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struct fpattern exported
This commit is contained in:
Zeno Rogue
parent
9647cbd47e
commit
fedb170b55
900
fieldpattern.cpp
900
fieldpattern.cpp
@ -31,41 +31,45 @@ struct fgeomextra {
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extern int subpathid;
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extern int subpathorder;
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#define MWDIM (prod ? 3 : WDIM+1)
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bool isprime(int n) {
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for(int k=2; k<n; k++) if(n%k == 0) return false;
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return true;
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}
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#if HDR
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#define MWDIM (prod ? 3 : WDIM+1)
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struct matrix {
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int a[MAXMDIM][MAXMDIM];
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int* operator [] (int k) { return a[k]; }
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const int* operator [] (int k) const { return a[k]; }
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bool operator == (const matrix& B) const {
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for(int i=0; i<MWDIM; i++) for(int j=0; j<MWDIM; j++)
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if(self[i][j] != B[i][j]) return false;
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return true;
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}
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bool operator != (const matrix& B) const {
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for(int i=0; i<MWDIM; i++) for(int j=0; j<MWDIM; j++)
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if(self[i][j] != B[i][j]) return true;
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return false;
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}
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bool operator < (const matrix& B) const {
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for(int i=0; i<MWDIM; i++) for(int j=0; j<MWDIM; j++)
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if(self[i][j] != B[i][j]) return self[i][j] < B[i][j];
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return false;
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}
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};
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#endif
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bool operator == (const matrix& A, const matrix& B) {
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for(int i=0; i<MWDIM; i++) for(int j=0; j<MWDIM; j++)
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if(A[i][j] != B[i][j]) return false;
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return true;
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}
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bool operator != (const matrix& A, const matrix& B) {
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for(int i=0; i<MWDIM; i++) for(int j=0; j<MWDIM; j++)
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if(A[i][j] != B[i][j]) return true;
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return false;
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}
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bool operator < (const matrix& A, const matrix& B) {
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for(int i=0; i<MWDIM; i++) for(int j=0; j<MWDIM; j++)
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if(A[i][j] != B[i][j]) return A[i][j] < B[i][j];
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return false;
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}
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int btspin(int id, int d) {
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EX int btspin(int id, int d) {
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return S7*(id/S7) + (id + d) % S7;
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}
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#if HDR
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struct fpattern {
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int Prime, wsquare, Field;
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@ -217,12 +221,7 @@ struct fpattern {
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return make_pair(gmul(a.first,b), a.second);
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}
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int order(const matrix& M) {
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int cnt = 1;
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matrix Po = M;
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while(Po != Id) Po = mmul(Po, M), cnt++;
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return cnt;
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}
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int order(const matrix& M);
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string decodepath(int i) {
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string s;
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@ -237,154 +236,9 @@ struct fpattern {
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int cs, sn, ch, sh;
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int solve() {
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for(int a=0; a<MWDIM; a++) for(int b=0; b<MWDIM; b++) Id[a][b] = a==b?1:0;
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int solve();
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if(!isprime(Prime)) {
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return 1;
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}
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rotations = WDIM == 2 ? S7 : 4;
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local_group = WDIM == 2 ? S7 : 24;
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for(int pw=1; pw<3; pw++) {
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if(pw>3) break;
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Field = pw==1? Prime : Prime*Prime;
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if(pw == 2) {
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for(wsquare=1; wsquare<Prime; wsquare++) {
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int roots = 0;
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for(int a=0; a<Prime; a++) if((a*a)%Prime == wsquare) roots++;
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if(!roots) break;
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}
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} else wsquare = 0;
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#ifdef EASY
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std::vector<int> sqrts(Prime, 0);
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for(int k=1-Prime; k<Prime; k++) sqrts[sqr(k)] = k;
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int fmax = Prime;
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#else
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std::vector<int> sqrts(Field);
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for(int k=0; k<Field; k++) sqrts[sqr(k)] = k;
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int fmax = Field;
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#endif
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if(Prime == 13 && wsquare && false) {
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for(int i=0; i<Prime; i++) printf("%3d", sqrts[i]);
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printf("\n");
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}
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R = P = X = Id;
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X[1][1] = 0; X[2][2] = 0;
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X[1][2] = 1; X[2][1] = Prime-1;
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for(cs=0; cs<fmax; cs++) {
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int sb = sub(1, sqr(cs));
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sn = sqrts[sb];
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R[0][0] = cs; R[1][1] = cs;
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R[0][1] = sn; R[1][0] = sub(0, sn);
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matrix Z = R;
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for(int i=1; i<rotations; i++) {
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if(Z == Id) goto nextcs;
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Z = mmul(Z, R);
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}
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if(Z != Id) continue;
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if(R[0][0] == 1) continue;
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for(ch=2; ch<fmax; ch++) {
