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#include <iostream>
#include <vector>
#include <queue>
#include <cstring>
#include <functional>
#include <cmath>
using namespace std;
#define DEBUG
enum Boja
{
BIJELA = 0, // Nije pronađeno
SIVA = 1, // Pronađeno
CRNA = 2 // Buka
};
struct Vector2i
{
Vector2i() { }
Vector2i(int x, int y) : x(x), y(y) { }
int x;
int y;
};
struct Node
{
Node()
{
B = BIJELA;
}
Boja B;
int C;
Vector2i P;
};
struct CompareNode : public binary_function<Node*, Node*, bool>
{
bool operator()(const Node* pFirst, const Node* pSecond) const
{
return pFirst->C > pSecond->C;
}
};
// Dirty implementation of heap: TODO: replace with a proper one
class Heap : public priority_queue<Node*, vector<Node*>, CompareNode>
{
public:
void decrease_key(Node* pNode)
{
for (int i = 0; i < this->c.size(); ++i)
{
if (this->c[i] == pNode)
{
push_heap(this->c.begin(), this->c.begin() + i + 1);
break;
}
}
}
};
class Hotel
{
public:
Hotel();
void Rasporedi();
void NapraviBuku(Node* pIzvor);
void Relax(Node* pIzvor, Node* pTrenutna);
void IzracunajCijene();
int Cijena(Node* pNode);
private:
vector<vector<Node> > G;
vector<Node*> L;
Heap O;
int X, Y, B, R, LI;
};
Hotel::Hotel() : R(0)
{
cin >> X >> Y >> B;
G.resize(Y, vector<Node>(X, Node()));
L.resize(Y * X);
for (int y = 0; y < Y; ++y)
for (int x = 0; x < X; ++x)
G[y][x].P = Vector2i(x, y);
}
void Hotel::Rasporedi()
{
Node* pIzvor;
// Kutevi imaju najmanju cijenu na pocetku
G[0][0].C = Cijena(&G[0][0]);
G[Y-1][0].C = Cijena(&G[Y-1][0]);
G[0][X-1].C = Cijena(&G[0][X-1]);
G[Y-1][X-1].C = Cijena(&G[Y-1][X-1]);
O.push(&G[0][0]);
O.push(&G[Y-1][0]);
O.push(&G[0][X-1]);
O.push(&G[Y-1][X-1]);
while (!O.empty())
{
pIzvor = O.top();
O.pop();
if (pIzvor->B != CRNA)
{
LI = 0;
NapraviBuku(pIzvor);
IzracunajCijene();
#ifdef DEBUG
cout << "Klingonac u sobi: " << pIzvor->P.x << " " << pIzvor->P.y << endl;
#endif
++R;
}
}
cout << R << endl;
}
void Hotel::IzracunajCijene()
{
for (int i = 0; i < LI; ++i)
{
L[i]->C = Cijena(L[i]);
O.push(L[i]);
}
}
int Hotel::Cijena(Node* pNode)
{
int Cijena = 0;
for (int y = pNode->P.y - B; y < pNode->P.y + B; ++y)
for (int x = pNode->P.x - B; x < pNode->P.x + B; ++x)
if (x >= 0 && y >= 0 && x < X && y < Y)
if (G[y][x].B != CRNA)
++Cijena;
return Cijena;
}
void Hotel::Relax(Node* pIzvor, Node* pTrenutna)
{
switch (pTrenutna->B)
{
case BIJELA:
pTrenutna->B = SIVA;
L[LI++] = pTrenutna;
break;
case SIVA:
pTrenutna->C = Cijena(pTrenutna);
O.decrease_key(pTrenutna);
break;
default:
break;
}
}
void Hotel::NapraviBuku(Node* pIzvor)
{
for (int y = pIzvor->P.y - 2 * B; y < pIzvor->P.y + B * 2; ++y)
{
for (int x = pIzvor->P.x - 2 * B; x < pIzvor->P.x + 2 * B; ++x)
{
if (x >= 0 && y >= 0 && x < X && y < Y)
{
int Udaljenost = abs(x - pIzvor->P.x) + abs(y - pIzvor->P.y);
if (Udaljenost <= B)
G[y][x].B = CRNA;
else if (Udaljenost <= B * 2)
Relax(pIzvor, &G[y][x]);
}
}
}
}
int main()
{
Hotel Klingonci;
Klingonci.Rasporedi();
return 0;
}
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