PLOTLIB_INLINE PVec::PVec( const PVec &x, std::function< double( double ) > function )
{
for ( const auto &val : x.GetData() )
{
mData.push_back( function( val ) );
}
}
int shortestDistance(int xMe, int yMe, int xHome, int yHome, vector <string> teleports) {
#if 1
PVec points;
points.push_back(P(xMe, yMe));
points.push_back(P(xHome, yHome));
PPMap warp;
int i;
for (i = 0; i < (int)teleports.size(); ++i) {
istringstream s(teleports[i]);
P p1, p2;
s >> p1.first >> p1.second >> p2.first >> p2.second;
points.push_back(p1);
points.push_back(p2);
warp[p1] = p2;
warp[p2] = p1;
}
LLV Done(points.size());
PLLMap Costs;
LL total = 0;
int min_index = 0;
while (min_index != 1) {
Done[min_index] = 1;
P Last = points[min_index];
LL min_cost = INF;
for (i = 1; i < (int)points.size(); ++i) {
if (Done[i]) {
continue;
}
LL prev = Costs[points[i]];
LL d = Distance(Last, points[i]);
PPMap::const_iterator it = warp.find(points[i]);
if (it != warp.end()) {
LL w = 10 + Distance(Last, it->second);
d = min(d, w);
}
LL cost = total + d;
if (!prev || cost < prev) {
Costs[points[i]] = cost;
} else {
cost = prev;
}
if (cost < min_cost) {
min_index = i;
min_cost = cost;
}
}
total = min_cost;
}
return (int)total;
#else
P Me(xMe, yMe);
P Home(xHome, yHome);
PVec pv1, pv2;
LLV GoalCost;
int i, j;
for (i = 0; i < (int)teleports.size(); ++i) {
int x1, y1, x2, y2;
if (sscanf(teleports[i].c_str(), "%d %d %d %d", &x1, &y1, &x2, &y2) != 4) {
return -1;
}
pv1.push_back(P(x1, y1));
pv2.push_back(P(x2, y2));
// teleport + walk to goal
GoalCost.push_back(10 + Distance(*pv2.rbegin(), Home));
pv1.push_back(P(x2, y2));
pv2.push_back(P(x1, y1));
GoalCost.push_back(10 + Distance(*pv2.rbegin(), Home));
}
bool f = true;
while (f) {
f = false;
for (i = 0; i < (int)pv1.size(); ++i) {
for (j = 0; j < (int)pv1.size(); ++j) {
if (i == j) {
continue;
}
// teleport + walk to anther spot + teleport
LL cost = 10 + Distance(pv2[i], pv1[j]) + GoalCost[j];
if (cost < GoalCost[i]) {
f = true;
GoalCost[i] = cost;
}
}
}
}
LL Min = Distance(Me, Home);
for (i = 0; i < (int)pv1.size(); ++i) {
Min = min(Min, Distance(Me, pv1[i]) + GoalCost[i]);
}
return (int)Min;
#endif
}
int main()
{
using jlt::operator<<;
using std::cout;
using std::cerr;
using std::endl;
using std::setw;
typedef jlt::mathmatrix<int> Mat;
typedef std::vector<int> Vec;
typedef jlt::polynomial<int> Poly;
typedef std::vector<Poly> PVec;
typedef std::vector<Mat> MVec;
typedef long long int llint;
#if 1
std::ifstream indata;
indata.open("polycoeffs_n=7.m");
const int n = 7;
PVec pl;
// Read in Mathematica file of polynomials.
skipstring(indata,
"(* Created by Wolfram Mathematica ??? : www.wolfram.com *)");
skipstring(indata,"{");
do
{
skipstring(indata,"{");
Poly p;
for (int i = n; i >= 0; --i)
{
indata >> p[i];
if (i > 0) skipstring(indata,",");
}
skipstring(indata,"}");
pl.push_back(p);
}
while (skipstring(indata,","));
Poly p = pl[0];
#else
const int n = 4;
Poly p;
p[0] = 1;
p[n] = 1;
p[n/2] = -1;
p[n/2+1] = -1;
p[n/2-1] = -1;
#endif
int tr = -p[n-1];
cerr << "Checking polynomial " << p;
double lambdamax = findroot(p,2.0,1e-8);
cerr << " with root " << lambdamax << endl;
// Create lower-triangle of matrices.