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int chx = sub(mul(ch,ch), 1);
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sh = sqrts[chx];
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P[0][0] = sub(0, ch);
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P[0][WDIM] = sub(0, sh);
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P[1][1] = Prime-1;
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P[WDIM][0] = sh;
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P[WDIM][WDIM] = ch;
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matrix Z1 = mmul(P, R);
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matrix Z = Z1;
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for(int i=1; i<S3; i++) {
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if(Z == Id) goto nextch;
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Z = mmul(Z, Z1);
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}
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if(Z == Id) return 0;
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nextch: ;
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}
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nextcs: ;
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}
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}
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return 2;
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}
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void build() {
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for(int i=0; i<isize(qpaths); i++) {
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matrix M = strtomatrix(qpaths[i]);
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qcoords.push_back(M);
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printf("Solved %s as matrix of order %d\n", qpaths[i].c_str(), order(M));
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}
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matcode.clear(); matrices.clear();
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add(Id);
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if(isize(matrices) != local_group) { printf("Error: rotation crash #1 (%d)\n", isize(matrices)); exit(1); }
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connections.clear();
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for(int i=0; i<(int)matrices.size(); i++) {
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matrix M = matrices[i];
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matrix PM = mmul(P, M);
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add(PM);
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if(isize(matrices) % local_group) { printf("Error: rotation crash (%d)\n", isize(matrices)); exit(1); }
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if(!matcode.count(PM)) { printf("Error: not marked\n"); exit(1); }
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connections.push_back(matcode[PM]);
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}
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DEBB(DF_FIELD, ("Computing inverses...\n"));
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int N = isize(matrices);
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DEBB(DF_FIELD, ("Number of heptagons: %d\n", N));
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if(WDIM == 3) return;
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rrf.resize(N); rrf[0] = S7-1;
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for(int i=0; i<N; i++)
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rrf[btspin(i,1)] = btspin(rrf[i], 1),
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rrf[connections[i]] = connections[rrf[i]];
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rpf.resize(N); rpf[0] = S7;
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for(int i=0; i<N; i++)
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rpf[btspin(i,1)] = btspin(rpf[i], 1),
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rpf[connections[i]] = connections[rpf[i]];
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inverses.resize(N);
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inverses[0] = 0;
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for(int i=0; i<N; i++) // inverses[i] = gpow(i, N-1);
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inverses[btspin(i,1)] = rrf[inverses[i]], // btspin(inverses[i],6),
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inverses[connections[i]] = rpf[inverses[i]];
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int errs = 0;
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for(int i=0; i<N; i++) if(gmul(i, inverses[i])) errs++;
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if(errs) printf("errs = %d\n", errs);
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if(0) for(int i=0; i<isize(matrices); i++) {
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printf("%5d/%4d", connections[i], inverses[i]);
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if(i%S7 == S7-1) printf("\n");
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}
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DEBB(DF_FIELD, ("Built.\n"));
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}
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void build();
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static const int MAXDIST = 120;
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@ -395,265 +249,14 @@ struct fpattern {
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int distflower0;
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vector<eItem> markers;
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int getdist(pair<int,bool> a, vector<char>& dists);
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int getdist(pair<int,bool> a, pair<int,bool> b);
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int dijkstra(vector<char>& dists, vector<int> indist[MAXDIST]);
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void analyze();
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int getdist(pair<int,bool> a, vector<char>& dists) {
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if(!a.second) return dists[a.first];
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int m = MAXDIST;
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int ma = dists[a.first];
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int mb = dists[connections[btspin(a.first, 3)]];
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int mc = dists[connections[btspin(a.first, 4)]];
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m = min(m, 1 + ma);
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m = min(m, 1 + mb);
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m = min(m, 1 + mc);
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if(m <= 2 && ma+mb+mc <= m*3-2) return m-1; // special case
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m = min(m, 2 + dists[connections[btspin(a.first, 2)]]);
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m = min(m, 2 + dists[connections[btspin(a.first, 5)]]);
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m = min(m, 2 + dists[connections[btspin(connections[btspin(a.first, 3)], 5)]]);
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return m;
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}
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int getdist(pair<int,bool> a, pair<int,bool> b) {
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if(a.first == b.first) return a.second == b.second ? 0 : 1;
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if(b.first) a.first = gmul(a.first, inverses[b.first]), b.first = 0;
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return getdist(a, b.second ? disthex : disthep);
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}
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int maxdist, otherpole, circrad, wallid, wallorder, riverid;
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int dijkstra(vector<char>& dists, vector<int> indist[MAXDIST]) {
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int N = connections.size();
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dists.resize(N);
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for(int i=0; i<N; i++) dists[i] = MAXDIST-1;
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int maxd = 0;
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for(int i=0; i<MAXDIST; i++) while(!indist[i].empty()) {
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int at = indist[i].back();
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indist[i].pop_back();
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if(dists[at] <= i) continue;
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maxd = i;
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dists[at] = i;
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for(int q=0; q<S7; q++) {
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dists[at] = i;
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if(PURE) // todo-variation: PURE here?
