files / problems / kissing-5d / compute / q5 / t5_share.c
/* Exact 36-cliques that share s vertices with a published 35.
*
* Usage: ./t5_share <adj.txt> <published.json> <share> [node_limit]
*
* For each published 35-clique P and each (35-share)-subset L of P,
* S = P \ L has size share. A 36-clique meeting P in S is S plus a
* (36-share)-clique in the common neighbourhood of S minus S.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#define MAXN 512
#define W ((MAXN + 63) / 64)
typedef uint64_t u64;
static int n, nwords, target;
static u64 adj[MAXN][W];
static int best, found;
static long nodes, node_limit;
static int found_idx[64];
static int popc(const u64 *a)
{
int s = 0;
for (int i = 0; i < nwords; i++)
s += __builtin_popcountll(a[i]);
return s;
}
static int first_bit(const u64 *a)
{
for (int i = 0; i < nwords; i++)
if (a[i])
return i * 64 + __builtin_ctzll(a[i]);
return -1;
}
static void bit_clear(u64 *a, int v)
{
a[v >> 6] &= ~(1ULL << (v & 63));
}
static int bit_test(const u64 *a, int v)
{
return (int)((a[v >> 6] >> (v & 63)) & 1U);
}
static void bit_set(u64 *a, int v)
{
a[v >> 6] |= 1ULL << (v & 63);
}
static int colour_order(const u64 *P, int *ord, int *col)
{
u64 rem[W];
memcpy(rem, P, nwords * sizeof(u64));
int m = 0, c = 0;
while (popc(rem)) {
c++;
u64 avail[W];
memcpy(avail, rem, nwords * sizeof(u64));
int v;
while ((v = first_bit(avail)) >= 0) {
ord[m] = v;
col[m] = c;
m++;
bit_clear(avail, v);
for (int w = 0; w < nwords; w++)
avail[w] &= ~adj[v][w];
bit_clear(rem, v);
}
}
return m;
}
static void expand(u64 *P, int rsz, int *stack)
{
nodes++;
if (found || nodes > node_limit)
return;
int psz = popc(P);
if (rsz + psz <= best)
return;
if (psz == 0) {
if (rsz > best)
best = rsz;
return;
}
int ord[MAXN], col[MAXN];
int m = colour_order(P, ord, col);
u64 Q[W];
memcpy(Q, P, nwords * sizeof(u64));
for (int i = m - 1; i >= 0; i--) {
if (found || nodes > node_limit)
return;
if (rsz + col[i] <= best)
return;
int v = ord[i];
u64 P2[W];
for (int w = 0; w < nwords; w++)
P2[w] = Q[w] & adj[v][w];
stack[rsz] = v;
if (rsz + 1 >= target) {
found = 1;
best = rsz + 1;
memcpy(found_idx, stack, (size_t)target * sizeof(int));
return;
}
expand(P2, rsz + 1, stack);
bit_clear(Q, v);
}
}
static int read_graph(FILE *fp)
{
if (fscanf(fp, "%d", &n) != 1)
return 0;
if (n <= 0 || n > MAXN)
return 0;
nwords = (n + 63) / 64;
memset(adj, 0, sizeof adj);
for (int i = 0; i < n; i++) {
for (int w = 0; w < nwords; w++) {
unsigned long long x;
if (fscanf(fp, "%llx", &x) != 1)
return 0;
adj[i][w] = (u64)x;
}
bit_clear(adj[i], i);
}
return 1;
}
static int parse_published(const char *path, int cl[4][40], int *ncl)
{
FILE *f = fopen(path, "r");
if (!f)
return 0;
char buf[1 << 16];
size_t m = fread(buf, 1, sizeof buf - 1, f);
buf[m] = 0;
fclose(f);
*ncl = 0;
const char *p = buf;
while (*p && *ncl < 4) {
const char *r = strstr(p, "remainder_clique");
if (!r)
break;
r = strchr(r, '[');
if (!r)
break;
r++;
int k = 0;
