// clang-format off
#include<bits/stdc++.h>
using namespace std;
using LL=long long;
#define FOR(i,l,r) for(auto i=(l);i<=(r);++i)
#define REP(i,n) FOR(i,0,(n)-1)
#define ssize(x) int(x.size())
template<class A,class B>auto&operator<<(ostream&o,pair<A,B>p){return o<<"("<<p.first<<", "<<p.second<<")";}
template<class T>auto operator<<(ostream&o,T x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<(", ")+2*!i++<<e;return o<<"}";}
#ifdef DEBUG
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<"\n";}(X)
#else
#define debug(...) {}
#endif
// clang-format on
#include <ext/pb_ds/assoc_container.hpp>
template<typename A, typename B>
using htable_t = __gnu_pbds::gp_hash_table<A, B>;
class ContiSet
{
set<pair<int, int>> ranges; // (l, r)
public:
void insert(int x);
void erase(int x);
bool conti(int l, int r) const;
};
struct Board
{
// Objects allocation
int nrows, ncols;
htable_t<LL, int> htable;
vector<pair<int, int>> obj_pos;
vector<int> freed;
// About squares
int nsquares = 0;
vector<bool> obj_square;
// Diagonals
vector<map<int, int>> squares_in_diag[2];
vector<ContiSet> objs_in_diag[2];
Board(int nrows, int ncols);
// Object id at given field or -1 if empty
int getid(int r, int c) const;
bool isSquare(int id) const { return obj_square[id]; }
// Squares
void setSquare(int id);
void unsetSquare(int id);
int getStairsLen(int id, int type) const;
int getPrevSqOnDiag(int r, int c, int type) const;
// Creates new object id and sets it at given field
int new_atp(int r, int c);
// Removes object at given field
void rem_atp(int r, int c);
void debug_print();
protected:
static const int margin = 4;
LL hash_pos(int r, int c) const { return 1LL * r * (ncols + margin) + c; }
int diag_id0(int r, int c) const { return nrows - r + c + margin; }
int diag_id1(int r, int c) const { return r + c + margin; }
int id_to_diagid(int id, int type) const;
int getNextSqOnDiag(int id, int type) const;
bool checkConti(int from, int to, int type) const;
};
class Solution
{
int nall = 0, nstairs = 0;
Board* board;
set<int> removable;
public:
Solution(Board* board);
void qadd(int r, int c, bool calc_influe = true);
void qrem(int r, int c);
int query(bool brute_stairs = false);
protected:
int calc_stairs_brutally();
pair<set<int>, bool> set_of_changing_ids(int r, int c, bool add = true);
};
int
main()
{
cin.tie(0)->sync_with_stdio(0);
int nrows, ncols, ninit, nqueries;
cin >> nrows >> ncols >> ninit >> nqueries;
Board board(nrows, ncols);
Solution solution(&board);
REP (i, ninit) {
int r, c;
cin >> r >> c;
solution.qadd(r, c, false);
}
cout << solution.query(true) << "\n";
REP (q, nqueries) {
int r, c;
cin >> r >> c;
if (board.getid(r, c) == -1)
solution.qadd(r, c);
else
solution.qrem(r, c);
cout << solution.query() << "\n";
}
return 0;
}
/* ========================== Solution ===================================== */
void
Solution::qadd(int r, int c, bool calc_influ)
{
// Generate set of ids that will be set to squares
auto [set_to_sq, if_mid_sq] = set_of_changing_ids(r, c, true);
debug("ADD", r, c, set_to_sq);
// Remove influence of all stairs that might depend on set_to_sq
set<pair<int, int>> touched;
if (calc_influ) {
for (const auto& id : set_to_sq) {
const auto& [r, c] = board->obj_pos[id];
touched.insert({board->getPrevSqOnDiag(r, c, 0), 0});