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indist[i+1].push_back(connections[at]);
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else {
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indist[i+2].push_back(connections[at]);
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indist[i+3].push_back(connections[btspin(connections[at], 2)]);
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}
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at = btspin(at, 1);
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}
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}
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return maxd;
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}
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void analyze() {
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if(WDIM == 3) return;
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DEBB(DF_FIELD, ("variation = %d\n", int(variation)));
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int N = connections.size();
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markers.resize(N);
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vector<int> indist[MAXDIST];
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indist[0].push_back(0);
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int md0 = dijkstra(disthep, indist);
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indist[1].push_back(0);
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indist[1].push_back(connections[3]);
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indist[1].push_back(connections[4]);
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indist[2].push_back(connections[btspin(connections[3], 5)]);
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indist[2].push_back(connections[2]);
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indist[2].push_back(connections[5]);
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int md1 = dijkstra(disthex, indist);
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maxdist = max(md0, md1);
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otherpole = 0;
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for(int i=0; i<N; i+=S7) {
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int mp = 0;
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for(int q=0; q<S7; q++) if(disthep[connections[i+q]] < disthep[i]) mp++;
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if(mp == S7) {
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bool eq = true;
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for(int q=0; q<S7; q++) if(disthep[connections[i+q]] != disthep[connections[i]]) eq = false;
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if(eq) {
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// for(int q=0; q<S7; q++) printf("%3d", disthep[connections[i+q]]);
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// printf(" (%2d) at %d\n", disthep[i], i);
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if(disthep[i] > disthep[otherpole]) otherpole = i;
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// for(int r=0; r<S7; r++) {
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// printf("Matrix: "); for(int a=0; a<3; a++) for(int b=0; b<3; b++)
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// printf("%4d", matrices[i+r][a][b]); printf("\n");
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// }
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}
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}
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}
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circrad = 99;
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for(int i=0; i<N; i++) for(int u=2; u<4; u++) if(disthep[i] < circrad)
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if(disthep[connections[i]] < disthep[i] && disthep[connections[btspin(i,u)]] < disthep[i])
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circrad = disthep[i];
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DEBB(DF_FIELD, ("maxdist = %d otherpole = %d circrad = %d\n", maxdist, otherpole, circrad));
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matrix PRRR = strtomatrix("PRRR");
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matrix PRRPRRRRR = strtomatrix("PRRPRRRRR");
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matrix PRRRP = strtomatrix("PRRRP");
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matrix PRP = strtomatrix("PRP");
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matrix PR = strtomatrix("PR");