while (*r && *r != ']') {
if (*r >= '0' && *r <= '9') {
int v = 0;
while (*r >= '0' && *r <= '9') {
v = v * 10 + (*r - '0');
r++;
}
if (k < 40)
cl[*ncl][k++] = v;
} else {
r++;
}
}
if (k == 35)
(*ncl)++;
p = r;
}
return *ncl == 4;
}
int main(int argc, char **argv)
{
if (argc < 4) {
fprintf(stderr, "usage: %s adj.txt published.json share [node_limit]\n",
argv[0]);
return 1;
}
FILE *fp = fopen(argv[1], "r");
if (!fp || !read_graph(fp)) {
fprintf(stderr, "bad graph\n");
return 1;
}
fclose(fp);
int cl[4][40], ncl;
if (!parse_published(argv[2], cl, &ncl)) {
fprintf(stderr, "bad published json (need 4 remainder 35-cliques)\n");
return 1;
}
int share = atoi(argv[3]);
node_limit = (argc >= 5) ? atol(argv[4]) : 200000L;
if (share < 15 || share > 34) {
fprintf(stderr, "share out of range\n");
return 1;
}
int leave = 35 - share;
int need = 36 - share;
long tried = 0, empty = 0, incomplete = 0, hits = 0;
int best_out = 0;
int comb[16];
printf("{\n \"n\": %d,\n \"share\": %d,\n \"leave\": %d, \"need\": %d,\n",
n, share, leave, need);
printf(" \"by_code\": {\n");
for (int c = 0; c < ncl; c++) {
long c_tried = 0, c_empty = 0, c_inc = 0, c_hit = 0;
int c_best = 0;
/* enumerate leave-subsets of the 35 */
for (int i = 0; i < leave; i++)
comb[i] = i;
for (;;) {
u64 S[W];
memset(S, 0, sizeof S);
int inL[MAXN];
memset(inL, 0, sizeof inL);
for (int i = 0; i < leave; i++)
inL[cl[c][comb[i]]] = 1;
for (int i = 0; i < 35; i++)
if (!inL[cl[c][i]])
bit_set(S, cl[c][i]);
u64 N[W];
memset(N, 0xFF, sizeof N);
if (n & 63)
N[nwords - 1] = (1ULL << (n & 63)) - 1;
else
N[nwords - 1] = ~0ULL;
for (int i = 0; i < 35; i++) {
int v = cl[c][i];
if (inL[v])
continue;
for (int w = 0; w < nwords; w++)
N[w] &= adj[v][w];
}
for (int w = 0; w < nwords; w++)
N[w] &= ~S[w];
target = need;
found = 0;
best = need - 1;
if (c_best > best)
best = c_best;
nodes = 0;
int stack[64];
expand(N, 0, stack);
c_tried++;
tried++;
if (best > c_best)
c_best = best;
if (best > best_out)
best_out = best;
if (found) {
c_hit++;
hits++;
} else if (nodes > node_limit) {
c_inc++;
incomplete++;
} else {
c_empty++;
empty++;
}
/* next combination */
int i = leave - 1;
while (i >= 0 && comb[i] == 35 - leave + i)
i--;
if (i < 0)
break;
comb[i]++;
for (int j = i + 1; j < leave; j++)
comb[j] = comb[j - 1] + 1;
}
if (c)
printf(",\n");
printf(" \"%d\": {\"tried\": %ld, \"empty\": %ld, \"incomplete\": %ld, "
"\"found\": %ld, \"best_extra\": %d, \"complete\": %s}",
c, c_tried, c_empty, c_inc, c_hit, c_best,
c_inc == 0 && c_hit == 0 ? "true" : "false");
fprintf(stderr, "code %d tried=%ld empty=%ld inc=%ld hit=%ld best=%d\n",
c, c_tried, c_empty, c_inc, c_hit, c_best);
}
printf("\n },\n");
printf(" \"tried\": %ld,\n \"empty\": %ld,\n \"incomplete\": %ld,\n",
tried, empty, incomplete);
printf(" \"found_36\": %s,\n", hits ? "true" : "false");
printf(" \"best_extra\": %d,\n", best_out);
printf(" \"complete\": %s\n}\n",
incomplete == 0 && hits == 0 ? "true" : "false");
return 0;
}