touched.insert({board->getPrevSqOnDiag(r, c + 1, 0), 0});
touched.insert({board->getPrevSqOnDiag(r, c, 1), 1});
touched.insert({board->getPrevSqOnDiag(r, c - 1, 1), 1});
}
// What mid touches
touched.insert({board->getPrevSqOnDiag(r, c, 0), 0});
touched.insert({board->getPrevSqOnDiag(r, c + 1, 0), 0});
touched.insert({board->getPrevSqOnDiag(r, c, 1), 1});
touched.insert({board->getPrevSqOnDiag(r, c - 1, 1), 1});
for (const auto& t : touched) {
if (t.first == -1) continue;
nstairs -= board->getStairsLen(t.first, t.second);
}
}
// Mark our ids as squares
auto mid = board->new_atp(r, c);
if (if_mid_sq) set_to_sq.insert(mid);
for (const auto& id : set_to_sq) board->setSquare(id);
// Add back influence of touched
if (calc_influ) {
for (const auto& t : touched) {
if (t.first == -1) continue;
nstairs += board->getStairsLen(t.first, t.second);
}
}
// Add influence of our new squares
if (calc_influ) {
for (const auto& id : set_to_sq)
nstairs += board->getStairsLen(id, 0) + board->getStairsLen(id, 1);
}
board->debug_print();
nall += 1;
}
void
Solution::qrem(int r, int c)
{
// Generate set of ids that might be no longer a square due to mid
auto mid = board->getid(r, c);
auto [will_unset, if_mid_sq] = set_of_changing_ids(r, c, false);
// Eliminate ids that are secured by squares around
static const array<pair<int, int>, 12> offsets = {{
{-2, -2},
{-2, -1},
{-2, 0},
{-2, 1},
{-1, -2},
{-1, 1},
{0, -2},
{0, 1},
{1, -2},
{1, -1},
{1, 0},
{1, 1},
}};
for (const auto& offset : offsets) {
int rp = r + offset.first, cp = c + offset.second;
auto a = board->getid(rp, cp), b = board->getid(rp, cp + 1),
c = board->getid(rp + 1, cp), d = board->getid(rp + 1, cp + 1);
if (a == -1 || b == -1 || c == -1 || d == -1) continue;
will_unset.erase(a), will_unset.erase(b);
will_unset.erase(c), will_unset.erase(d);
}
// Generate set of ids that will be affected due to some ids being unset
set<pair<int, int>> touched;
for (const auto& id : will_unset) {
const auto& [r, c] = board->obj_pos[id];
touched.insert({board->getPrevSqOnDiag(r, c, 0), 0});
touched.insert({board->getPrevSqOnDiag(r, c + 1, 0), 0});
touched.insert({board->getPrevSqOnDiag(r, c, 1), 1});
touched.insert({board->getPrevSqOnDiag(r, c - 1, 1), 1});
}
// and due to mid being removed
touched.insert({board->getPrevSqOnDiag(r, c, 0), 0});
touched.insert({board->getPrevSqOnDiag(r, c + 1, 0), 0});
touched.insert({board->getPrevSqOnDiag(r, c, 1), 1});
touched.insert({board->getPrevSqOnDiag(r, c - 1, 1), 1});
// And now remove influence of them
vector<pair<int, int>> really_touched;
for (const auto& t : touched) {
if (t.first == -1 || t.first == mid || will_unset.count(t.first))
continue;
really_touched.emplace_back(t);
nstairs -= board->getStairsLen(t.first, t.second);
}
// And also remove influence of those that we will unset
for (const auto& id : will_unset)
nstairs -= board->getStairsLen(id, 0) + board->getStairsLen(id, 1);
if (if_mid_sq)
nstairs -= board->getStairsLen(mid, 0) + board->getStairsLen(mid, 1);
// Unset squares and remove mid
debug("REM", r, c, will_unset);
for (const auto& id : will_unset) board->unsetSquare(id);
if (if_mid_sq) board->unsetSquare(mid);
board->rem_atp(r, c);
// Bring back influence of touched
for (const auto& t : really_touched)
nstairs += board->getStairsLen(t.first, t.second);