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matrix Wall = strtomatrix("RRRPRRRRRPRRRP");
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wallorder = order(Wall);
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wallid = matcode[Wall];
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DEBB(DF_FIELD, ("wall order = %d\n", wallorder));
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#define SETDIST(X, d, it) {int c = matcode[X]; indist[d].push_back(c); if(it == itNone) ; else if(markers[c] && markers[c] != it) markers[c] = itBuggy; else markers[c] = it; }
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matrix W = Id;
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for(int i=0; i<wallorder; i++) {
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SETDIST(W, 0, itAmethyst)
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W = mmul(W, Wall);
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}
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W = P;
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for(int i=0; i<wallorder; i++) {
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SETDIST(W, 0, itEmerald)
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W = mmul(W, Wall);
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}
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int walldist = dijkstra(distwall, indist);
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DEBB(DF_FIELD, ("wall dist = %d\n", walldist));
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W = strtomatrix("RRRRPR");
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for(int j=0; j<wallorder; j++) {
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W = mmul(W, Wall);
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for(int i=0; i<wallorder; i++) {
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SETDIST(W, 0, itNone)
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SETDIST(mmul(PRRR, W), 1, itNone)
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W = mmul(Wall, W);
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}
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}
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dijkstra(distwall2, indist);
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int rpushid = matcode[PRRPRRRRR];
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riverid = 0;
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for(int i=0; i<N; i++) {
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int j = i;
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int ipush = gmul(rpushid, i);
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for(int k=0; k<wallorder; k++) {
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if(ipush == j) {
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DEBB(DF_FIELD, ("River found at %d:%d\n", i, k));
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riverid = i;
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goto riveridfound;
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}
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j = gmul(j, wallid);
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}
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}
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riveridfound: ;
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W = strtomatrix("RRRRPR");
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for(int j=0; j<wallorder; j++) {
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W = mmul(W, Wall);
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for(int i=0; i<wallorder; i++) {
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if(i == 7) SETDIST(W, 0, itCoast)
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if(i == 3) SETDIST(mmul(PRRRP, W), 0, itWhirlpool)
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W = mmul(Wall, W);
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}
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}
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dijkstra(PURE ? distriver : distflower, indist);
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W = matrices[riverid];
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for(int i=0; i<wallorder; i++) {
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SETDIST(W, 0, itStatue)
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W = mmul(W, Wall);
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}
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W = mmul(P, W);
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for(int i=0; i<wallorder; i++) {
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SETDIST(W, 0, itSapphire)
