English
#include <cstdio>
#include <set>
#include <iostream>
#include <assert.h>
#include <algorithm>
#include <string>
#include <vector>
#include <string.h>
#include <stdio.h>
#include <unordered_map>
// TODO: Maybe comment this out before submit.
//#define DBG_CHECKS
//#define DBG_FULL
#define DEB 0
// #define DBG_CHECKS
#define USE_SUBPROBLEM_CACHE 1
#define USE_NS_CACHE 0
#if DEB == 1
#include <sys/types.h>
#include <unistd.h>
void sleepSec(float t) {
usleep(t * 1E6);
}
#endif
// TODO: UWAGA NA TO PRZED WYSLANIEM
//#include "message.h"
//#include "palindromy.h"
#define deb(x) cout << #x << " = " << x << endl;
using namespace std;
// Dwa z najczesciej uzywanych typow o dlugich nazwach
// - ich skrocenie jest bardzo istotne
typedef vector<int> VI;
typedef long long LL;
// W programach bardzo rzadko mozna znalezc w pelni zapisana instrukcje petli.
// Zamiast niej wykorzystywane sa trzy nastepujace makra:
// FOR - petla zwiekszajaca zmienna x od b do e wlacznie
#define FOR(x, b, e) for(int x = b; x <= (e); ++x)
// FORD - petla zmniejszajaca zmienna x od b do e wlacznie
#define FORD(x, b, e) for(int x = b; x >= (e); --x)
// REP - petla zwiekszajaca zmienna x od 0 do n. Jest ona bardzo czesto
// wykorzystywana do konstruowania i przegladania struktur danych
#define REP(x, n) for(int x = 0; x < (n); ++x)
// Makro VAR(v,n) deklaruje nowa zmienna o nazwie v oraz typie i wartosci
// zmiennej n. Jest ono czesto wykorzystywane podczas operowania na
// iteratorach struktur danych z biblioteki STL, ktorych nazwy typow sa bardzo dlugie
#define VAR(v, n) __typeof(n) v = (n)
// ALL(c) reprezentuje pare iteratorow wskazujacych odpowiednio na pierwszy
// i za ostatni element w strukturach danych STL. Makro to jest bardzo
// przydatne chociazby w przypadku korzystania z funkcji sort, ktora jako
// parametry przyjmuje pare iteratorow reprezentujacych przedzial
// elementow do posortowania
#define ALL(c) (c).begin(), (c).end()
// Ponizsze makro sluzy do wyznaczania rozmiaru struktur danych STL.
// Uzywa sie go w programach, zamiast pisac po prostu x.size() ze wzgledu na to,
// iz wyrazenie x.size() jest typu unsigned int i w przypadku porownywania
// z typem int w procesie kompilacji generowane jest ostrzezenie
#define SIZE(x) ((int)(x).size())
// Bardzo pozyteczne makro sluzace do iterowania po wszystkich elementach
// w strukturach danych STL
#define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
// Skrot - zamiast pisac push_back podczas wstawiania elementow na koniec
// struktury danych, takiej jak vector, wystarczy napisac PB
#define PB push_back
// Podobnie - zamiast first bedziemy pisali po prostu ST
#define ST first
// a zamiast second - ND
#define ND second
// tl tr br bl
int arrow_chr[4][4] = {
{3, 0xE2, 0x86, 0x96},
{3, 0xE2, 0x86, 0x97},
{3, 0xE2, 0x86, 0x98},
{3, 0xE2, 0x86, 0x99},
};
int sqr_chr[] = {4,0xF0,0x9F,0x9E,0x8E};
int box_chr[] = {3, 0xE2,0x8C,0xB7};
int SWNEOfs[4][2] = { {0,-1}, {-1,0}, {0,1}, {1, 0}};
string pc8(const int *s) {
char buf[10];
REP(i, s[0])
sprintf(buf+i, "%c", s[i+1]);
return buf;
}
const char *MAP_LVL0[] =
{
" - ",
"| |",
" ",
};
const int LVL0_SZ = 3;
const char *MAP_LVLN[] =
{
" H H ",
"HcH HcH",
" h - h ",
"| |",
" H H ",
"hcH Hch",
" H H ",
};
const int LVLN_SZ = 7;
struct Pt {
char x, y;
Pt(): x(0), y(0) {}
Pt(char x, char y): x(x), y(y) {}
Pt operator+(const Pt &s) const { return Pt(x+s.x, y+s.y); }
Pt operator-(const Pt &s) const { return Pt(x-s.x, y-s.y); }
Pt operator*(const int &n) const { return Pt(x*n, y*n); }
bool operator==(const Pt &s) const { return x == s.x && y == s.y; }
bool operator!=(const Pt &s) const { return !(*this == s); }
Pt bounce(bool horiz) {
if (horiz) y = -y; else x = -x;
return *this;
}
LL hash() {
const LL LPRIME = 1000000007;
LL h = 37*LPRIME;
h = h*LPRIME+x;
h = h*LPRIME+y;
return h*LPRIME;
}
};
ostream &operator<<(ostream &o, const Pt &p) {
return o << "Pt("<<(int)p.x<<", "<<(int)p.y<<")";
}
struct CharHolder {
int refs;
vector<vector<char> > m;
LL _hash;
LL hash() {
const LL LPRIME = 43594442599UL;
if (_hash != -1) return _hash;
_hash = 0;
REP(x, SIZE(m)) REP(y, SIZE(m[0]))
_hash = _hash * LPRIME + m[x][y];
return _hash*LPRIME;
}
CharHolder(): refs(0), _hash(-1) {
}
};
struct Map {
CharHolder *chld;
char w, h; // x \in [0,w-1]; y \in [0,h-1]; (0,0) bottom left on screen
Map():chld(NULL) {
defCopy();
}
Map(const Map &mp) {
h = mp.h;
w = mp.w;
chld = mp.chld;
if (chld != NULL)
chld->refs += 1;
}
Map &operator=(const Map &mp) {
h = mp.h;
w = mp.w;
chld = mp.chld;
if (chld != NULL)
chld->refs += 1;
return *this;
}
~Map() {
freeChld();
}
void freeChld() {
if (chld != NULL) {
chld->refs -= 1;
if (chld->refs == 0)
delete chld;
chld = NULL;
}
}
void defCopy() {
CharHolder *ch = new CharHolder();
ch->refs = 1;
if (chld != NULL) {
