700 lines
18 KiB
C++
Executable File
700 lines
18 KiB
C++
Executable File
/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2009
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#ifndef GRID_GRAPH_H
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#define GRID_GRAPH_H
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#include <lemon/core.h>
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#include <lemon/bits/graph_extender.h>
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#include <lemon/dim2.h>
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#include <lemon/assert.h>
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///\ingroup graphs
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///\file
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///\brief GridGraph class.
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namespace lemon {
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class GridGraphBase {
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public:
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typedef GridGraphBase Graph;
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class Node;
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class Edge;
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class Arc;
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public:
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GridGraphBase() {}
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protected:
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void construct(int width, int height) {
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_width = width; _height = height;
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_node_num = width * height;
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_edge_num = 2 * _node_num - width - height;
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_edge_limit = _node_num - _width;
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}
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public:
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Node operator()(int i, int j) const {
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LEMON_DEBUG(0 <= i && i < _width &&
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0 <= j && j < _height, "Index out of range");
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return Node(i + j * _width);
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}
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int col(Node n) const {
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return n._id % _width;
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}
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int row(Node n) const {
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return n._id / _width;
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}
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dim2::Point<int> pos(Node n) const {
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return dim2::Point<int>(col(n), row(n));
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}
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int width() const {
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return _width;
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}
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int height() const {
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return _height;
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}
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typedef True NodeNumTag;
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typedef True EdgeNumTag;
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typedef True ArcNumTag;
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int nodeNum() const { return _node_num; }
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int edgeNum() const { return _edge_num; }
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int arcNum() const { return 2 * _edge_num; }
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Node u(Edge edge) const {
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if (edge._id < _edge_limit) {
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return edge._id;
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} else {
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return (edge._id - _edge_limit) % (_width - 1) +
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(edge._id - _edge_limit) / (_width - 1) * _width;
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}
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}
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Node v(Edge edge) const {
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if (edge._id < _edge_limit) {
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return edge._id + _width;
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} else {
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return (edge._id - _edge_limit) % (_width - 1) +
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(edge._id - _edge_limit) / (_width - 1) * _width + 1;
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}
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}
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Node source(Arc arc) const {
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return (arc._id & 1) == 1 ? u(arc) : v(arc);
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}
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Node target(Arc arc) const {
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return (arc._id & 1) == 1 ? v(arc) : u(arc);
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}
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static int id(Node node) { return node._id; }
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static int id(Edge edge) { return edge._id; }
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static int id(Arc arc) { return arc._id; }
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int maxNodeId() const { return _node_num - 1; }
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int maxEdgeId() const { return _edge_num - 1; }
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int maxArcId() const { return 2 * _edge_num - 1; }
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static Node nodeFromId(int id) { return Node(id);}
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static Edge edgeFromId(int id) { return Edge(id);}
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static Arc arcFromId(int id) { return Arc(id);}
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typedef True FindEdgeTag;
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typedef True FindArcTag;
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Edge findEdge(Node u, Node v, Edge prev = INVALID) const {
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if (prev != INVALID) return INVALID;
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if (v._id > u._id) {
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if (v._id - u._id == _width)
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return Edge(u._id);
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if (v._id - u._id == 1 && u._id % _width < _width - 1) {
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return Edge(u._id / _width * (_width - 1) +
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u._id % _width + _edge_limit);
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}
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} else {
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if (u._id - v._id == _width)
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return Edge(v._id);
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if (u._id - v._id == 1 && v._id % _width < _width - 1) {
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return Edge(v._id / _width * (_width - 1) +
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v._id % _width + _edge_limit);
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}
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}
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return INVALID;
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}
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Arc findArc(Node u, Node v, Arc prev = INVALID) const {
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if (prev != INVALID) return INVALID;
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if (v._id > u._id) {
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if (v._id - u._id == _width)
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return Arc((u._id << 1) | 1);
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if (v._id - u._id == 1 && u._id % _width < _width - 1) {
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return Arc(((u._id / _width * (_width - 1) +
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u._id % _width + _edge_limit) << 1) | 1);
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}
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} else {
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if (u._id - v._id == _width)
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return Arc(v._id << 1);
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if (u._id - v._id == 1 && v._id % _width < _width - 1) {
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return Arc((v._id / _width * (_width - 1) +
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v._id % _width + _edge_limit) << 1);
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}
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}
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return INVALID;
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}
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class Node {
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friend class GridGraphBase;
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protected:
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int _id;
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Node(int id) : _id(id) {}
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public:
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Node() {}
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Node (Invalid) : _id(-1) {}
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bool operator==(const Node node) const {return _id == node._id;}
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bool operator!=(const Node node) const {return _id != node._id;}
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bool operator<(const Node node) const {return _id < node._id;}
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};
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class Edge {
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friend class GridGraphBase;
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friend class Arc;
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protected:
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int _id;