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W = mmul(W, Wall);
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}
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W = mmul(PRP, matrices[riverid]);
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for(int i=0; i<wallorder; i++) {
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SETDIST(W, 1, itShard)
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W = mmul(W, Wall);
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}
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W = mmul(PR, matrices[riverid]);
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for(int i=0; i<wallorder; i++) {
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SETDIST(W, 1, itGold)
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W = mmul(W, Wall);
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}
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int riverdist = dijkstra(PURE ? distflower : distriver, indist);
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DEBB(DF_FIELD, ("river dist = %d\n", riverdist));
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for(int i=0; i<isize(currfp.matrices); i++)
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if(currfp.distflower[i] == 0) {
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distflower0 = currfp.inverses[i]+1;
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break;
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}
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||||
if(!PURE) {
|
||||
W = matrices[riverid];
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itStatue)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(PR, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itGold)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(P, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 1, itSapphire)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
dijkstra(distriverleft, indist);
|
||||
W = mmul(PRP, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itShard)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(P, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itSapphire)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = matrices[riverid];
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 1, itStatue)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
dijkstra(distriverright, indist);
|
||||
}
|
||||
else {
|
||||
W = strtomatrix("RRRRPR");
|
||||
for(int j=0; j<wallorder; j++) {
|
||||
W = mmul(W, Wall);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
if(i == 7) SETDIST(W, 0, itCoast)
|
||||
W = mmul(Wall, W);
|
||||
}
|
||||
}
|
||||
dijkstra(distriverleft, indist);
|
||||
W = strtomatrix("RRRRPR");
|
||||
for(int j=0; j<wallorder; j++) {
|
||||
W = mmul(W, Wall);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
if(i == 3) SETDIST(mmul(PRRRP, W), 0, itWhirlpool)
|
||||
W = mmul(Wall, W);
|
||||
}
|
||||
}
|
||||
dijkstra(distriverright, indist);
|
||||
}
|
||||
|
||||
DEBB(DF_FIELD, ("wall-river distance = %d\n", distwall[riverid]));
|
||||
DEBB(DF_FIELD, ("river-wall distance = %d\n", distriver[0]));
|
||||
}
|
||||
|
||||
bool easy(int i) {
|
||||
return i < Prime || !(i % Prime);
|
||||
}
|
||||
@ -676,17 +279,421 @@ struct fpattern {
|
||||
init(p);
|
||||
}
|
||||
|
||||
void findsubpath() {
|
||||
int N = isize(matrices);
|
||||
for(int i=1; i<N; i++)
|
||||
if(gpow(i, Prime) == 0) {
|
||||
subpathid = i;
|
||||
subpathorder = Prime;
|
||||
DEBB(DF_FIELD, ("Subpath found: %s\n", decodepath(i).c_str()));
|
||||
return;
|
||||
}
|
||||
}
|
||||
void findsubpath();
|
||||
};
|
||||
#endif
|
||||
|
||||
int fpattern::solve() {
|
||||
|
||||
for(int a=0; a<MWDIM; a++) for(int b=0; b<MWDIM; b++) Id[a][b] = a==b?1:0;
|
||||
|
||||
if(!isprime(Prime)) {
|
||||
return 1;
|
||||
}
|
||||
|
||||
rotations = WDIM == 2 ? S7 : 4;
|
||||
local_group = WDIM == 2 ? S7 : 24;
|
||||
|
||||
for(int pw=1; pw<3; pw++) {
|
||||
if(pw>3) break;
|
||||
Field = pw==1? Prime : Prime*Prime;
|
||||
|
||||
if(pw == 2) {
|
||||
for(wsquare=1; wsquare<Prime; wsquare++) {
|
||||
int roots = 0;
|
||||
for(int a=0; a<Prime; a++) if((a*a)%Prime == wsquare) roots++;
|
||||
if(!roots) break;
|
||||
}
|
||||
} else wsquare = 0;
|
||||
|
||||
#ifdef EASY
|
||||
std::vector<int> sqrts(Prime, 0);
|
||||
for(int k=1-Prime; k<Prime; k++) sqrts[sqr(k)] = k;
|
||||
int fmax = Prime;
|
||||
#else
|
||||
std::vector<int> sqrts(Field);
|
||||
for(int k=0; k<Field; k++) sqrts[sqr(k)] = k;
|
||||
int fmax = Field;
|
||||
#endif
|
||||
|
||||
if(Prime == 13 && wsquare && false) {
|
||||
for(int i=0; i<Prime; i++) printf("%3d", sqrts[i]);
|
||||
printf("\n");
|