ch->m = chld->m;
freeChld();
}
ch->_hash = -1;
chld = ch;
}
bool inMap(Pt p) const {
if (p.x < 0 || p.x >= w) return false;
if (p.y < 0 || p.y >= h) return false;
return true;
}
bool inBorder(Pt p, bool &horizBord) {
if (p.x == 0 || p.x == w-1) {
horizBord = false;
return true;
}
if (p.y == 0 || p.y == h-1) {
horizBord = true;
return true;
}
return false;
}
bool inBorder(Pt p) { bool u; return inBorder(p, u); }
char cell(const Pt &p) const {
if (DEB && !inMap(p)) {
if (DEB) cerr << "ERROR: Read cell " << p << " outside map!" << endl;
}
return chld->m[p.x][p.y];
}
char cell(int x, int y) const { return cell(Pt(x, y)); }
char &cellW(const Pt &p) {
if (!inMap(p)) {
if (DEB) cerr << "ERROR: Read cell " << p << " outside map!" << endl;
}
chld->_hash = -1;
return chld->m[p.x][p.y];
}
char &cellW(int x, int y) { return cellW(Pt(x, y)); }
void resize(char w, char h) {
this->w=w;
this->h=h;
defCopy();
chld->_hash = -1;
chld->m.clear(); chld->m.resize(w, vector<char>(h, ' '));
}
// TODO probably integrate with higher mechanism
void loadMap(const char *lines[], int sz) {
resize(sz+2, sz+2);
REP(r, sz) {
REP(c, sz) {
cellW(c+1, sz-r) = lines[r][c];
}
}
REP(x, w) REP(y, h) {
Pt p(x, y);
if (inBorder(p)) cellW(p) = '#';
}
}
LL hash() {
const LL LPRIME = 19168104274513UL;
LL hsVal = 47*LPRIME;
hsVal = hsVal*LPRIME+w;
hsVal = hsVal*LPRIME+h;
hsVal = hsVal*LPRIME+chld->hash();
return hsVal*LPRIME;
}
};
ostream &operator<<(ostream &o, Map &m) {
o << "Map(w=" << (int)m.w << ", h=" << (int)m.h << "):" << endl;
FORD(y, m.h-1, 0) {
FOR(x, 0, m.w-1) {
Pt cur(x, y);
o << m.cell(x, y);
}
o << endl;
}
return o;
}
struct MapTransform {
private:
Map m;
public:
vector<Pt> fixPts;
MapTransform(){}
MapTransform(Map &m) {
setMap(m);
}
void setMap(Map &m) {
this->m = m;
this->m.defCopy();
}
Map getMap() {
Map nm = m;
nm.defCopy();
return nm;
}
int mapW() { return m.w; }
int mapH() { return m.h; }
void cropTo(const vector<Pt> &pts) {
int minX=1E9, maxX=-1E9;
int minY=minX, maxY=maxX;
FOREACH(it, pts) {
minX = min(minX, (int)it->x);
minY = min(minY, (int)it->y);
maxX = max(maxX, (int)it->x);
maxY = max(maxY, (int)it->y);
}
auto &mv = m.chld->m;
_trimTo(mv, minX, maxX);
m.w = SIZE(mv);
REP(x, m.w) {
_trimTo(mv[x], minY, maxY);
m.h = SIZE(mv[x]);
}
FOREACH(it, fixPts) {
it->x -= minX;
it->y -= minY;
}
}
void cropTo(Pt p, Pt q) {
vector<Pt> v;
v.PB(p);
v.PB(q);
cropTo(v);
}
void extendX(int x, int newW) {
auto &mv = m.chld->m;
_extendVec(mv, x, newW);
m.w = SIZE(mv);
int incr = newW-1;
FOREACH(it, fixPts)
if (it->x > x) it->x += incr;
}
void extendY(int y, int newW) {
auto &mv = m.chld->m;
REP(x, m.w)
_extendVec(mv[x], y, newW);
m.h = SIZE(mv[0]);
int incr = newW-1;
FOREACH(it, fixPts)
if (it->y > y) it->y += incr;
}
void rotate(int k) {
REP(i, k) {
Map mr;
mr.resize(m.h, m.w);
REP(x, m.w) REP(y, m.h) {
Pt bef(x, y), aft(y, m.w-1-x);
char c = m.cell(bef);
if (c == '-') c = '|';
else if (c == '|') c = '-';
mr.cellW(aft) = c;
}
m = mr;
}
if (!fixPts.empty() && DEB)
cerr << "ERROR! fixPts not available for rotate()" << endl;
}
void paste(Pt p, Map &ms) {
REP(x, ms.w) REP(y, ms.h) {
Pt c(x, y);
m.cellW(c+p) = ms.cell(c);
}
}
template<typename T>
void _extendVec(vector<T> &v, int x, int newW){
vector<T> ncentr(newW-1, v[x]);
v.insert(v.begin()+x, ALL(ncentr));
}
template<typename T>
void _trimTo(vector<T> &v, int l, int h) {
v.erase(v.begin()+h+1, v.end());
v.erase(v.begin(), v.begin()+l);
}
};
struct HilbertSqr {
Pt p; // bot.-left cor.
Pt tr; // top-right cor.
Pt c; // hil. center
char rotation; // nr of clockwise turns 0 - hil. entrance on bottom
bool horizEntry; // entered from top/bot.
};
struct MapState {
Map m;
Pt p; // pos of the ball
Pt v; // vel of the ball
Pt t; // map target loc
#if USE_NS_CACHE == 1
bool isHilHit; // TODO Possibly unneeded
#endif
void loadState(const char *lines[], int sz) {
p = Pt(1, 0);
v = Pt(1, 1);
t = Pt(0, 1);
m.loadMap(lines, sz);
}
string pickArrow() {
// tl tr br bl
if (v == Pt(-1, 1)) return pc8(arrow_chr[0]);
if (v == Pt(1, 1)) return pc8(arrow_chr[1]);
if (v == Pt(1, -1)) return pc8(arrow_chr[2]);
if (v == Pt(-1, -1)) return pc8(arrow_chr[3]);
assert(false); return "";
}
LL hash() {
const LL LPRIME = 592344878353UL;
LL h = 31*LPRIME;
h = h*LPRIME+p.hash();
h = h*LPRIME+v.hash();
h = h*LPRIME+t.hash();
h = h*LPRIME+m.hash();
return h*LPRIME;
}
};
ostream &operator<<(ostream &o, MapState &s) {
FORD(y, s.m.h-1, 0) {
FOR(x, 0, s.m.w-1) {
Pt cur(x, y);
if (cur == s.p) o << s.pickArrow();
else if(cur == s.t) o << '+';
// else if(s.m.cell(x, y) == ' ') o << pc8(box_chr);
else o << s.m.cell(x, y);
}
o << endl;
}
return o;
}
struct StateResult {
StateResult():steps(0), dx(0), dy(0) {}
StateResult(LL st, LL dx, LL dy):steps(st), dx(dx), dy(dy) {}
LL steps;
LL dx, dy;
StateResult operator+(const StateResult &s) const {