board->debug_print();
nall -= 1;
}
int
Solution::query(bool brute_stairs)
{
if (brute_stairs) nstairs = calc_stairs_brutally();
debug("QUERY", nall, board->nsquares, nstairs);
return nall - board->nsquares - nstairs;
}
pair<set<int>, bool>
Solution::set_of_changing_ids(int r, int c, bool add)
{
set<int> idset;
bool if_mid_sq = false;
// Get ids of fields around us
auto left = board->getid(r, c - 1);
auto right = board->getid(r, c + 1);
auto up = board->getid(r - 1, c);
auto down = board->getid(r + 1, c);
auto uleft = board->getid(r - 1, c - 1);
auto uright = board->getid(r - 1, c + 1);
auto dleft = board->getid(r + 1, c - 1);
auto dright = board->getid(r + 1, c + 1);
// We create a square with:
// 1. up left corner
if (uleft != -1 && up != -1 && left != -1) {
if_mid_sq = true;
if (add ^ board->isSquare(uleft)) idset.insert(uleft);
if (add ^ board->isSquare(up)) idset.insert(up);
if (add ^ board->isSquare(left)) idset.insert(left);
}
// 2. up right corner
if (uright != -1 && up != -1 && right != -1) {
if_mid_sq = true;
if (add ^ board->isSquare(uright)) idset.insert(uright);
if (add ^ board->isSquare(up)) idset.insert(up);
if (add ^ board->isSquare(right)) idset.insert(right);
}
// 3. down left corner
if (dleft != -1 && down != -1 && left != -1) {
if_mid_sq = true;
if (add ^ board->isSquare(dleft)) idset.insert(dleft);
if (add ^ board->isSquare(down)) idset.insert(down);
if (add ^ board->isSquare(left)) idset.insert(left);
}
// 4. down right corner
if (dright != -1 && down != -1 && right != -1) {
if_mid_sq = true;
if (add ^ board->isSquare(dright)) idset.insert(dright);
if (add ^ board->isSquare(down)) idset.insert(down);
if (add ^ board->isSquare(right)) idset.insert(right);
}
return {idset, if_mid_sq};
}
int
Solution::calc_stairs_brutally()
{
int res = 0;
set<int> to_skip(board->freed.begin(), board->freed.end());
REP (id, ssize(board->obj_pos)) {
if (to_skip.count(id)) continue;
if (!board->isSquare(id)) continue;
res += board->getStairsLen(id, 0);
res += board->getStairsLen(id, 1);
}
return res;
}
Solution::Solution(Board* board)
: board(board) {};
/* ========================== Board ======================================== */
Board::Board(int nrows, int ncols)
: nrows(nrows)
, ncols(ncols)
{
squares_in_diag[0].resize(diag_id0(-2, ncols) + margin);
squares_in_diag[1].resize(diag_id1(nrows + 2, ncols) + margin);
objs_in_diag[0].resize(diag_id0(-2, ncols) + margin);
objs_in_diag[1].resize(diag_id1(nrows + 2, ncols) + margin);
}
int
Board::getid(int r, int c) const
{
auto it = htable.find(hash_pos(r, c));
if (it == htable.end()) return -1;
return it->second;
}
void
Board::setSquare(int id)
{
obj_square[id] = true, ++nsquares;
const auto& [r, c] = obj_pos[id];
squares_in_diag[0][diag_id0(r, c)][r] = id;
squares_in_diag[1][diag_id1(r, c)][r] = id;
}
void
Board::unsetSquare(int id)
{
if (!obj_square[id]) return;
obj_square[id] = false, --nsquares;
const auto& [r, c] = obj_pos[id];
squares_in_diag[0][diag_id0(r, c)].erase(r);
squares_in_diag[1][diag_id1(r, c)].erase(r);
}
int
Board::id_to_diagid(int id, int type) const
{
const auto& [r, c] = obj_pos[id];
return type == 0 ? diag_id0(r, c) : diag_id1(r, c);
}
int
Board::getNextSqOnDiag(int id, int type) const
{
const auto& [r, c] = obj_pos[id];
const auto& diag = squares_in_diag[type][id_to_diagid(id, type)];