||||
}
|
||||
|
||||
R = P = X = Id;
|
||||
X[1][1] = 0; X[2][2] = 0;
|
||||
X[1][2] = 1; X[2][1] = Prime-1;
|
||||
|
||||
for(cs=0; cs<fmax; cs++) {
|
||||
int sb = sub(1, sqr(cs));
|
||||
|
||||
sn = sqrts[sb];
|
||||
|
||||
R[0][0] = cs; R[1][1] = cs;
|
||||
R[0][1] = sn; R[1][0] = sub(0, sn);
|
||||
|
||||
matrix Z = R;
|
||||
for(int i=1; i<rotations; i++) {
|
||||
if(Z == Id) goto nextcs;
|
||||
Z = mmul(Z, R);
|
||||
}
|
||||
|
||||
if(Z != Id) continue;
|
||||
if(R[0][0] == 1) continue;
|
||||
|
||||
for(ch=2; ch<fmax; ch++) {
|
||||
int chx = sub(mul(ch,ch), 1);
|
||||
|
||||
sh = sqrts[chx];
|
||||
P[0][0] = sub(0, ch);
|
||||
P[0][WDIM] = sub(0, sh);
|
||||
P[1][1] = Prime-1;
|
||||
P[WDIM][0] = sh;
|
||||
P[WDIM][WDIM] = ch;
|
||||
|
||||
matrix Z1 = mmul(P, R);
|
||||
matrix Z = Z1;
|
||||
for(int i=1; i<S3; i++) {
|
||||
if(Z == Id) goto nextch;
|
||||
Z = mmul(Z, Z1);
|
||||
}
|
||||
if(Z == Id) return 0;
|
||||
nextch: ;
|
||||
}
|
||||
nextcs: ;
|
||||
}
|
||||
}
|
||||
|
||||
return 2;
|
||||
}
|
||||
|
||||
int fpattern::order(const matrix& M) {
|
||||
int cnt = 1;
|
||||
matrix Po = M;
|
||||
while(Po != Id) Po = mmul(Po, M), cnt++;
|
||||
return cnt;
|
||||
}
|
||||
|
||||
void fpattern::build() {
|
||||
|
||||
for(int i=0; i<isize(qpaths); i++) {
|
||||
matrix M = strtomatrix(qpaths[i]);
|
||||
qcoords.push_back(M);
|
||||
printf("Solved %s as matrix of order %d\n", qpaths[i].c_str(), order(M));
|
||||
}
|
||||
|
||||
matcode.clear(); matrices.clear();
|
||||
add(Id);
|
||||
if(isize(matrices) != local_group) { printf("Error: rotation crash #1 (%d)\n", isize(matrices)); exit(1); }
|
||||
|
||||
connections.clear();
|
||||
|
||||
for(int i=0; i<(int)matrices.size(); i++) {
|
||||
|
||||
matrix M = matrices[i];
|
||||
|
||||
matrix PM = mmul(P, M);
|
||||
|
||||
add(PM);
|
||||
|
||||
if(isize(matrices) % local_group) { printf("Error: rotation crash (%d)\n", isize(matrices)); exit(1); }
|
||||
|
||||
if(!matcode.count(PM)) { printf("Error: not marked\n"); exit(1); }
|
||||
|
||||
connections.push_back(matcode[PM]);
|
||||
}
|
||||
|
||||
DEBB(DF_FIELD, ("Computing inverses...\n"));
|
||||
int N = isize(matrices);
|
||||
|
||||
DEBB(DF_FIELD, ("Number of heptagons: %d\n", N));
|
||||
|
||||
if(WDIM == 3) return;
|
||||
|
||||
rrf.resize(N); rrf[0] = S7-1;
|
||||
for(int i=0; i<N; i++)
|
||||
rrf[btspin(i,1)] = btspin(rrf[i], 1),
|
||||
rrf[connections[i]] = connections[rrf[i]];
|
||||
|
||||
rpf.resize(N); rpf[0] = S7;
|
||||
for(int i=0; i<N; i++)
|
||||
rpf[btspin(i,1)] = btspin(rpf[i], 1),
|
||||
rpf[connections[i]] = connections[rpf[i]];
|
||||
|
||||
inverses.resize(N);
|
||||
inverses[0] = 0;
|
||||
for(int i=0; i<N; i++) // inverses[i] = gpow(i, N-1);
|
||||
inverses[btspin(i,1)] = rrf[inverses[i]], // btspin(inverses[i],6),
|
||||
inverses[connections[i]] = rpf[inverses[i]];
|
||||
|
||||
int errs = 0;
|
||||
for(int i=0; i<N; i++) if(gmul(i, inverses[i])) errs++;
|
||||
if(errs) printf("errs = %d\n", errs);
|
||||
|
||||
if(0) for(int i=0; i<isize(matrices); i++) {
|
||||
printf("%5d/%4d", connections[i], inverses[i]);
|
||||
if(i%S7 == S7-1) printf("\n");
|
||||
}
|
||||
|
||||
DEBB(DF_FIELD, ("Built.\n"));
|
||||
}
|
||||
|
||||
int fpattern::getdist(pair<int,bool> a, vector<char>& dists) {
|
||||
if(!a.second) return dists[a.first];
|
||||
int m = MAXDIST;
|
||||
int ma = dists[a.first];
|
||||
int mb = dists[connections[btspin(a.first, 3)]];
|
||||
int mc = dists[connections[btspin(a.first, 4)]];
|
||||
m = min(m, 1 + ma);
|
||||
m = min(m, 1 + mb);
|
||||
m = min(m, 1 + mc);
|
||||
if(m <= 2 && ma+mb+mc <= m*3-2) return m-1; // special case
|
||||
m = min(m, 2 + dists[connections[btspin(a.first, 2)]]);
|
||||
m = min(m, 2 + dists[connections[btspin(a.first, 5)]]);
|
||||
m = min(m, 2 + dists[connections[btspin(connections[btspin(a.first, 3)], 5)]]);
|
||||
return m;
|
||||
}
|
||||
|
||||
int fpattern::getdist(pair<int,bool> a, pair<int,bool> b) {
|
||||
if(a.first == b.first) return a.second == b.second ? 0 : 1;
|
||||
if(b.first) a.first = gmul(a.first, inverses[b.first]), b.first = 0;
|
||||
return getdist(a, b.second ? disthex : disthep);
|
||||
}
|
||||
|
||||
int fpattern::dijkstra(vector<char>& dists, vector<int> indist[MAXDIST]) {
|
||||
int N = connections.size();
|
||||
dists.resize(N);
|
||||
for(int i=0; i<N; i++) dists[i] = MAXDIST-1;
|
||||
int maxd = 0;
|
||||
for(int i=0; i<MAXDIST; i++) while(!indist[i].empty()) {
|
||||
int at = indist[i].back();
|
||||
indist[i].pop_back();
|
||||
if(dists[at] <= i) continue;
|
||||
maxd = i;
|
||||
dists[at] = i;
|
||||
for(int q=0; q<S7; q++) {
|
||||
dists[at] = i;
|
||||
if(PURE) // todo-variation: PURE here?