MVec Alow;
// Vector of positions of the "1" entry.
// 0 <= al[k] <= k+1. al[k]=k+1 corresponds to no 1 at all.
Vec al(n), almax(n);
for (int k = 0; k < n; ++k) almax[k] = k+1;
do
{
Mat A(n,n);
int trA = 0;
for (int k = 0; k < n; ++k)
{
if (al[k] < k+1) A(k,al[k]) = 1;
if (al[k] == k) ++trA;
}
if (trA == tr) Alow.push_back(A);
}
while(increment_vector(al,almax));
cerr << Alow.size() << " lower-triangular forms\n";
int todo = Alow.size();
//
// Upper-triangle of matrices: find valid patterns
//
int Nup = (n*(n-1))/2;
Vec aup(Nup), aupmax(Nup);
for (int k = 0; k < Nup; ++k) {
aupmax[k] = 1;
}
// Make index pair for eack k.
Vec rowidx(Nup), colidx(Nup);
{
int row = 0, col = 1;
for (int k = 0; k < Nup; ++k)
{
rowidx[k] = row;
colidx[k] = col++;
if (col == n) {
++row;
col = row+1;
}
}
}
llint N = 0;
llint validpatterns = 0;
llint reduciblepatterns = 0;
llint rootexceeded = 0;
cout << "{\n";
bool thefirst = true;
for (int li = 0; li < (int)todo; ++li)
{
cerr << "Lower-triangular form " << setw(4) << li+1 << ": ";
// Vector of allowable patterns.
std::vector<Vec> pattern;
int n1min = -1, n1max = -1;
do
{
// Form matrix.
Mat A(Alow[li]);
for (int k = 0; k < Nup; ++k) A(rowidx[k],colidx[k]) = aup[k];
++N;
if (spectral_radius(A) <= lambdamax)
{
if (!A.isReducible())
{
++validpatterns;
pattern.push_back(aup);
int n1 = std::count(aup.begin(),aup.end(),1);
if (n1 < n1min || n1min == -1) n1min = n1;
if (n1 > n1max || n1max == -1) n1max = n1;
}
else
{
++reduciblepatterns;
}
}
else
{
++rootexceeded;
}
}
while(increment_vector(aup,aupmax));
cerr << setw(5) << pattern.size() << " valid patterns";
// Skip lower-triangular forms with no allowable patterns.
if (pattern.empty()) {
cerr << endl;
continue;
}
cerr << " (size ";
int Alownorm = matrix_norm(Alow[li]);
cerr << setw(2) << n1min+Alownorm << " to ";
cerr << setw(2) << n1max+Alownorm << ")\n";
for (int pa = 0; pa < (int)pattern.size(); ++pa)
{
// How many 1's in this pattern?
int Npat = std::count(pattern[pa].begin(),pattern[pa].end(),1);
// Make index pair for eack k.
Vec patrowidx(Npat), patcolidx(Npat);
{
int row = 0, col = 1, m = 0;
for (int k = 0; k < (n*(n-1))/2; ++k)
{
if (pattern[pa][k] == 1)
{
patrowidx[m] = row;
patcolidx[m] = col;
++m;
}
if (++col == n) {
++row;
col = row+1;
}
}
}
// Form matrix.
// Start with the pattern equal to all ones.
Mat A(Alow[li]);
for (int k = 0; k < Npat; ++k) A(patrowidx[k],patcolidx[k]) = 1;
// Now loop over vales of the entries of the pattern
do
{
++N;
// Compute characteristic polynomial.
Poly cpoly(A.charpoly());
if (cpoly == p)
{
cerr << "Got it!\n";
if (!thefirst) cout << "," << endl;
else thefirst = false;
A.printMathematicaForm(cout);
}
}
while(increment_upper_triangle(A,patrowidx,patcolidx,lambdamax));
}
}
cout << "\n}\n";
cerr << validpatterns << endl;
cerr << reduciblepatterns << endl;
cerr << rootexceeded << endl;
cerr << N << endl;
}
PLOTLIB_INLINE std::string AbstractPlot::ToArray( const PVec &vec )
{
const std::vector< std::string > vecStr = vec.GetStrings();
return vecStr.size() ? ToArray( vecStr ) : ToArray( vec.GetData() );
}