auto it = diag.upper_bound(r);
if (it == diag.end()) return -1;
return it->second;
}
int
Board::getPrevSqOnDiag(int r, int c, int type) const
{
const auto& diag
= squares_in_diag[type][type == 0 ? diag_id0(r, c) : diag_id1(r, c)];
auto it = diag.lower_bound(r);
if (it == diag.begin()) return -1;
return prev(it)->second;
}
bool
Board::checkConti(int from, int to, int type) const
{
auto fdiagid = id_to_diagid(from, type);
const auto& diag = objs_in_diag[type][fdiagid];
return diag.conti(obj_pos[from].first, obj_pos[to].first);
}
int
Board::getStairsLen(int curr, int type) const
{
auto nxt = getNextSqOnDiag(curr, type);
if (nxt == -1) return 0;
if (!checkConti(curr, nxt, type)) return 0;
// Obtain ids of first objects in stairs
const auto& [curr_r, curr_c] = obj_pos[curr];
const auto& [nxt_r, nxt_c] = obj_pos[nxt];
auto curr2 = getid(curr_r + 1, curr_c);
auto nxt2 = getid(nxt_r, (type == 0 ? nxt_c - 1 : nxt_c + 1));
if (curr2 == -1 || nxt2 == -1) return 0;
if (!checkConti(curr2, nxt2, type)) return 0;
// Calculate len
int len = (nxt_r - curr_r) * 2 - 1;
if (isSquare(curr2)) len -= 1;
if (nxt2 != curr2 && isSquare(nxt2)) len -= 1;
if (len) debug(curr_r, curr_c, nxt_r, nxt_c, len);
return len;
}
int
Board::new_atp(int r, int c)
{
int id = ssize(obj_pos);
if (!freed.empty()) {
id = freed.back();
freed.pop_back();
} else {
obj_pos.emplace_back();
obj_square.emplace_back();
}
obj_pos[id] = {r, c};
htable[hash_pos(r, c)] = id;
// Update data
objs_in_diag[0][diag_id0(r, c)].insert(r);
objs_in_diag[1][diag_id1(r, c)].insert(r);
return id;
}
void
Board::rem_atp(int r, int c)
{
auto it = htable.find(hash_pos(r, c));
const auto& [key, id] = *it;
// Update data
unsetSquare(id);
objs_in_diag[0][diag_id0(r, c)].erase(r);
objs_in_diag[1][diag_id1(r, c)].erase(r);
freed.emplace_back(id);
htable.erase(key);
}
void
Board::debug_print()
{
#ifdef DEBUG
vector<string> output(nrows + 1, string(ncols + 1, ' '));
output[0] = string(ncols + 1, '_');
output[0][0] = ' ';
FOR (r, 1, nrows) output[r][0] = '|';
set<int> to_skip(freed.begin(), freed.end());
REP (id, ssize(obj_pos)) {
if (to_skip.count(id)) continue;
const auto& [r, c] = obj_pos[id];
output[r][c] = (obj_square[id] ? '#' : '+');
}
for (const auto& row : output) cerr << row.c_str() << "\n";
#endif
}
/* ========================== ContiSet ===================================== */
void
ContiSet::insert(int x)
{
pair<int, int> to_insert = {x, x};
auto after = ranges.lower_bound({x, 0});
// Merge with range before
if (after != ranges.begin() && prev(after)->second + 1 == x) {
to_insert.first = prev(after)->first;
ranges.erase(prev(after));
}
// Merge with range after
if (after != ranges.end() && after->first == x + 1) {
to_insert.second = after->second;
ranges.erase(after);
}
ranges.insert(to_insert);
}
void
ContiSet::erase(int x)
{
auto it = ranges.lower_bound({x + 1, 0});
const auto& [l, r] = *(--it);
// Insert part of range before it
if (l < x) ranges.insert(it, {l, x - 1});
// Insert part of range after it
if (x < r) ranges.insert(next(it), {x + 1, r});
// Perform erasion
ranges.erase(it);
}
bool
ContiSet::conti(int l, int r) const
{
auto lit = ranges.lower_bound({l + 1, 0});
return lit != ranges.begin() && prev(lit)->first <= l
&& r <= prev(lit)->second;
}