return StateResult(steps+s.steps, dx+s.dx, dy+s.dy);
}
StateResult operator+(const Pt &p) const {
return StateResult(steps+1, dx+p.x, dy+p.y);
}
};
ostream &operator<<(ostream &o, const StateResult &s) {
o << "StateResult(" << s.steps << ", " << s.dx << ", " << s.dy << ")";
return o;
}
struct AnswerGather {
vector<LL> queries, x, y;
void check() {
if(DEB)
REP(i, SIZE(queries)-1) {
if (queries[i] > queries[i+1] && DEB)
cerr << "ERROR: Input contains a decreasing query" << endl;
}
}
bool hasNext() {
return SIZE(x) < SIZE(queries);
}
LL next() {
return queries[SIZE(x)];
}
void answer(LL ax, LL ay) {
x.PB(ax); y.PB(ay);
}
};
struct HilbertBall {
MapTransform hilNLvl;
MapTransform hil0Lvl;
std::unordered_map<LL, StateResult> stateCache;
std::unordered_map<LL, MapState> subprCache;
#if USE_NS_CACHE == 1
std::unordered_map<LL, MapState> nextStateCache;
#endif
LL solveCalls, cashHits;
HilbertBall() {
hilNLvl = _loadHilLvl(MAP_LVLN, LVLN_SZ);
hil0Lvl = _loadHilLvl(MAP_LVL0, LVL0_SZ);
solveCalls = cashHits = 0;
}
MapTransform _loadHilLvl(const char *lines[], int sz) {
MapTransform mt;
MapState ms;
ms.loadState(lines, sz);
mt.setMap(ms.m);
mt.cropTo(Pt(1,1), Pt(sz, sz));
return mt;
}
bool inHilbert(Map &m, Pt p, HilbertSqr &hs) {
if (tolower(m.cell(p)) == 'h') {
hs.c = _findCentr(m, p);
hs.rotation = _findRot(m, hs.c);
hs.p = hs.c - Pt(1, 1);
hs.tr = hs.c + Pt(1, 1);
hs.horizEntry = (p.x == hs.c.x);
return true;
}
return false;
}
bool inHilbert(MapState &s, HilbertSqr &hs) {
return inHilbert(s.m, s.p, hs);
}
char _findRot(Map &m, Pt c) {
REP(r, 4) {
Pt ofs(SWNEOfs[r][0], SWNEOfs[r][1]);
if (m.cell(c+ofs) == 'h')
return r;
}
if (DEB) cerr << "ERROR: _findRot: 'h' not found!" << endl;
return 0;
}
Pt _findCentr(Map &m, Pt p) {
REP(r, 4) {
Pt c(SWNEOfs[r][0], SWNEOfs[r][1]);
c = c+p;
if(m.cell(c)=='c') {
return c;
}
}
if (DEB) cerr << "ERROR: _findCentr: Center not found!" << endl;
return Pt();
}
// s - base state - must be inHilbert
MapState hilSubproblem(MapState &s, bool lvl0Case=false,
bool useGeneralSubs=false) {
LL h;
if(USE_SUBPROBLEM_CACHE) {
solveCalls += 1;
const LL LPRIME = 3206828235229UL;
h = s.hash()*LPRIME + lvl0Case;
h *= LPRIME;
auto it = subprCache.find(h);
if (it != subprCache.end()) {
cashHits += 1;
return it->ND;
}
}
HilbertSqr hs;
if (!inHilbert(s, hs)) {
if(DEB)
cerr << "ERROR: hilSubproblem called for not inHilbert" << endl;
}
Pt vBeforeEntry = Pt(s.v).bounce(hs.horizEntry);
Pt nStart = s.p-vBeforeEntry, nTrg = s.v + s.p;
MapTransform mt(s.m);
mt.fixPts.PB(nStart); // 0
mt.fixPts.PB(nTrg); // 1
if (useGeneralSubs)
_generalHilbSubst(mt, s.m, lvl0Case);
else
_twoCaseHilbSubst(hs, mt, s, nStart, lvl0Case);
MapState ns;
ns.m = mt.getMap();
ns.p = mt.fixPts[0];
ns.v = vBeforeEntry;
ns.t = mt.fixPts[1];
if(USE_SUBPROBLEM_CACHE) {
subprCache[h] = ns;
}
return ns;
}
MapState hilSubstitute(MapState &s, bool lvl0Case=false) {
MapTransform mt(s.m);
mt.fixPts.PB(s.p); // 0
mt.fixPts.PB(s.t); // 1
_generalHilbSubst(mt, s.m, lvl0Case);
MapState ns;
ns.m = mt.getMap();
ns.p = mt.fixPts[0];
ns.v = s.v;
ns.t = mt.fixPts[1];
return ns;
}
void _twoCaseHilbSubst(HilbertSqr &hs, MapTransform &mt, MapState &s,
Pt nStart, bool lvl0Case) {
mt.fixPts.PB(hs.c); // 2
mt.fixPts.PB(hs.p); // 3
mt.fixPts.PB(hs.tr); // 4
if (s.m.cell(nStart) == '#') {
// Just one hilbert.
mt.cropTo(mt.fixPts);
_insertHilb(mt, 2, 3, hs.rotation, 0, lvl0Case);
}
else {
HilbertSqr hs2;
Pt othHilbP = s.p + (s.p-hs.c)*2;
if (!inHilbert(s.m, othHilbP, hs2) && DEB)
cerr << "ERROR: Ohter hilbert not found!" << endl;
mt.fixPts.PB(hs2.p); // 5
mt.fixPts.PB(hs2.tr); // 6
mt.fixPts.PB(hs2.c); // 7
mt.cropTo(mt.fixPts);
_insertHilb(mt, 2, 3, hs.rotation, 0, lvl0Case);
// If same x, do only y. Do only x otherwise.
int extOpt = (hs2.c.x == hs.c.x) ? 2 : 1;
_insertHilb(mt, 7, 5, hs2.rotation, extOpt, lvl0Case);
}
}
// extOpt == 0 - both ways, extOpt == 1 only X, extOpt == 2 only Y
// extOpt == -1 - no extending
void _insertHilb(MapTransform &mt, int cFpNr, int pasteFpNr, int rot,
int extOpt, bool lvl0Case) {
MapTransform *lvl = (lvl0Case ? &hil0Lvl : &hilNLvl);
Pt cc;
if (extOpt >= 0) {
if (extOpt != 2) {
cc = mt.fixPts[cFpNr];
mt.extendX(cc.x, lvl->mapW()-2);
}
if (extOpt != 1) {
cc = mt.fixPts[cFpNr];
mt.extendY(cc.y, lvl->mapH()-2);
}
}
Pt pp = mt.fixPts[pasteFpNr];
MapTransform pasteEl = *lvl;
pasteEl.rotate(rot);
Map mp = pasteEl.getMap();
mt.paste(pp, mp);
}
void _generalHilbSubst(MapTransform &mt, Map &m, bool lvl0Case) {
VI xs, ys;
VI corPos, rot;
REP(x, m.w) REP(y, m.h) {
Pt cp(x, y);
HilbertSqr sprop;
if (m.cell(cp) == 'h' && inHilbert(m, cp, sprop)) {
corPos.PB(SIZE(mt.fixPts));
rot.PB(sprop.rotation);
mt.fixPts.PB(sprop.p);
mt.fixPts.PB(sprop.tr);
xs.PB(sprop.c.x);
ys.PB(sprop.c.y);
}
}
// Save the border!