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Edge(int id) : _id(id) {}
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public:
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Edge() {}
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Edge (Invalid) : _id(-1) {}
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bool operator==(const Edge edge) const {return _id == edge._id;}
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bool operator!=(const Edge edge) const {return _id != edge._id;}
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bool operator<(const Edge edge) const {return _id < edge._id;}
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};
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class Arc {
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friend class GridGraphBase;
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protected:
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int _id;
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Arc(int id) : _id(id) {}
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public:
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Arc() {}
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Arc (Invalid) : _id(-1) {}
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operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }
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bool operator==(const Arc arc) const {return _id == arc._id;}
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bool operator!=(const Arc arc) const {return _id != arc._id;}
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bool operator<(const Arc arc) const {return _id < arc._id;}
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};
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static bool direction(Arc arc) {
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return (arc._id & 1) == 1;
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}
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static Arc direct(Edge edge, bool dir) {
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return Arc((edge._id << 1) | (dir ? 1 : 0));
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}
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void first(Node& node) const {
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node._id = _node_num - 1;
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}
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static void next(Node& node) {
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--node._id;
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}
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void first(Edge& edge) const {
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edge._id = _edge_num - 1;
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}
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static void next(Edge& edge) {
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--edge._id;
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}
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void first(Arc& arc) const {
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arc._id = 2 * _edge_num - 1;
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}
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static void next(Arc& arc) {
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--arc._id;
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}
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void firstOut(Arc& arc, const Node& node) const {
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if (node._id % _width < _width - 1) {
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arc._id = (_edge_limit + node._id % _width +
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(node._id / _width) * (_width - 1)) << 1 | 1;
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return;
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}
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if (node._id < _node_num - _width) {
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arc._id = node._id << 1 | 1;
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return;
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}
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if (node._id % _width > 0) {
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arc._id = (_edge_limit + node._id % _width +
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(node._id / _width) * (_width - 1) - 1) << 1;
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return;
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}
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if (node._id >= _width) {
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arc._id = (node._id - _width) << 1;
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return;
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}
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arc._id = -1;
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}
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void nextOut(Arc& arc) const {
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int nid = arc._id >> 1;
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if ((arc._id & 1) == 1) {
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if (nid >= _edge_limit) {
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nid = (nid - _edge_limit) % (_width - 1) +
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(nid - _edge_limit) / (_width - 1) * _width;
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if (nid < _node_num - _width) {
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arc._id = nid << 1 | 1;
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return;
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}
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}
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if (nid % _width > 0) {
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arc._id = (_edge_limit + nid % _width +
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(nid / _width) * (_width - 1) - 1) << 1;
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return;
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}
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if (nid >= _width) {
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arc._id = (nid - _width) << 1;
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return;
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}
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} else {
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if (nid >= _edge_limit) {
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nid = (nid - _edge_limit) % (_width - 1) +
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(nid - _edge_limit) / (_width - 1) * _width + 1;
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if (nid >= _width) {
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arc._id = (nid - _width) << 1;
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return;
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}
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}
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}
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arc._id = -1;
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}
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void firstIn(Arc& arc, const Node& node) const {
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if (node._id % _width < _width - 1) {
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arc._id = (_edge_limit + node._id % _width +
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(node._id / _width) * (_width - 1)) << 1;
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return;
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}
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if (node._id < _node_num - _width) {
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arc._id = node._id << 1;
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return;
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}
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if (node._id % _width > 0) {
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arc._id = (_edge_limit + node._id % _width +
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(node._id / _width) * (_width - 1) - 1) << 1 | 1;
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return;
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}
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if (node._id >= _width) {
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arc._id = (node._id - _width) << 1 | 1;
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return;
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}
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arc._id = -1;
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}
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void nextIn(Arc& arc) const {
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int nid = arc._id >> 1;
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if ((arc._id & 1) == 0) {
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if (nid >= _edge_limit) {
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nid = (nid - _edge_limit) % (_width - 1) +
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(nid - _edge_limit) / (_width - 1) * _width;
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if (nid < _node_num - _width) {
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arc._id = nid << 1;
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return;
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}
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}
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if (nid % _width > 0) {
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arc._id = (_edge_limit + nid % _width +
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(nid / _width) * (_width - 1) - 1) << 1 | 1;
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return;
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}
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if (nid >= _width) {
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arc._id = (nid - _width) << 1 | 1;
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return;
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}
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} else {
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if (nid >= _edge_limit) {
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nid = (nid - _edge_limit) % (_width - 1) +
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(nid - _edge_limit) / (_width - 1) * _width + 1;
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if (nid >= _width) {
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arc._id = (nid - _width) << 1 | 1;
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return;
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}
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}
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}
