in 1..(Nodes-3), b in (a+1)..(Nodes-2), c in (b+1)..(Nodes-1), d in (c+1)..Nodes} : 1 <= Arc[a,b] + Arc[a,c] + Arc[a,d] + Arc[b,c] + Arc[b,d] + Arc[c,d] <= 5;
end;</lang>
This may be run with: <lang bash>glpsol --minisat --math R_4_4_17.mprog --output R_4_4_17.sol</lang> The solution may be viewed on this page. In the solution file, the first section identifies the number of nodes connected in this clique. In the second part of the solution, the status of each arc in the graph (connected=1, unconnected=0) is shown.
PARI/GP
This takes the C solution to its logical extreme. <lang parigp>
check(M)={
my(n=#M);
for(a=1,n-3,
for(b=a+1,n-2,
my(goal=!M[a,b]);
for(c=b+1,n-1,
if(M[a,c]==goal || M[b,c]==goal, next(2));
for(d=c+1,n,
if(M[a,d]==goal || M[b,d]==goal || M[c,d]==goal, next(3));
)
);
print(a" "b);
return(0)
)
);
1
};
M=matrix(17,17,x,y,my(t=abs(x-y)%17);t==2^min(valuation(t,2),3)) check(M)</lang>
Perl
<lang perl>use ntheory qw(forcomb); use Math::Cartesian::Product;
$n = 17; push @a, [(0) x $n] for 0..$n-1; $a[$_][$_] = '-' for 0..$n-1;
for $x (cartesian {@_} [(0..$n-1)], [(1,2,4,8)]) {
$i = @$x[0]; $k = @$x[1]; $j = ($i + $k) % $n; $a[$i][$j] = $a[$j][$i] = 1;
}
forcomb {
my $l = 0;
@i = @_;
forcomb { $l += $a[ $i[$_[0]] ][ $i[$_[1]] ]; } (4,2);
die "Bogus!" unless 0 < $l and $l < 6;
} ($n,4);
print join(' ' ,@$_) . "\n" for @a; print 'OK'</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - OK
Phix
<lang Phix>sequence a = repeat(repeat('0',17),17),
idx = repeat(0,4)
function findGroup(integer ch, lo, hi, depth)
if depth == 4 then
string cs = iff(ch='1'?"":"un")
printf(1,"Totally %sconnected group:%s\n", {cs,sprint(idx)})
return true
end if
for i=lo to hi do
bool all_same = true
for n=1 to depth do
if a[idx[n]][i] != ch then
all_same = false
exit
end if
end for
if all_same then
idx[depth+1] = i
if findGroup(ch, 1, hi, depth+1) then
return true
end if
end if
end for
return false
end function
for i=1 to 17 do
a[i][i] = '-'
end for
integer k = 1 while k<=8 do
for i=1 to 17 do
integer j = mod(i-1+k,17)+1
{a[i][j], a[j][i]} = "11"
end for
k *= 2
end while
-- Test case breakage --{a[2][1],a[1][2]} @= '0'
puts(1,join(a,'\n')&"\n\n")
bool all_good = true for i=1 to 17 do
idx[1] = i
if findGroup('1', i+1, 17, 1)
or findGroup('0', i+1, 17, 1) then
all_good = false
exit
end if
end for printf(1,iff(all_good?"Satisfies Ramsey condition.\n":"No good.\n"))</lang>
- Output:
-1101000110001011 1-110100011000101 11-11010001100010 011-1101000110001 1011-110100011000 01011-11010001100 001011-1101000110 0001011-110100011 10001011-11010001 110001011-1101000 0110001011-110100 00110001011-11010 000110001011-1101 1000110001011-110 01000110001011-11 101000110001011-1 1101000110001011- Satisfies Ramsey condition.