mt.fixPts.PB(Pt(0,0));
mt.fixPts.PB(Pt(m.w-1, m.h-1));
mt.cropTo(mt.fixPts);
sort(ALL(xs)); xs.erase(unique(ALL(xs)), xs.end());
sort(ALL(ys)); ys.erase(unique(ALL(ys)), ys.end());
reverse(ALL(xs));
reverse(ALL(ys));
MapTransform *lvl = (lvl0Case ? &hil0Lvl : &hilNLvl);
FOREACH(it, xs) mt.extendX(*it, lvl->mapW()-2);
FOREACH(it, ys) mt.extendY(*it, lvl->mapH()-2);
REP(i, SIZE(corPos)) {
_insertHilb(mt, 0, corPos[i], rot[i], -1, lvl0Case);
}
}
MapState nextState(MapState &s, bool &hilHit) {
#if USE_NS_CACHE == 1
LL h;
// cout << "Cache query for " << endl << s << endl;
h = s.hash();
auto it = nextStateCache.find(h);
if (it != nextStateCache.end()) {
hilHit = it->ND.isHilHit;
// cout << "CH: " << it->ND << " ih:" << it->ND.isHilHit << " H:" << h << endl;
return it->ND;
}
#endif
MapState ns = s;
Pt np = s.p + s.v;
ns.p = np;
bool horiz;
if (ns.m.cell(np) == '#' && ns.m.inBorder(np, horiz))
ns.v.bounce(horiz);
if(ns.m.cell(np) == '|') ns.v.bounce(false);
if(ns.m.cell(np) == '-') ns.v.bounce(true);
//HilbertSqr hs;
//if ((hilHit = inHilbert(ns, hs)))
hilHit = (tolower(ns.m.cell(ns.p)) == 'h');
if (hilHit) {
Pt horBncP = ns.p+Pt(ns.v).bounce(true);
if (ns.m.inMap(horBncP) && tolower(ns.m.cell(horBncP)) == 'h')
ns.v.bounce(false);
else
ns.v.bounce(true);
}
#if USE_NS_CACHE == 1
ns.isHilHit = hilHit;
// cout << "PC: " << ns << " ih:" << ns.isHilHit << " H:" << h << endl;
nextStateCache[h] = ns;
#endif
return ns;
}
StateResult solveState(MapState &s, int hilLvl, bool ldeb=false) {
StateResult r;
solveCalls += 1;
const LL LPRIME = 107814156778397UL;
LL h = s.hash()*LPRIME + hilLvl;
auto it = stateCache.find(h);
if (it != stateCache.end()) {
cashHits += 1;
return it->ND;
}
if(ldeb) cout << "solveState call (lvl=" << hilLvl << "): " << endl << s << endl;
MapState cs = s;
while (cs.p != cs.t) {
bool hilHit;
Pt p0 = cs.p;
cs = nextState(cs, hilHit);
if(ldeb) cout << "Step: " << endl << cs << endl;
if (hilHit) {
MapState substate = hilSubproblem(cs, hilLvl==1);
if(ldeb) cout << "solveState generated subproblem (lvl="
<<hilLvl<<"):" << endl << substate << endl;
StateResult subr = solveState(substate, hilLvl-1);
r = r + subr;
cs = nextState(cs, hilHit);
}
else
r = r + (cs.p - p0);
if(ldeb) cout << "Result after step: " << r << endl;
}
if(ldeb) cout << "Final result: " << r << endl;
stateCache[h] = r;
return r;
}
StateResult resAfterSteps(LL steps, MapState &s, int hilLvl, bool ldeb=false) {
StateResult r;
if(ldeb) cout << "resAfterSteps call lvl="<<hilLvl << " steps=" << steps
<< ": " << endl << s << endl;
MapState cs = s;
while (cs.p != cs.t) {
bool hilHit;
Pt p0 = cs.p;
cs = nextState(cs, hilHit);
if(ldeb) cout << "Step: " << r << endl;
if (hilHit) {
MapState substate = hilSubproblem(cs, hilLvl==1);
if(ldeb) cout << "resAfterSteps generated subproblem (lvl="
<<hilLvl<<"):" << endl << substate << endl;
StateResult cumr = r + solveState(substate, hilLvl-1, ldeb);
if(ldeb) cout << "Subproblem return with cumr=" << cumr << endl;
if (cumr.steps > steps) {
if(ldeb) cout << "Will solve subproblem, and then add " << r << endl;
return resAfterSteps(steps - r.steps, substate,
hilLvl-1, ldeb) + r;
}
else if (cumr.steps == steps) {
return cumr;
}
else {
r = cumr;
cs = nextState(cs, hilHit);
}
}
else
r = r + (cs.p - p0);
if(ldeb) cout << "Result after step: " << r << endl << cs << endl;
if (r.steps == steps) {
return r;
}
}
if (DEB) cerr << "ERROR: We should never get to end of resAfterSteps"
<< endl;
return r;
}
void posAfterSteps(int lvl, LL steps, LL &x, LL &y, bool ldeb=false) {
MapState ms;
if (lvl == 0)
ms.loadState(MAP_LVL0, LVL0_SZ);
else
ms.loadState(MAP_LVLN, LVLN_SZ);
StateResult r = resAfterSteps(steps, ms, lvl, ldeb);
if(DEB && r.steps != steps) cerr << "ERROR: bad steps" << endl;
x = ms.p.x; x += r.dx;
y = ms.p.y; y += r.dy;
}
void batchResAfterSteps(StateResult r, AnswerGather &ag,
MapState &s, int hilLvl, bool ldeb=false) {
if(ldeb) cout << "batchResAfterSteps call lvl="<<hilLvl << ": " << endl << s << endl;
MapState cs = s;
while (cs.p != cs.t) {
bool hilHit;
Pt p0 = cs.p;
cs = nextState(cs, hilHit);
if(ldeb) cout << "Step: " << r << endl;
if (hilHit) {
MapState substate = hilSubproblem(cs, hilLvl==1);
if(ldeb) cout << "batchResAfterSteps generated subproblem (lvl="
<<hilLvl<<"):" << endl << substate << endl;
StateResult cumr = r + solveState(substate, hilLvl-1, ldeb);
if(ldeb) cout << "Subproblem return with cumr=" << cumr << endl;
if (cumr.steps > ag.next()) {
if(ldeb) cout << "Will solve subproblem " << endl;
batchResAfterSteps(r, ag, substate, hilLvl-1, ldeb);
}
if (!ag.hasNext()) return;
while (cumr.steps == ag.next()) {
ag.answer(cumr.dx, cumr.dy);
if (!ag.hasNext()) return;
}
r = cumr;
cs = nextState(cs, hilHit);
}
else
r = r + (cs.p - p0);
if(ldeb) cout << "Result after step: " << r << endl << cs << endl;
while (r.steps == ag.next()) {
ag.answer(r.dx, r.dy);
if (!ag.hasNext()) return;
}
}
}
void batchPosAfterSteps(int lvl, AnswerGather &ag, bool ldeb=false) {
MapState ms;
if (lvl == 0)
ms.loadState(MAP_LVL0, LVL0_SZ);
else
ms.loadState(MAP_LVLN, LVLN_SZ);
batchResAfterSteps(StateResult(), ag, ms, lvl, ldeb);
REP(i, SIZE(ag.x)) {
ag.x[i] += ms.p.x;
ag.y[i] += ms.p.y;
}
}
void printStats() {
deb(solveCalls);
double hitPerc = 100;
hitPerc *= cashHits;
hitPerc /= solveCalls;
deb(hitPerc);
deb(SIZE(stateCache))
deb(SIZE(subprCache))
}
};
void playHilbertOnLvl(int lvl, int stepLimit=-1) {
MapState ms;
if (lvl > 0)
ms.loadState(MAP_LVLN, LVLN_SZ);
else
ms.loadState(MAP_LVL0, LVL0_SZ);
HilbertBall hb;
while(1) {
lvl--;
ms = hb.hilSubstitute(ms, lvl==0);
if (lvl == 0) break;
}
cout << ms << endl;
int steps = 0;
while (true) {
cin.get();
bool hilHit;
ms = hb.nextState(ms, hilHit);
steps += 1;