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using LL=long long; #define FOR(i,l,r) for(auto i=(l);i<=(r);++i) #define REP(i,n) FOR(i,0,(n)-1) #define ssize(x) int(x.size()) template<class A,class B>auto&operator<<(ostream&o,pair<A,B>p){return o<<"("<<p.first<<", "<<p.second<<")";} template<class T>auto operator<<(ostream&o,T x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<(", ")+2*!i++<<e;return o<<"}";} #ifdef DEBUG #define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<"\n";}(X) #else #define debug(...) {} #endif // clang-format on #include <ext/pb_ds/assoc_container.hpp> template<typename A, typename B> using htable_t = __gnu_pbds::gp_hash_table<A, B>; class ContiSet { set<pair<int, int>> ranges; // (l, r) public: void insert(int x); void erase(int x); bool conti(int l, int r) const; }; struct Board { // Objects allocation int nrows, ncols; htable_t<LL, int> htable; vector<pair<int, int>> obj_pos; vector<int> freed; // About squares int nsquares = 0; vector<bool> obj_square; // Diagonals vector<map<int, int>> squares_in_diag[2]; vector<ContiSet> objs_in_diag[2]; Board(int nrows, int ncols); // Object id at given field or -1 if empty int getid(int r, int c) const; bool isSquare(int id) const { return obj_square[id]; } // Squares void setSquare(int id); void unsetSquare(int id); int getStairsLen(int id, int type) const; int getPrevSqOnDiag(int r, int c, int type) const; // Creates new object id and sets it at given field int new_atp(int r, int c); // Removes object at given field void rem_atp(int r, int c); void debug_print(); protected: static const int margin = 4; LL hash_pos(int r, int c) const { return 1LL * r * (ncols + margin) + c; } int diag_id0(int r, int c) const { return nrows - r + c + margin; } int diag_id1(int r, int c) const { return r + c + margin; } int id_to_diagid(int id, int type) const; int getNextSqOnDiag(int id, int type) const; bool checkConti(int from, int to, int type) const; }; class Solution { int nall = 0, nstairs = 0; Board* board; set<int> removable; public: Solution(Board* board); void qadd(int r, int c, bool calc_influe = true); void qrem(int r, int c); int query(bool brute_stairs = false); protected: int calc_stairs_brutally(); pair<set<int>, bool> set_of_changing_ids(int r, int c, bool add = true); }; int main() { cin.tie(0)->sync_with_stdio(0); int nrows, ncols, ninit, nqueries; cin >> nrows >> ncols >> ninit >> nqueries; Board board(nrows, ncols); Solution solution(&board); REP (i, ninit) { int r, c; cin >> r >> c; solution.qadd(r, c, false); } cout << solution.query(true) << "\n"; REP (q, nqueries) { int r, c; cin >> r >> c; if (board.getid(r, c) == -1) solution.qadd(r, c); else solution.qrem(r, c); cout << solution.query() << "\n"; } return 0; } /* ========================== Solution ===================================== */ void Solution::qadd(int r, int c, bool calc_influ) { // Generate set of ids that will be set to squares auto [set_to_sq, if_mid_sq] = set_of_changing_ids(r, c, true); debug("ADD", r, c, set_to_sq); // Remove influence of all stairs that might depend on set_to_sq set<pair<int, int>> touched; if (calc_influ) { for (const auto& id : set_to_sq) { const auto& [r, c] = board->obj_pos[id]; touched.insert({board->getPrevSqOnDiag(r, c, 0), 0}); touched.insert({board->getPrevSqOnDiag(r, c + 1, 0), 0}); touched.insert({board->getPrevSqOnDiag(r, c, 1), 1}); touched.insert({board->getPrevSqOnDiag(r, c - 1, 1), 1}); } // What mid touches touched.insert({board->getPrevSqOnDiag(r, c, 0), 0}); touched.insert({board->getPrevSqOnDiag(r, c + 1, 0), 0}); touched.insert({board->getPrevSqOnDiag(r, c, 1), 1}); touched.insert({board->getPrevSqOnDiag(r, c - 1, 1), 1}); for (const auto& t : touched) { if (t.first == -1) continue; nstairs -= board->getStairsLen(t.first, t.second); } } // Mark our ids as squares auto mid = board->new_atp(r, c); if (if_mid_sq) set_to_sq.insert(mid); for (const auto& id : set_to_sq) board->setSquare(id); // Add back influence of touched if (calc_influ) { for (const auto& t : touched) { if (t.first == -1) continue; nstairs += board->getStairsLen(t.first, t.second); } } // Add influence of our new squares if (calc_influ) { for (const auto& id : set_to_sq) nstairs += board->getStairsLen(id, 0) + board->getStairsLen(id, 1); } board->debug_print(); nall += 1; } void Solution::qrem(int r, int c) { // Generate set of ids that might be no longer a square due to mid auto mid = board->getid(r, c); auto [will_unset, if_mid_sq] = set_of_changing_ids(r, c, false); // Eliminate ids that are secured by squares around static const array<pair<int, int>, 12> offsets = {{ {-2, -2}, {-2, -1}, {-2, 0}, {-2, 1}, {-1, -2}, {-1, 1}, {0, -2}, {0, 1}, {1, -2}, {1, -1}, {1, 0}, {1, 1}, }}; for (const auto& offset : offsets) { int rp = r + offset.first, cp = c + offset.second; auto a = board->getid(rp, cp), b = board->getid(rp, cp + 1), c = board->getid(rp + 1, cp), d = board->getid(rp + 1, cp + 1); if (a == -1 || b == -1 || c == -1 || d == -1) continue; will_unset.erase(a), will_unset.erase(b); will_unset.erase(c), will_unset.erase(d); } // Generate set of ids that will be affected due to some ids being unset set<pair<int, int>> touched; for (const auto& id : will_unset) { const auto& [r, c] = board->obj_pos[id]; touched.insert({board->getPrevSqOnDiag(r, c, 0), 0}); touched.insert({board->getPrevSqOnDiag(r, c + 1, 0), 0}); touched.insert({board->getPrevSqOnDiag(r, c, 1), 1}); touched.insert({board->getPrevSqOnDiag(r, c - 1, 1), 1}); } // and due to mid being removed touched.insert({board->getPrevSqOnDiag(r, c, 0), 0}); touched.insert({board->getPrevSqOnDiag(r, c + 1, 0), 0}); touched.insert({board->getPrevSqOnDiag(r, c, 1), 1}); touched.insert({board->getPrevSqOnDiag(r, c - 1, 1), 1}); // And now remove influence of them vector<pair<int, int>> really_touched; for (const auto& t : touched) { if (t.first == -1 || t.first == mid || will_unset.count(t.first)) continue; really_touched.emplace_back(t); nstairs -= board->getStairsLen(t.first, t.second); } // And also remove influence of those that we will unset for (const auto& id : will_unset) nstairs -= board->getStairsLen(id, 0) + board->getStairsLen(id, 1); if (if_mid_sq) nstairs -= board->getStairsLen(mid, 0) + board->getStairsLen(mid, 1); // Unset squares and remove mid debug("REM", r, c, will_unset); for (const auto& id : will_unset) board->unsetSquare(id); if (if_mid_sq) board->unsetSquare(mid); board->rem_atp(r, c); // Bring back influence of touched for (const auto& t : really_touched) nstairs += board->getStairsLen(t.first, t.second); board->debug_print(); nall -= 1; } int