|
||||
indist[i+1].push_back(connections[at]);
|
||||
else {
|
||||
indist[i+2].push_back(connections[at]);
|
||||
indist[i+3].push_back(connections[btspin(connections[at], 2)]);
|
||||
}
|
||||
at = btspin(at, 1);
|
||||
}
|
||||
}
|
||||
return maxd;
|
||||
}
|
||||
|
||||
void fpattern::analyze() {
|
||||
|
||||
if(WDIM == 3) return;
|
||||
|
||||
DEBB(DF_FIELD, ("variation = %d\n", int(variation)));
|
||||
int N = connections.size();
|
||||
|
||||
markers.resize(N);
|
||||
|
||||
vector<int> indist[MAXDIST];
|
||||
|
||||
indist[0].push_back(0);
|
||||
int md0 = dijkstra(disthep, indist);
|
||||
|
||||
indist[1].push_back(0);
|
||||
indist[1].push_back(connections[3]);
|
||||
indist[1].push_back(connections[4]);
|
||||
indist[2].push_back(connections[btspin(connections[3], 5)]);
|
||||
indist[2].push_back(connections[2]);
|
||||
indist[2].push_back(connections[5]);
|
||||
int md1 = dijkstra(disthex, indist);
|
||||
|
||||
maxdist = max(md0, md1);
|
||||
|
||||
otherpole = 0;
|
||||
|
||||
for(int i=0; i<N; i+=S7) {
|
||||
int mp = 0;
|
||||
for(int q=0; q<S7; q++) if(disthep[connections[i+q]] < disthep[i]) mp++;
|
||||
if(mp == S7) {
|
||||
bool eq = true;
|
||||
for(int q=0; q<S7; q++) if(disthep[connections[i+q]] != disthep[connections[i]]) eq = false;
|
||||
if(eq) {
|
||||
// for(int q=0; q<S7; q++) printf("%3d", disthep[connections[i+q]]);
|
||||
// printf(" (%2d) at %d\n", disthep[i], i);
|
||||
if(disthep[i] > disthep[otherpole]) otherpole = i;
|
||||
// for(int r=0; r<S7; r++) {
|
||||
// printf("Matrix: "); for(int a=0; a<3; a++) for(int b=0; b<3; b++)
|
||||
// printf("%4d", matrices[i+r][a][b]); printf("\n");
|
||||
// }
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
circrad = 99;
|
||||
|
||||
for(int i=0; i<N; i++) for(int u=2; u<4; u++) if(disthep[i] < circrad)
|
||||
if(disthep[connections[i]] < disthep[i] && disthep[connections[btspin(i,u)]] < disthep[i])
|
||||
circrad = disthep[i];
|
||||
|
||||
DEBB(DF_FIELD, ("maxdist = %d otherpole = %d circrad = %d\n", maxdist, otherpole, circrad));
|
||||
|
||||
matrix PRRR = strtomatrix("PRRR");
|
||||
matrix PRRPRRRRR = strtomatrix("PRRPRRRRR");
|
||||
matrix PRRRP = strtomatrix("PRRRP");
|
||||
matrix PRP = strtomatrix("PRP");
|
||||
matrix PR = strtomatrix("PR");
|
||||
matrix Wall = strtomatrix("RRRPRRRRRPRRRP");
|
||||
|
||||
wallorder = order(Wall);
|
||||
wallid = matcode[Wall];
|
||||
|
||||
DEBB(DF_FIELD, ("wall order = %d\n", wallorder));
|
||||
|
||||
#define SETDIST(X, d, it) {int c = matcode[X]; indist[d].push_back(c); if(it == itNone) ; else if(markers[c] && markers[c] != it) markers[c] = itBuggy; else markers[c] = it; }
|
||||
|
||||
matrix W = Id;
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itAmethyst)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = P;
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itEmerald)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
|
||||
int walldist = dijkstra(distwall, indist);
|
||||
DEBB(DF_FIELD, ("wall dist = %d\n", walldist));
|
||||
|
||||
|
||||
W = strtomatrix("RRRRPR");
|
||||
for(int j=0; j<wallorder; j++) {
|
||||
W = mmul(W, Wall);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itNone)
|
||||
SETDIST(mmul(PRRR, W), 1, itNone)
|
||||
W = mmul(Wall, W);
|
||||
}
|
||||
}
|
||||
dijkstra(distwall2, indist);
|
||||
|
||||
int rpushid = matcode[PRRPRRRRR];
|
||||
riverid = 0;
|
||||
|
||||
for(int i=0; i<N; i++) {
|
||||
int j = i;
|
||||
int ipush = gmul(rpushid, i);
|
||||
for(int k=0; k<wallorder; k++) {
|
||||
if(ipush == j) {
|
||||
DEBB(DF_FIELD, ("River found at %d:%d\n", i, k));
|
||||
riverid = i;
|
||||
goto riveridfound;
|
||||
}
|
||||
j = gmul(j, wallid);
|
||||
}
|
||||
}
|
||||
|
||||
riveridfound: ;
|