cout << "After " << steps << " steps p=" << ms.p << endl;
cout << ms << endl;
if (stepLimit == steps)
return;
if (ms.p == Pt(0,1)) {
cout << "Ended after " << steps << " steps" << endl;
break;
}
}
}
void playHilbertShowSubprob() {
MapState ms; ms.loadState(MAP_LVLN, LVLN_SZ);
cout << ms << endl;
HilbertBall hb;
REP(i, 50) {
cin.get();
bool hilHit;
cout << "This is the next step:" << endl;
ms = hb.nextState(ms, hilHit);
cout << ms << endl;
if (hilHit) {
cin.get();
cout << "Hilbert was hit. This is the subproblem:" << endl;
MapState sms = hb.hilSubproblem(ms, true, true);
cout << sms << endl;
while(sms.t != sms.p) {
cin.get();
bool hit;
sms = hb.nextState(sms, hit);
cout << sms << endl<<endl;
}
cout << "Subproblem solved." << endl;
}
}
}
int main(int argc, char *argv[]) {
#define deb(x) cout << #x << " = " << x << endl;
if (argc == 2 && strcmp(argv[1], "debug") == 0 ) {
// printf("== [RUNNING IN DEBUG MODE]==\n\n");
char test_file_path[] = "/home/horban/workspace/Zadanka/in.txt";
freopen(test_file_path, "r", stdin);
}
// TODO: UWAGA NA TO PRZED WYSLANIEM
std::ios_base::sync_with_stdio(0);
HilbertBall hb;
int n, z;
cin >> n >> z;
AnswerGather ag;
REP(tnr, z) {
LL steps; cin >> steps;
ag.queries.PB(steps);
}
ag.check();
hb.batchPosAfterSteps(n-1, ag, false);
REP(tnr, z) {
cout << ag.x[tnr] << ' ' << ag.y[tnr] << endl;
}
if (DEB) hb.printStats();
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 | #include <cstdio> #include <set> #include <iostream> #include <assert.h> #include <algorithm> #include <string> #include <vector> #include <string.h> #include <stdio.h> #include <unordered_map> // TODO: Maybe comment this out before submit. //#define DBG_CHECKS //#define DBG_FULL #define DEB 0 // #define DBG_CHECKS #define USE_SUBPROBLEM_CACHE 1 #define USE_NS_CACHE 0 #if DEB == 1 #include <sys/types.h> #include <unistd.h> void sleepSec(float t) { usleep(t * 1E6); } #endif // TODO: UWAGA NA TO PRZED WYSLANIEM //#include "message.h" //#include "palindromy.h" #define deb(x) cout << #x << " = " << x << endl; using namespace std; // Dwa z najczesciej uzywanych typow o dlugich nazwach // - ich skrocenie jest bardzo istotne typedef vector<int> VI; typedef long long LL; // W programach bardzo rzadko mozna znalezc w pelni zapisana instrukcje petli. // Zamiast niej wykorzystywane sa trzy nastepujace makra: // FOR - petla zwiekszajaca zmienna x od b do e wlacznie #define FOR(x, b, e) for(int x = b; x <= (e); ++x) // FORD - petla zmniejszajaca zmienna x od b do e wlacznie #define FORD(x, b, e) for(int x = b; x >= (e); --x) // REP - petla zwiekszajaca zmienna x od 0 do n. Jest ona bardzo czesto // wykorzystywana do konstruowania i przegladania struktur danych #define REP(x, n) for(int x = 0; x < (n); ++x) // Makro VAR(v,n) deklaruje nowa zmienna o nazwie v oraz typie i wartosci // zmiennej n. Jest ono czesto wykorzystywane podczas operowania na // iteratorach struktur danych z biblioteki STL, ktorych nazwy typow sa bardzo dlugie #define VAR(v, n) __typeof(n) v = (n) // ALL(c) reprezentuje pare iteratorow wskazujacych odpowiednio na pierwszy // i za ostatni element w strukturach danych STL. Makro to jest bardzo // przydatne chociazby w przypadku korzystania z funkcji sort, ktora jako // parametry przyjmuje pare iteratorow reprezentujacych przedzial // elementow do posortowania #define ALL(c) (c).begin(), (c).end() // Ponizsze makro sluzy do wyznaczania rozmiaru struktur danych STL. // Uzywa sie go w programach, zamiast pisac po prostu x.size() ze wzgledu na to, // iz wyrazenie x.size() jest typu unsigned int i w przypadku porownywania // z typem int w procesie kompilacji generowane jest ostrzezenie #define SIZE(x) ((int)(x).size()) // Bardzo pozyteczne makro sluzace do iterowania po wszystkich elementach // w strukturach danych STL #define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i) // Skrot - zamiast pisac push_back podczas wstawiania elementow na koniec // struktury danych, takiej jak vector, wystarczy napisac PB #define PB push_back // Podobnie - zamiast first bedziemy pisali po prostu ST #define ST first // a zamiast second - ND #define ND second // tl tr br bl int arrow_chr[4][4] = { {3, 0xE2, 0x86, 0x96}, {3, 0xE2, 0x86, 0x97}, {3, 0xE2, 0x86, 0x98}, {3, 0xE2, 0x86, 0x99}, }; int sqr_chr[] = {4,0xF0,0x9F,0x9E,0x8E}; int box_chr[] = {3, 0xE2,0x8C,0xB7}; int SWNEOfs[4][2] = { {0,-1}, {-1,0}, {0,1}, {1, 0}}; string pc8(const int *s) { char buf[10]; REP(i, s[0]) sprintf(buf+i, "%c", s[i+1]); return buf; } const char *MAP_LVL0[] = { " - ", "| |", " ", }; const int LVL0_SZ = 3; const char *MAP_LVLN[] = { " H H ", "HcH HcH", " h - h ", "| |", " H H ", "hcH Hch", " H H ", }; const int LVLN_SZ = 7; struct Pt { char x, y; Pt(): x(0), y(0) {} Pt(char x, char y): x(x), y(y) {} Pt operator+(const Pt &s) const { return Pt(x+s.x, y+s.y); } Pt operator-(const Pt &s) const { return Pt(x-s.x, y-s.y); } Pt operator*(const int &n) const { return Pt(x*n, y*n); } bool operator==(const Pt &s) const { return x == s.x && y == s.y; } bool operator!=(const Pt &s) const { return !