Solution::query(bool brute_stairs) { if (brute_stairs) nstairs = calc_stairs_brutally(); debug("QUERY", nall, board->nsquares, nstairs); return nall - board->nsquares - nstairs; } pair<set<int>, bool> Solution::set_of_changing_ids(int r, int c, bool add) { set<int> idset; bool if_mid_sq = false; // Get ids of fields around us auto left = board->getid(r, c - 1); auto right = board->getid(r, c + 1); auto up = board->getid(r - 1, c); auto down = board->getid(r + 1, c); auto uleft = board->getid(r - 1, c - 1); auto uright = board->getid(r - 1, c + 1); auto dleft = board->getid(r + 1, c - 1); auto dright = board->getid(r + 1, c + 1); // We create a square with: // 1. up left corner if (uleft != -1 && up != -1 && left != -1) { if_mid_sq = true; if (add ^ board->isSquare(uleft)) idset.insert(uleft); if (add ^ board->isSquare(up)) idset.insert(up); if (add ^ board->isSquare(left)) idset.insert(left); } // 2. up right corner if (uright != -1 && up != -1 && right != -1) { if_mid_sq = true; if (add ^ board->isSquare(uright)) idset.insert(uright); if (add ^ board->isSquare(up)) idset.insert(up); if (add ^ board->isSquare(right)) idset.insert(right); } // 3. down left corner if (dleft != -1 && down != -1 && left != -1) { if_mid_sq = true; if (add ^ board->isSquare(dleft)) idset.insert(dleft); if (add ^ board->isSquare(down)) idset.insert(down); if (add ^ board->isSquare(left)) idset.insert(left); } // 4. down right corner if (dright != -1 && down != -1 && right != -1) { if_mid_sq = true; if (add ^ board->isSquare(dright)) idset.insert(dright); if (add ^ board->isSquare(down)) idset.insert(down); if (add ^ board->isSquare(right)) idset.insert(right); } return {idset, if_mid_sq}; } int Solution::calc_stairs_brutally() { int res = 0; set<int> to_skip(board->freed.begin(), board->freed.end()); REP (id, ssize(board->obj_pos)) { if (to_skip.count(id)) continue; if (!board->isSquare(id)) continue; res += board->getStairsLen(id, 0); res += board->getStairsLen(id, 1); } return res; } Solution::Solution(Board* board) : board(board) {}; /* ========================== Board ======================================== */ Board::Board(int nrows, int ncols) : nrows(nrows) , ncols(ncols) { squares_in_diag[0].resize(diag_id0(-2, ncols) + margin); squares_in_diag[1].resize(diag_id1(nrows + 2, ncols) + margin); objs_in_diag[0].resize(diag_id0(-2, ncols) + margin); objs_in_diag[1].resize(diag_id1(nrows + 2, ncols) + margin); } int Board::getid(int r, int c) const { auto it = htable.find(hash_pos(r, c)); if (it == htable.end()) return -1; return it->second; } void Board::setSquare(int id) { obj_square[id] = true, ++nsquares; const auto& [r, c] = obj_pos[id]; squares_in_diag[0][diag_id0(r, c)][r] = id; squares_in_diag[1][diag_id1(r, c)][r] = id; } void Board::unsetSquare(int id) { if (!obj_square[id]) return; obj_square[id] = false, --nsquares; const auto& [r, c] = obj_pos[id]; squares_in_diag[0][diag_id0(r, c)].erase(r); squares_in_diag[1][diag_id1(r, c)].erase(r); } int Board::id_to_diagid(int id, int type) const { const auto& [r, c] = obj_pos[id]; return type == 0 ? diag_id0(r, c) : diag_id1(r, c); } int Board::getNextSqOnDiag(int id, int type) const { const auto& [r, c] = obj_pos[id]; const auto& diag = squares_in_diag[type][id_to_diagid(id, type)]; auto it = diag.upper_bound(r); if (it == diag.end()) return -1; return it->second; } int Board::getPrevSqOnDiag(int r, int c, int type) const { const auto& diag = squares_in_diag[type][type == 0 ? diag_id0(r, c) : diag_id1(r, c)]; auto it = diag.lower_bound(r); if (it == diag.begin()) return -1; return prev(it)->second; } bool Board::checkConti(int from, int to, int type) const { auto fdiagid = id_to_diagid(from, type); const auto& diag = objs_in_diag[type][fdiagid]; return diag.conti(obj_pos[from].first, obj_pos[to].first); } int Board::getStairsLen(int curr, int type) const { auto nxt = getNextSqOnDiag(curr, type); if (nxt == -1) return 0; if (!checkConti(curr, nxt, type)) return 0; // Obtain ids of first objects in stairs const auto& [curr_r, curr_c] = obj_pos[curr]; const auto& [nxt_r, nxt_c] = obj_pos[nxt]; auto curr2 = getid(curr_r + 1, curr_c); auto nxt2 = getid(nxt_r, (type == 0 ? nxt_c - 1 : nxt_c + 1)); if (curr2 == -1 || nxt2 == -1) return 0; if (!checkConti(curr2, nxt2, type)) return 0; // Calculate len int len = (nxt_r - curr_r) * 2 - 1; if (isSquare(curr2)) len -= 1; if (nxt2 != curr2 && isSquare(nxt2)) len -= 1; if (len) debug(curr_r, curr_c, nxt_r, nxt_c, len); return len; } int Board::new_atp(int r, int c) { int id = ssize(obj_pos); if (!freed.empty()) { id = freed.back(); freed.pop_back(); } else { obj_pos.emplace_back(); obj_square.emplace_back(); } obj_pos[id] = {r, c}; htable[hash_pos(r, c)] = id; // Update data objs_in_diag[0][diag_id0(r, c)].insert(r); objs_in_diag[1][diag_id1(r, c)].insert(r); return id; } void Board::rem_atp(int r, int c) { auto it = htable.find(hash_pos(r, c)); const auto& [key, id] = *it; // Update data unsetSquare(id); objs_in_diag[0][diag_id0(r, c)].erase(r); objs_in_diag[1][diag_id1(r, c)].erase(r); freed.emplace_back(id); htable.erase(key); } void Board::debug_print() { #ifdef DEBUG vector<string> output(nrows + 1, string(ncols + 1, ' ')); output[0] = string(ncols + 1, '_'); output[0][0] = ' '; FOR (r, 1, nrows) output[r][0] = '|'; set<int> to_skip(freed.begin(), freed.end()); REP (id, ssize(obj_pos)) { if (to_skip.count(id)) continue; const auto& [r, c] = obj_pos[id]; output[r][c] = (obj_square[id] ? '#' : '+'); } for (const auto& row : output) cerr << row.c_str() << "\n"; #endif } /* ========================== ContiSet ===================================== */ void ContiSet::insert(int x) { pair<int, int> to_insert = {x, x}; auto after = ranges.lower_bound({x, 0}); // Merge with range before if (after != ranges.begin() && prev(after)->second + 1 == x) { to_insert.first = prev(after)->first; ranges.erase(prev(after)); } // Merge with range after if (after != ranges.end() && after->first == x + 1) { to_insert.second = after->second; ranges.erase(after); } ranges.insert(to_insert); } void ContiSet::erase(int x) { auto it = ranges.lower_bound({x + 1, 0}); const auto& [l, r] = *(--it); // Insert part of range before it if (l < x) ranges.insert(it, {l, x - 1}); // Insert part of range after it if (x < r) ranges.insert(next(it), {x + 1, r}); // Perform erasion ranges.erase(it); } bool ContiSet::conti(int l, int r) const { auto lit = ranges.lower_bound({l + 1, 0}); return lit != ranges.begin() && prev(lit)->first <= l && r <= prev(lit)->second; } |
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