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arc._id = -1;
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}
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void firstInc(Edge& edge, bool& dir, const Node& node) const {
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if (node._id % _width < _width - 1) {
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edge._id = _edge_limit + node._id % _width +
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(node._id / _width) * (_width - 1);
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dir = true;
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return;
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}
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if (node._id < _node_num - _width) {
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edge._id = node._id;
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dir = true;
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return;
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}
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if (node._id % _width > 0) {
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edge._id = _edge_limit + node._id % _width +
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(node._id / _width) * (_width - 1) - 1;
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dir = false;
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return;
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}
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if (node._id >= _width) {
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edge._id = node._id - _width;
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dir = false;
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return;
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}
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edge._id = -1;
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dir = true;
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}
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void nextInc(Edge& edge, bool& dir) const {
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int nid = edge._id;
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if (dir) {
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if (nid >= _edge_limit) {
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nid = (nid - _edge_limit) % (_width - 1) +
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(nid - _edge_limit) / (_width - 1) * _width;
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if (nid < _node_num - _width) {
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edge._id = nid;
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return;
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}
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}
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if (nid % _width > 0) {
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edge._id = _edge_limit + nid % _width +
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(nid / _width) * (_width - 1) - 1;
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dir = false;
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return;
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}
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if (nid >= _width) {
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edge._id = nid - _width;
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dir = false;
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return;
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}
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} else {
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if (nid >= _edge_limit) {
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nid = (nid - _edge_limit) % (_width - 1) +
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(nid - _edge_limit) / (_width - 1) * _width + 1;
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if (nid >= _width) {
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edge._id = nid - _width;
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return;
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}
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}
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}
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edge._id = -1;
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dir = true;
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}
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Arc right(Node n) const {
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if (n._id % _width < _width - 1) {
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return Arc(((_edge_limit + n._id % _width +
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(n._id / _width) * (_width - 1)) << 1) | 1);
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} else {
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return INVALID;
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}
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}
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Arc left(Node n) const {
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if (n._id % _width > 0) {
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return Arc((_edge_limit + n._id % _width +
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(n._id / _width) * (_width - 1) - 1) << 1);
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} else {
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return INVALID;
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}
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}
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Arc up(Node n) const {
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if (n._id < _edge_limit) {
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return Arc((n._id << 1) | 1);
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} else {
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return INVALID;
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}
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}
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Arc down(Node n) const {
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if (n._id >= _width) {
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return Arc((n._id - _width) << 1);
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} else {
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return INVALID;
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}
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}
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private:
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int _width, _height;
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int _node_num, _edge_num;
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int _edge_limit;
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};
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typedef GraphExtender<GridGraphBase> ExtendedGridGraphBase;
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/// \ingroup graphs
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///
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/// \brief Grid graph class
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///
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/// GridGraph implements a special graph type. The nodes of the
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/// graph can be indexed by two integer values \c (i,j) where \c i is
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/// in the range <tt>[0..width()-1]</tt> and j is in the range
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/// <tt>[0..height()-1]</tt>. Two nodes are connected in the graph if
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/// the indices differ exactly on one position and the difference is
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/// also exactly one. The nodes of the graph can be obtained by position
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/// using the \c operator()() function and the indices of the nodes can
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/// be obtained using \c pos(), \c col() and \c row() members. The outgoing
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/// arcs can be retrieved with the \c right(), \c up(), \c left()
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/// and \c down() functions, where the bottom-left corner is the
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/// origin.
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///
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/// This class is completely static and it needs constant memory space.
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/// Thus you can neither add nor delete nodes or edges, however
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/// the structure can be resized using resize().
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///
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/// \image html grid_graph.png
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/// \image latex grid_graph.eps "Grid graph" width=\textwidth
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///
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/// A short example about the basic usage:
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///\code
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/// GridGraph graph(rows, cols);
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/// GridGraph::NodeMap<int> val(graph);
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/// for (int i = 0; i < graph.width(); ++i) {
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/// for (int j = 0; j < graph.height(); ++j) {
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/// val[graph(i, j)] = i + j;
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/// }
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/// }
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///\endcode
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///
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/// This type fully conforms to the \ref concepts::Graph "Graph concept".
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/// Most of its member functions and nested classes are documented
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/// only in the concept class.
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///
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/// This class provides constant time counting for nodes, edges and arcs.
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class GridGraph : public ExtendedGridGraphBase {
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typedef ExtendedGridGraphBase Parent;
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public:
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/// \brief Map to get the indices of the nodes as \ref dim2::Point
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/// "dim2::Point<int>".