(*this == s); } Pt bounce(bool horiz) { if (horiz) y = -y; else x = -x; return *this; } LL hash() { const LL LPRIME = 1000000007; LL h = 37*LPRIME; h = h*LPRIME+x; h = h*LPRIME+y; return h*LPRIME; } }; ostream &operator<<(ostream &o, const Pt &p) { return o << "Pt("<<(int)p.x<<", "<<(int)p.y<<")"; } struct CharHolder { int refs; vector<vector<char> > m; LL _hash; LL hash() { const LL LPRIME = 43594442599UL; if (_hash != -1) return _hash; _hash = 0; REP(x, SIZE(m)) REP(y, SIZE(m[0])) _hash = _hash * LPRIME + m[x][y]; return _hash*LPRIME; } CharHolder(): refs(0), _hash(-1) { } }; struct Map { CharHolder *chld; char w, h; // x \in [0,w-1]; y \in [0,h-1]; (0,0) bottom left on screen Map():chld(NULL) { defCopy(); } Map(const Map &mp) { h = mp.h; w = mp.w; chld = mp.chld; if (chld != NULL) chld->refs += 1; } Map &operator=(const Map &mp) { h = mp.h; w = mp.w; chld = mp.chld; if (chld != NULL) chld->refs += 1; return *this; } ~Map() { freeChld(); } void freeChld() { if (chld != NULL) { chld->refs -= 1; if (chld->refs == 0) delete chld; chld = NULL; } } void defCopy() { CharHolder *ch = new CharHolder(); ch->refs = 1; if (chld != NULL) { ch->m = chld->m; freeChld(); } ch->_hash = -1; chld = ch; } bool inMap(Pt p) const { if (p.x < 0 || p.x >= w) return false; if (p.y < 0 || p.y >= h) return false; return true; } bool inBorder(Pt p, bool &horizBord) { if (p.x == 0 || p.x == w-1) { horizBord = false; return true; } if (p.y == 0 || p.y == h-1) { horizBord = true; return true; } return false; } bool inBorder(Pt p) { bool u; return inBorder(p, u); } char cell(const Pt &p) const { if (DEB && !inMap(p)) { if (DEB) cerr << "ERROR: Read cell " << p << " outside map!" << endl; } return chld->m[p.x][p.y]; } char cell(int x, int y) const { return cell(Pt(x, y)); } char &cellW(const Pt &p) { if (!inMap(p)) { if (DEB) cerr << "ERROR: Read cell " << p << " outside map!" << endl; } chld->_hash = -1; return chld->m[p.x][p.y]; } char &cellW(int x, int y) { return cellW(Pt(x, y)); } void resize(char w, char h) { this->w=w; this->h=h; defCopy(); chld->_hash = -1; chld->m.clear(); chld->m.resize(w, vector<char>(h, ' ')); } // TODO probably integrate with higher mechanism void loadMap(const char *lines[], int sz) { resize(sz+2, sz+2); REP(r, sz) { REP(c, sz) { cellW(c+1, sz-r) = lines[r][c]; } } REP(x, w) REP(y, h) { Pt p(x, y); if (inBorder(p)) cellW(p) = '#'; } } LL hash() { const LL LPRIME = 19168104274513UL; LL hsVal = 47*LPRIME; hsVal = hsVal*LPRIME+w; hsVal = hsVal*LPRIME+h; hsVal = hsVal*LPRIME+chld->hash(); return hsVal*LPRIME; } }; ostream &operator<<(ostream &o, Map &m) { o << "Map(w=" << (int)m.w << ", h=" << (int)m.h << "):" << endl; FORD(y, m.h-1, 0) { FOR(x, 0, m.w-1) { Pt cur(x, y); o << m.cell(x, y); } o << endl; } return o; } struct MapTransform { private: Map m; public: vector<Pt> fixPts; MapTransform(){} MapTransform(Map &m) { setMap(m); } void setMap(Map &m) { this->m = m; this->m.defCopy(); } Map getMap() { Map nm = m; nm.defCopy(); return nm; } int mapW() { return m.w; } int mapH() { return m.h; } void cropTo(const vector<Pt> &pts) { int minX=1E9, maxX=-1E9; int minY=minX, maxY=maxX; FOREACH(it, pts) { minX = min(minX, (int)it->x); minY = min(minY, (int)it->y); maxX = max(maxX, (int)it->x); maxY = max(maxY, (int)it->y); } auto &mv = m.chld->m; _trimTo(mv, minX, maxX); m.w = SIZE(mv); REP(x, m.w) { _trimTo(mv[x], minY, maxY); m.h = SIZE(mv[x]); } FOREACH(it, fixPts) { it->x -= minX; it->y -= minY; } } void cropTo(Pt p, Pt q) { vector<Pt> v; v.PB(p); v.PB(q); cropTo(v); } void extendX(int x, int newW) { auto &mv = m.chld->m; _extendVec(mv, x, newW); m.w = SIZE(mv); int incr = newW-1; FOREACH(it, fixPts) if (it->x > x) it->x += incr; } void extendY(int y, int newW) { auto &mv = m.chld->m; REP(x, m.w) _extendVec(mv[x], y, newW); m.h = SIZE(mv[0]); int incr = newW-1; FOREACH(it, fixPts) if (it->y > y) it->y += incr; } void rotate(int k) { REP(i, k) { Map mr; mr.resize(m.h, m.w); REP(x, m.w) REP(y, m.h) { Pt bef(x, y), aft(y, m.w-1-x); char c = m.cell(bef); if (c == '-') c = '|'; else if (c == '|') c = '-'; mr.cellW(aft) = c; } m = mr; } if (!fixPts.empty() && DEB) cerr << "ERROR! fixPts not available for rotate()" << endl; } void paste(Pt p, Map &ms) { REP(x, ms.w) REP(y, ms.h) { Pt c(x, y); m.cellW(c+p) = ms.cell(c); } } template<typename T> void _extendVec(vector<T> &v, int x, int newW){ vector<T> ncentr(newW-1, v[x]); v.insert(v.begin()+x, ALL(ncentr)); } template<typename T> void _trimTo(vector<T> &v, int l, int h) { v.erase(v.begin()+h+1, v.end()); v.erase(v.begin(), v.begin()+l); } }; struct HilbertSqr { Pt p; // bot.-left cor. Pt tr; // top-right cor. Pt c; // hil. center char rotation; // nr of clockwise turns 0 - hil. entrance on bottom bool horizEntry; // entered from top/bot. }; struct MapState { Map m; Pt p; // pos of the ball Pt v; // vel of the ball Pt t; // map target loc #if USE_NS_CACHE == 1 bool isHilHit; // TODO Possibly unneeded #endif void loadState(const char *lines[], int sz) { p = Pt(1, 0); v = Pt(1, 1); t = Pt(0, 1); m.loadMap(lines, sz); } string pickArrow() { // tl tr br bl if (v == Pt(-1, 1)) return pc8(arrow_chr[0]); if (v == Pt(1, 1)) return pc8(arrow_chr[1]); if (v == Pt(1, -1)) return pc8(arrow_chr[2]); if (v == Pt(-1, -1)) return pc8(arrow_chr[3]); assert(false); return ""; } LL hash() { const LL LPRIME = 592344878353UL; LL h = 31*LPRIME; h = h*LPRIME+p.hash(); h = h*LPRIME+v.hash(); h = h*LPRIME+t.hash(); h = h*LPRIME+m.hash(); return h*LPRIME; } }; ostream &operator<<(ostream &o, MapState &s) { FORD(y, s.m.h-1, 0) { FOR(x, 0, s.m.w-1) { Pt cur(x, y); if (cur == s.p) o << s.pickArrow(); else if(cur == s.t) o << '+'; // else if(s.m.cell(x, y) == ' ') o << pc8(box_chr); else o << s.m.cell(x, y); } o << endl; } return o; } struct StateResult { StateResult():steps(0), dx(0), dy(0) {} StateResult(LL st, LL dx, LL dy):steps(st), dx(dx), dy(dy) {} LL steps; LL dx, dy; StateResult operator+(const StateResult &s) const { return StateResult(steps+s.steps, dx+s.dx, dy+s.dy); } StateResult operator+(const Pt &p) const { return StateResult(steps+1, dx+p.x, dy+p.y); } }; ostream &operator<<(ostream &o, const StateResult &s) { o << "StateResult(" << s.steps << ", " << s.dx << ", " << s.dy << ")"; return o; } struct AnswerGather { vector<LL> queries, x, y; void check() { if(DEB) REP(i, SIZE(queries)-1) { if (queries[i] > queries[i+1] && DEB) cerr << "ERROR: Input contains a decreasing query" << endl; } } bool hasNext() { return SIZE(x) < SIZE(queries); } LL next() { return queries[SIZE(x)]; } void answer(LL ax, LL ay) { x.PB(ax); y.PB(ay); } }; struct HilbertBall { MapTransform hilNLvl; MapTransform hil0Lvl; std::unordered_map<LL, StateResult> stateCache; std::unordered_map<LL, MapState> subprCache; #if USE_NS_CACHE == 1 std::unordered_map<LL, MapState> nextStateCache; #endif LL solveCalls, cashHits; HilbertBall() { hilNLvl = _loadHilLvl(MAP_LVLN, LVLN_SZ); hil0Lvl = _loadHilLvl(MAP_LVL0, LVL0_SZ); solveCalls = cashHits = 0; } MapTransform _loadHilLvl(const char *lines[], int sz) { MapTransform mt; MapState ms; ms.loadState(lines, sz); mt.setMap(ms.m); mt.cropTo(Pt(1,1), Pt(sz, sz)); return mt; } bool inHilbert(Map &m, Pt p, HilbertSqr &hs) { if (tolower(m.cell(p)) == 'h') { hs.c = _findCentr(m, p); hs.rotation = _findRot(m, hs.c); hs.p = hs.c - Pt(1, 1); hs.tr = hs.c + Pt(1, 1); hs.horizEntry = (p.x == hs.c.x); return true; } return false; } bool inHilbert(MapState &s, HilbertSqr &hs) { return inHilbert(s.m, s.p, hs); } char _findRot(Map &m, Pt c) { REP(r, 4) { Pt ofs(SWNEOfs[r][0], SWNEOfs[r][1]); if (m.cell(c+ofs) == 'h') return r; } if (DEB) cerr << "ERROR: _findRot: 'h' not found!" << endl; return 0; } Pt _findCentr(Map &m, Pt p) { REP(r, 4) { Pt c(SWNEOfs[r][0], SWNEOfs[r][1]); c = c+p; if(m.cell(c)=='c') { return c; } } if (DEB) cerr << "ERROR: _findCentr: Center not found!" << endl; return Pt(); } // s - base state - must be inHilbert MapState hilSubproblem(MapState &s, bool lvl0Case=false, bool useGeneralSubs=false) { LL h; if(USE_SUBPROBLEM_CACHE) { solveCalls += 1; const LL LPRIME = 3206828235229UL; h = s.hash()*LPRIME + lvl0Case; h *= LPRIME; auto it = subprCache.find(h); if (it != subprCache.end()) { cashHits += 1; return it->ND; } } HilbertSqr hs; if (!inHilbert(s, hs)) { if(DEB) cerr << "ERROR: hilSubproblem called for not inHilbert" << endl; } Pt vBeforeEntry = Pt(s.v).bounce(hs.horizEntry); Pt nStart = s.p-vBeforeEntry, nTrg = s.v + s.p; MapTransform mt(s.m); mt.fixPts.PB(nStart); // 0 mt.fixPts.PB(nTrg); // 1 if (useGeneralSubs) _generalHilbSubst(mt, s.m, lvl0Case); else _twoCaseHilbSubst(hs, mt, s, nStart, lvl0Case); MapState ns; ns.m = mt.getMap(); ns.p = mt.fixPts[0]; ns.v = vBeforeEntry; ns.t = mt.fixPts[1]; if(USE_SUBPROBLEM_CACHE) { subprCache[h] = ns; } return ns; } MapState hilSubstitute(MapState &s, bool lvl0Case=false) { MapTransform mt(s.m); mt.fixPts.PB(s.p); // 0 mt.fixPts.PB(s.t); // 1 _generalHilbSubst(mt, s.m, lvl0Case); MapState ns; ns.m = mt.getMap(); ns.p = mt.fixPts[0]; ns.v = s.v; ns.t = mt.fixPts[1]; return ns; } void _twoCaseHilbSubst(HilbertSqr &hs, MapTransform &mt, MapState &s, Pt nStart, bool lvl0Case) { mt.fixPts.PB(hs.c); // 2 mt.fixPts.PB(hs.p); // 3 mt.fixPts.PB(hs.tr); // 4 if (s.m.cell(nStart) == '#') { // Just one hilbert. mt.cropTo(mt.fixPts); _insertHilb(mt, 2, 3, hs.rotation, 0, lvl0Case); } else { HilbertSqr hs2; Pt othHilbP = s.p + (s.p-hs.c)*2; if (!inHilbert(s.m, othHilbP, hs2) && DEB) cerr << "ERROR: Ohter hilbert not found!" << endl; mt.fixPts.PB(hs2.p); // 5 mt.fixPts.PB(hs2.tr); // 6 mt.fixPts.PB(hs2.c); // 7 mt.cropTo(mt.fixPts); _insertHilb(mt, 2, 3, hs.rotation, 0, lvl0Case); // If same x, do only y. Do only x otherwise. int extOpt = (hs2.c.x == hs.c.x) ? 2 : 1; _insertHilb(mt, 7, 5, hs2.rotation, extOpt, lvl0Case); } } // extOpt == 0 - both ways, extOpt == 1 only X, extOpt == 2 only Y // extOpt == -1 - no extending void _insertHilb(MapTransform &mt, int cFpNr, int pasteFpNr, int rot, int extOpt, bool lvl0Case) { MapTransform *lvl = (lvl0Case ? &hil0Lvl : &hilNLvl); Pt cc; if (extOpt >= 0) { if (extOpt != 2) { cc = mt.fixPts[cFpNr]; mt.extendX(cc.x, lvl->mapW()-2); } if (extOpt != 1) { cc = mt.fixPts[cFpNr]; mt.extendY(cc.y, lvl->mapH()-2); } } Pt pp = mt.fixPts[pasteFpNr]; MapTransform pasteEl = *lvl; pasteEl.rotate(rot); Map mp = pasteEl.getMap(); mt.paste(pp, mp); } void _generalHilbSubst(MapTransform &mt, Map &m, bool lvl0Case) { VI xs, ys; VI corPos, rot; REP(x, m.w) REP(y, m.h) { Pt cp(x, y); HilbertSqr sprop; if (m.cell(cp) == 'h' && inHilbert(m, cp, sprop)) { corPos.PB(SIZE(mt.fixPts)); rot.PB(sprop.rotation); mt.fixPts.PB(sprop.p); mt.fixPts.PB(sprop.tr); xs.PB(sprop.c.x); ys.PB(sprop.c.y); } } // Save the border! mt.fixPts.PB(Pt(0,0)); mt.fixPts.PB(Pt(m.w-1, m.h-1)); mt.cropTo(mt.fixPts); sort(ALL(xs)); xs.erase(unique(ALL(xs)), xs.end()); sort(ALL(ys)); ys.erase(unique(ALL(ys)), ys.end()); reverse(ALL(xs)); reverse(ALL(ys)); MapTransform *lvl = (lvl0Case ? &hil0Lvl : &hilNLvl); FOREACH(it, xs) mt.extendX(*it, lvl->mapW()-2); FOREACH(it, ys) mt.extendY(*it, lvl->mapH()-2); REP(i, SIZE(corPos)) { _insertHilb(mt, 0, corPos[i], rot[i], -1, lvl0Case); } } MapState nextState(MapState &s, bool &hilHit) { #if USE_NS_CACHE == 1 LL h; // cout << "Cache query for " << endl << s << endl; h = s.hash(); auto it = nextStateCache.find(h); if (it != nextStateCache.end()) { hilHit = it->ND.isHilHit; // cout << "CH: " << it->ND << " ih:" << it->ND.isHilHit << " H:" << h << endl; return it->ND; } #endif MapState ns = s; Pt np = s.p + s.v; ns.p = np; bool horiz; if (ns.m.cell(np) == '#' && ns.m.inBorder(np, horiz)) ns.v.bounce(horiz); if(ns.m.cell(np) == '|') ns.v.bounce(false); if(ns.m.cell(np) == '-') ns.v.bounce(true); //HilbertSqr hs; //if ((hilHit = inHilbert(ns, hs))) hilHit = (tolower(ns.m.cell(ns.p)) == 'h'); if (hilHit) { Pt horBncP = ns.p+Pt(ns.v).bounce(true); if (ns.m.inMap(horBncP) && tolower(ns.m.cell(horBncP)) == 'h') ns.v.bounce(false); else ns.v.bounce(true); } #if USE_NS_CACHE == 1 ns.isHilHit = hilHit; // cout << "PC: " << ns << " ih:" << ns.isHilHit << " H:" << h << endl; nextStateCache[h] = ns; #endif return ns; } StateResult solveState(MapState &s, int hilLvl, bool ldeb=false) { StateResult r; solveCalls += 1; const LL LPRIME = 107814156778397UL; LL h = s.hash()*LPRIME + hilLvl; auto it = stateCache.find(h); if (it != stateCache.end()) { cashHits += 1; return it->ND; } if(ldeb) cout << "solveState call (lvl=" << hilLvl << "): " << endl << s << endl; MapState cs = s; while (cs.p != cs.t) { bool hilHit; Pt p0 = cs.p; cs = nextState(cs, hilHit); if(ldeb) cout << "Step: " << endl << cs << endl; if (hilHit) { MapState substate = hilSubproblem(cs, hilLvl==1); if(ldeb) cout << "solveState generated subproblem (lvl=" <<hilLvl<<"):" << endl << substate << endl; StateResult subr = solveState(substate, hilLvl-1); r = r + subr; cs = nextState(cs, hilHit); } else r = r + (cs.p - p0); if(ldeb) cout << "Result after step: " << r << endl; } if(ldeb) cout << "Final result: " << r << endl; stateCache[h] = r; return r; } StateResult resAfterSteps(LL steps, MapState &s, int hilLvl, bool ldeb=false) { StateResult r; if(ldeb) cout << "resAfterSteps call lvl="<<hilLvl << " steps=" << steps << ": " << endl << s << endl; MapState cs = s; while (cs.p != cs.t) { bool hilHit; Pt p0 = cs.p; cs = nextState(cs, hilHit); if(ldeb) cout << "Step: " << r << endl; if (hilHit) { MapState substate = hilSubproblem(cs, hilLvl==1); if(ldeb) cout << "resAfterSteps generated subproblem (lvl=" <<hilLvl<<"):" << endl << substate << endl; StateResult cumr = r + solveState(substate, hilLvl-1, ldeb); if(ldeb) cout << "Subproblem return with cumr=" << cumr << endl; if (cumr.steps > steps) { if(ldeb) cout << "Will solve subproblem, and then add " << r << endl; return resAfterSteps(steps - r.steps, substate, hilLvl-1, ldeb) + r; } else if (cumr.steps == steps) { return cumr; } else { r = cumr; cs = nextState(cs, hilHit); } } else r = r + (cs.p - p0); if(ldeb) cout << "Result after step: " << r << endl << cs << endl; if (r.steps == steps) { return r; } } if (DEB) cerr << "ERROR: We should never get to end of resAfterSteps" << endl; return r; } void posAfterSteps(int lvl, LL steps, LL &x, LL &y, bool ldeb=false) { MapState ms; if (lvl == 0) ms.loadState(MAP_LVL0, LVL0_SZ); else ms.loadState(MAP_LVLN, LVLN_SZ); StateResult r = resAfterSteps(steps, ms, lvl, ldeb); if(DEB && r.steps != steps) cerr << "ERROR: bad steps" << endl; x = ms.p.x; x += r.dx; y = ms.p.y; y += r.dy; } void batchResAfterSteps(StateResult r, AnswerGather &ag, MapState &s, int hilLvl, bool ldeb=false) { if(ldeb) cout << "batchResAfterSteps call lvl="<<hilLvl << ": " << endl << s << endl; MapState cs = s; while (cs.p != cs.t) { bool hilHit; Pt p0 = cs.p; cs = nextState(cs, hilHit); if(ldeb) cout << "Step: " << r << endl; if (hilHit) { MapState substate = hilSubproblem(cs, hilLvl==1); if(ldeb) cout << "batchResAfterSteps generated subproblem (lvl=" <<hilLvl<<"):" << endl << substate << endl; StateResult cumr = r + solveState(substate, hilLvl-1, ldeb); if(ldeb) cout << "Subproblem return with cumr=" << cumr << endl; if (cumr.steps > ag.next()) { if(ldeb) cout << "Will solve subproblem " << endl; batchResAfterSteps(r, ag, substate, hilLvl-1, ldeb); } if (!ag.hasNext()) return; while (cumr.steps == ag.next()) { ag.answer(cumr.dx, cumr.dy); if (!ag.hasNext()) return; } r = cumr; cs = nextState(cs, hilHit); } else r = r + (cs.p - p0); if(ldeb) cout << "Result after step: " << r << endl << cs << endl; while (r.steps == ag.next()) { ag.answer(r.dx, r.dy); if (!ag.hasNext()) return; } } } void batchPosAfterSteps(int lvl, AnswerGather &ag, bool ldeb=false) { MapState ms; if (lvl == 0) ms.loadState(MAP_LVL0, LVL0_SZ); else ms.loadState(MAP_LVLN, LVLN_SZ); batchResAfterSteps(StateResult(), ag, ms, lvl, ldeb); REP(i, SIZE(ag.x)) { ag.x[i] += ms.p.x; ag.y[i] += ms.p.y; } } void printStats() { deb(solveCalls); double hitPerc = 100; hitPerc *= cashHits; hitPerc /= solveCalls; deb(hitPerc); deb(SIZE(stateCache)) deb(SIZE(subprCache)) } }; void playHilbertOnLvl(int lvl, int stepLimit=-1) { MapState ms; if (lvl > 0) ms.loadState(MAP_LVLN, LVLN_SZ); else ms.loadState(MAP_LVL0, LVL0_SZ); HilbertBall hb; while(1) { lvl--; ms = hb.hilSubstitute(ms, lvl==0); if (lvl == 0) break; } cout << ms << endl; int steps = 0; while (true) { cin.get(); bool hilHit; ms = hb.nextState(ms, hilHit); steps += 1; cout << "After " << steps << " steps p=" << ms.p << endl; cout << ms << endl; if (stepLimit == steps) return; if (ms.p == Pt(0,1)) { cout << "Ended after " << steps << " steps" << endl; break; } } } void playHilbertShowSubprob() { MapState ms; ms.loadState(MAP_LVLN, LVLN_SZ); cout << ms << endl; HilbertBall hb; REP(i, 50) { cin.get(); bool hilHit; cout << "This is the next step:" << endl; ms = hb.nextState(ms, hilHit); cout << ms << endl; if (hilHit) { cin.get(); cout << "Hilbert was hit. This is the subproblem:" << endl; MapState sms = hb.hilSubproblem(ms, true, true); cout << sms << endl; while(sms.t != sms.p) { cin.get(); bool hit; sms = hb.nextState(sms, hit); cout << sms << endl<<endl; } cout << "Subproblem solved." << endl; } } } int main(int argc, char *argv[]) { #define deb(x) cout << #x << " = " << x << endl; if (argc == 2 && strcmp(argv[1], "debug") == 0 ) { // printf("== [RUNNING IN DEBUG MODE]==\n\n"); char test_file_path[] = "/home/horban/workspace/Zadanka/in.txt"; freopen(test_file_path, "r", stdin); } // TODO: UWAGA NA TO PRZED WYSLANIEM std::ios_base::sync_with_stdio(0); HilbertBall hb; int n, z; cin >> n >> z; AnswerGather ag; REP(tnr, z) { LL steps; cin >> steps; ag.queries.PB(steps); } ag.check(); hb.batchPosAfterSteps(n-1, ag, false); REP(tnr, z) { cout << ag.x[tnr] << ' ' << ag.y[tnr] << endl; } if (DEB) hb.printStats(); return 0; } |