Python
<lang python>range17 = range(17) a = [['0'] * 17 for i in range17] idx = [0] * 4
def find_group(mark, min_n, max_n, depth=1):
if (depth == 4):
prefix = "" if (mark == '1') else "un"
print("Fail, found totally {}connected group:".format(prefix))
for i in range(4):
print(idx[i])
return True
for i in range(min_n, max_n):
n = 0
while (n < depth):
if (a[idx[n]][i] != mark):
break
n += 1
if (n == depth):
idx[n] = i
if (find_group(mark, 1, max_n, depth + 1)):
return True
return False
if __name__ == '__main__':
for i in range17:
a[i][i] = '-'
for k in range(4):
for i in range17:
j = (i + pow(2, k)) % 17
a[i][j] = a[j][i] = '1'
# testcase breakage # a[2][1] = a[1][2] = '0'
for row in a:
print(' '.join(row))
for i in range17:
idx[0] = i
if (find_group('1', i + 1, 17) or find_group('0', i + 1, 17)):
print("no good")
exit()
print("all good")</lang>
- Output same as C:
Racket
Kind of a translation of C (ie, reducing this problem to generating a printout of a specific matrix). <lang racket>#lang racket
(define N 17)
(define (dist i j)
(define d (abs (- i j))) (if (<= d (quotient N 2)) d (- N d)))
(define v
(build-vector N
(λ(i) (build-vector N
(λ(j) (case (dist i j) [(0) '-] [(1 2 4 8) 1] [else 0]))))))
(for ([row v]) (displayln row))</lang>
Raku
(formerly Perl 6)
<lang perl6>my $n = 17; my @a = [ 0 xx $n ] xx $n; @a[$_;$_] = '-' for ^$n;
for flat ^$n X 1,2,4,8 -> $i, $k {
my $j = ($i + $k) % $n; @a[$i;$j] = @a[$j;$i] = 1;
} .say for @a;
for combinations($n,4) -> $quartet {
my $links = [+] $quartet.combinations(2).map: -> $i,$j { @a[$i;$j] }
die "Bogus!" unless 0 < $links < 6;
} say "OK";</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - OK
REXX
Mainline programming was borrowed from C. <lang rexx>/*REXX program finds and displays a 17 node graph such that any four nodes are neither */ /*─────────────────────────────────────────── totally connected nor totally unconnected.*/ @.=0; #=17 /*initialize the node graph to zero. */
do d=0 for #; @.d.d=2; end /*d*/ /*set the diagonal elements to two. */
do k=1 by 0 while k<=8 /*K is doubled each time through loop.*/
do i=0 for #; j= (i+k) // # /*set a row,column and column,row. */
@.i.j=1; @.j.i=1 /*set two array elements to unity. */
end /*i*/
k=k+k /*double the value of K for each loop*/
end /*k*/
/* [↓] display a connection grid. */
do r=0 for #; _=; do c=0 for # /*build rows; build column by column. */
_=_ @.r.c /*add (append) the column to the row.*/
end /*c*/
say left(, 9) translate(_, "-", 2) /*display the constructed row. */
end /*r*/
/*verify the sub-graphs connections. */
!.=0; ok=1 /*Ramsey's connections; OK (so far).*/
/* [↓] check col. with row connections*/
do v=0 for # /*check the sub-graphs # of connections*/
do h=0 for # /*check column connections to the rows.*/
if @.v.h==1 then !._v.v= !._v.v + 1 /*if connected, then bump the counter.*/
end /*h*/ /* [↑] Note: we're counting each */
ok=ok & !._v.v==# % 2 /* connection twice, so divide */
end /*v*/ /* the total by two. */
/* [↓] check col. with row connections*/
do h=0 for # /*check the sub-graphs # of connections*/
do v=0 for # /*check the row connection to a column.*/
if @.h.v==1 then !._h.h= !._h.h + 1 /*if connected, then bump the counter.*/
end /*v*/ /* [↑] Note: we're counting each */
ok=ok & !._h.h==# % 2 /* connection twice, so divide */
end /*h*/ /* the total by two. */
say /*stick a fork in it, we're all done. */ say space("Ramsey's condition is" word('not', 1+ok) "satisfied.") /*yea─or─nay.*/</lang>
- output (17x17 connectivity matrix):
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1
1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0
0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1
1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0
0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0
0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0
0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1
1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1
1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0
0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0
0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0
0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1
1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0
0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1
1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1
1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -
Ramsey's condition is satisfied.