||||
|
||||
W = strtomatrix("RRRRPR");
|
||||
for(int j=0; j<wallorder; j++) {
|
||||
W = mmul(W, Wall);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
if(i == 7) SETDIST(W, 0, itCoast)
|
||||
if(i == 3) SETDIST(mmul(PRRRP, W), 0, itWhirlpool)
|
||||
W = mmul(Wall, W);
|
||||
}
|
||||
}
|
||||
dijkstra(PURE ? distriver : distflower, indist);
|
||||
|
||||
W = matrices[riverid];
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itStatue)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(P, W);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itSapphire)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(PRP, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 1, itShard)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(PR, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 1, itGold)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
int riverdist = dijkstra(PURE ? distflower : distriver, indist);
|
||||
DEBB(DF_FIELD, ("river dist = %d\n", riverdist));
|
||||
|
||||
for(int i=0; i<isize(currfp.matrices); i++)
|
||||
if(currfp.distflower[i] == 0) {
|
||||
distflower0 = currfp.inverses[i]+1;
|
||||
break;
|
||||
}
|
||||
|
||||
if(!PURE) {
|
||||
W = matrices[riverid];
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itStatue)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(PR, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itGold)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(P, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 1, itSapphire)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
dijkstra(distriverleft, indist);
|
||||
W = mmul(PRP, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itShard)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = mmul(P, matrices[riverid]);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 0, itSapphire)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
W = matrices[riverid];
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
SETDIST(W, 1, itStatue)
|
||||
W = mmul(W, Wall);
|
||||
}
|
||||
dijkstra(distriverright, indist);
|
||||
}
|
||||
else {
|
||||
W = strtomatrix("RRRRPR");
|
||||
for(int j=0; j<wallorder; j++) {
|
||||
W = mmul(W, Wall);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
if(i == 7) SETDIST(W, 0, itCoast)
|
||||
W = mmul(Wall, W);
|
||||
}
|
||||
}
|
||||
dijkstra(distriverleft, indist);
|
||||
W = strtomatrix("RRRRPR");
|
||||
for(int j=0; j<wallorder; j++) {
|
||||
W = mmul(W, Wall);
|
||||
for(int i=0; i<wallorder; i++) {
|
||||
if(i == 3) SETDIST(mmul(PRRRP, W), 0, itWhirlpool)
|
||||
W = mmul(Wall, W);
|
||||
}
|
||||
}
|
||||
dijkstra(distriverright, indist);
|
||||
}
|
||||
|
||||
DEBB(DF_FIELD, ("wall-river distance = %d\n", distwall[riverid]));
|
||||
DEBB(DF_FIELD, ("river-wall distance = %d\n", distriver[0]));
|
||||
}
|
||||
|
||||
int fpattern::orderstats() {
|
||||
int N = isize(matrices);
|
||||
@ -713,6 +720,16 @@ int fpattern::orderstats() {
|
||||
return ordsample[Prime];
|
||||
}
|
||||
|
||||
void fpattern::findsubpath() {
|
||||
int N = isize(matrices);
|
||||
for(int i=1; i<N; i++)
|
||||
if(gpow(i, Prime) == 0) {
|
||||
subpathid = i;
|
||||
subpathorder = Prime;
|
||||
DEBB(DF_FIELD, ("Subpath found: %s\n", decodepath(i).c_str()));
|
||||
return;
|
||||
}
|
||||
}
|
||||
|
||||
fpattern fp43(43);
|
||||
|
||||
@ -747,7 +764,8 @@ void info() {
|
||||
printf("cases found = %d (%d hard)\n", cases, hard);
|
||||
}
|
||||
|
||||
fpattern current_quotient_field(0), fp_invalid(0);
|
||||
EX fpattern current_quotient_field = fpattern(0);
|
||||
EX fpattern fp_invalid = fpattern(0);
|
||||
bool quotient_field_changed;
|
||||
|
||||
EX struct fpattern& getcurrfp() {
|
||||
|
||||
Loading…
Reference in New Issue
Block a user