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///
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/// Map to get the indices of the nodes as \ref dim2::Point
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/// "dim2::Point<int>".
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class IndexMap {
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public:
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/// \brief The key type of the map
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typedef GridGraph::Node Key;
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/// \brief The value type of the map
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typedef dim2::Point<int> Value;
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/// \brief Constructor
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IndexMap(const GridGraph& graph) : _graph(graph) {}
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/// \brief The subscript operator
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Value operator[](Key key) const {
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return _graph.pos(key);
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}
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private:
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const GridGraph& _graph;
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};
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/// \brief Map to get the column of the nodes.
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///
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/// Map to get the column of the nodes.
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class ColMap {
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public:
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/// \brief The key type of the map
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typedef GridGraph::Node Key;
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/// \brief The value type of the map
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typedef int Value;
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/// \brief Constructor
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ColMap(const GridGraph& graph) : _graph(graph) {}
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/// \brief The subscript operator
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Value operator[](Key key) const {
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return _graph.col(key);
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}
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private:
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const GridGraph& _graph;
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};
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/// \brief Map to get the row of the nodes.
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///
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/// Map to get the row of the nodes.
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class RowMap {
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public:
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/// \brief The key type of the map
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typedef GridGraph::Node Key;
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/// \brief The value type of the map
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typedef int Value;
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/// \brief Constructor
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RowMap(const GridGraph& graph) : _graph(graph) {}
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/// \brief The subscript operator
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Value operator[](Key key) const {
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return _graph.row(key);
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}
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private:
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const GridGraph& _graph;
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};
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/// \brief Constructor
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///
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/// Construct a grid graph with the given size.
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GridGraph(int width, int height) { construct(width, height); }
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/// \brief Resizes the graph
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///
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/// This function resizes the graph. It fully destroys and
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/// rebuilds the structure, therefore the maps of the graph will be
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/// reallocated automatically and the previous values will be lost.
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void resize(int width, int height) {
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Parent::notifier(Arc()).clear();
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Parent::notifier(Edge()).clear();
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Parent::notifier(Node()).clear();
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construct(width, height);
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Parent::notifier(Node()).build();
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Parent::notifier(Edge()).build();
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Parent::notifier(Arc()).build();
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}
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/// \brief The node on the given position.
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///
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/// Gives back the node on the given position.
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Node operator()(int i, int j) const {
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return Parent::operator()(i, j);
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}
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/// \brief The column index of the node.
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///
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/// Gives back the column index of the node.
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int col(Node n) const {
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return Parent::col(n);
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}
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/// \brief The row index of the node.
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///
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/// Gives back the row index of the node.
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int row(Node n) const {
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return Parent::row(n);
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}
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/// \brief The position of the node.
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///
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/// Gives back the position of the node, ie. the <tt>(col,row)</tt> pair.
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dim2::Point<int> pos(Node n) const {
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return Parent::pos(n);
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}
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/// \brief The number of the columns.
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///
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/// Gives back the number of the columns.
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int width() const {
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return Parent::width();
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}
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/// \brief The number of the rows.
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///
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/// Gives back the number of the rows.
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int height() const {
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return Parent::height();
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}
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/// \brief The arc goes right from the node.
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///
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/// Gives back the arc goes right from the node. If there is not
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/// outgoing arc then it gives back INVALID.
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Arc right(Node n) const {
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return Parent::right(n);
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}
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/// \brief The arc goes left from the node.
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///
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/// Gives back the arc goes left from the node. If there is not
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/// outgoing arc then it gives back INVALID.
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Arc left(Node n) const {
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return Parent::left(n);
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}
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/// \brief The arc goes up from the node.
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///
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/// Gives back the arc goes up from the node. If there is not
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/// outgoing arc then it gives back INVALID.
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Arc up(Node n) const {
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return Parent::up(n);
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}
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/// \brief The arc goes down from the node.
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///
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/// Gives back the arc goes down from the node. If there is not
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/// outgoing arc then it gives back INVALID.
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Arc down(Node n) const {
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return Parent::down(n);
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}
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/// \brief Index map of the grid graph
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///
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/// Just returns an IndexMap for the grid graph.
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IndexMap indexMap() const {
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return IndexMap(*this);
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}
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/// \brief Row map of the grid graph
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///
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/// Just returns a RowMap for the grid graph.
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RowMap rowMap() const {
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return RowMap(*this);
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}
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/// \brief Column map of the grid graph
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///
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/// Just returns a ColMap for the grid graph.
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ColMap colMap() const {
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return ColMap(*this);
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}
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};
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}
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#endif
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