Ring
<lang ring>
- Project : Ramsey's theorem
load "stdlib.ring"
a = newlist(17,17) for i = 1 to 17
a[i][i] = -1
next k = 1 while k <= 8
for i = 1 to 17
j = (i + k) % 17
if j != 0
a[i][j] = 1
a[j][i] = 1
ok
next
k = k * 2
end for i = 1 to 17
for j = 1 to 17
see a[i][j] + " "
next
see nl
next </lang> Output:
-11101000110001011 1-1110100011000101 11-111010001100010 011-11101000110001 1011-1110100011000 01011-111010001100 001011-11101000110 0001011-1110100011 10001011-111010000 110001011-11101000 0110001011-1110100 00110001011-111010 000110001011-11100 1000110001011-1110 01000110001011-110 101000110001011-10 1101000100000000-1
Ruby
<lang ruby>a = Array.new(17){['0'] * 17} 17.times{|i| a[i][i] = '-'} 4.times do |k|
17.times do |i| j = (i + 2 ** k) % 17 a[i][j] = a[j][i] = '1' end
end a.each {|row| puts row.join(' ')}
- check taken from Raku version
(0...17).to_a.combination(4) do |quartet|
links = quartet.combination(2).map{|i,j| a[i][j].to_i}.reduce(:+)
abort "Bogus" unless 0 < links && links < 6
end puts "Ok" </lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - Ok
Run BASIC
<lang runbasic>dim a(17,17) for i = 1 to 17: a(i,i) = -1: next i k = 1 while k <= 8
for i = 1 to 17 j = (i + k) mod 17 a(i,j) = 1 a(j,i) = 1 next i k = k * 2
wend for i = 1 to 17
for j = 1 to 17 print a(i,j);" "; next j print
next i</lang>
-1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 -1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 -1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 -1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 -1
Sidef
<lang ruby>var a = 17.of { 17.of(0) }
17.times {|i| a[i][i] = '-' } 4.times { |k|
17.times { |i|
var j = ((i + 1<<k) % 17)
a[i][j] = (a[j][i] = 1)
}
}
a.each {|row| say row.join(' ') }
combinations(17, 4, { |*quartet|
var links = quartet.combinations(2).map{|p| a.dig(p...) }.sum
((0 < links) && (links < 6)) || die "Bogus!"
}) say "Ok"</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - Ok
Tcl
<lang tcl>package require Tcl 8.6
- Generate the connectivity matrix
set init [split [format -%b 53643] ""] set matrix {} for {set r $init} {$r ni $matrix} {set r [concat [lindex $r end] [lrange $r 0 end-1]]} {
lappend matrix $r
}
- Check that every clique of four has at least *one* pair connected and one
- pair unconnected. ASSUMES that the graph is symmetric.
proc ramseyCheck4 {matrix} {
set N [llength $matrix]
set connectivity [lrepeat 6 -]
for {set a 0} {$a < $N} {incr a} {
for {set b 0} {$b < $N} {incr b} { if {$a==$b} continue lset connectivity 0 [lindex $matrix $a $b] for {set c 0} {$c < $N} {incr c} { if {$a==$c || $b==$c} continue lset connectivity 1 [lindex $matrix $a $c] lset connectivity 2 [lindex $matrix $b $c] for {set d 0} {$d < $N} {incr d} { if {$a==$d || $b==$d || $c==$d} continue lset connectivity 3 [lindex $matrix $a $d] lset connectivity 4 [lindex $matrix $b $d] lset connectivity 5 [lindex $matrix $c $d]
# We've extracted a meaningful subgraph; check its connectivity if {0 ni $connectivity} { puts "FAIL! Found wholly connected: $a $b $c $d" return } elseif {1 ni $connectivity} { puts "FAIL! Found wholly unconnected: $a $b $c $d" return } } } }
} puts "Satisfies Ramsey condition"
}
puts [join $matrix \n] ramseyCheck4 $matrix</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - Satisfies Ramsey condition
Wren
<lang ecmascript>import "/fmt" for Fmt
var a = List.filled(17, null) for (i in 0..16) a[i] = List.filled(17, 0)
var idx = List.filled(4, 0)
var findGroup // recursive findGroup = Fn.new { |ctype, min, max, depth|
if (depth == 4) {
var cs = (ctype == 0) ? "un" : ""
System.write("Totally %(cs)connected group:")
for (i in 0..3) System.write(" %(idx[i])")
System.print()
return true
}
var i = min
while (i < max) {
var n = 0
while (n < depth) {
if (a[idx[n]][i] != ctype) break
n = n + 1
}
if (n == depth) {
idx[n] = i
if (findGroup.call(ctype, 1, max, depth+1)) return true
}
i = i + 1
}
return false
}
var mark = "01-" for (i in 0..16) a[i][i] = 2 var k = 1 while (k <= 8) {
for (i in 0..16) {
var j = (i + k) % 17
a[i][j] = 1
a[j][i] = 1
}
k = k << 1
} for (i in 0..16) {
for (j in 0..16) Fmt.write("$s ", mark[a[i][j]])
System.print()
}
// Test case breakage // a[2][1] = a[1][2] = 0
// It's symmetric, so only need to test groups containing node 0. for (i in 0..16) {
idx[0] = i
if (findGroup.call(1, i+1, 17, 1) || findGroup.call(0, i+1, 17, 1)) {
System.print("No good.")
return
}
} System.print("All good.")</lang>
- Output:
- 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 - All good.
- Draft Programming Tasks
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