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‎README.md

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@@ -64,9 +64,12 @@ Algorithms, 4th edition textbook code (using c++)
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## ch4. Graphs
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| REF | PROGRAM | DESCRIPTION / JAVADOC | REF | PROGRAM | DESCRIPTION / JAVADOC |
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| :---------------------------------------------------------: | :-----------------------------------------------: | :---------------------------: | :---------------------------------------------------------: | :----------------------------------------------------------: | :---------------------------: |
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| [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [Graph.h](ch4/head/Graph.h) | undirected graph | [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [GraphGenerator.java](https://algs4.cs.princeton.edu/41graph/GraphGenerator.java.html) | generate random graphs |
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| [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [DepthFirstSearch.h](ch4/head/DepthFirstSearch.h) | depth-first search in a graph | [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [NonrecursiveDFS.h](ch4/head/NonrecursiveDFS.h) | DFS in a graph (nonrecursive) |
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| [4.1](https://algs4.cs.princeton.edu/41graph/index.php#4.1) | [DepthFirstPaths.h](ch4/head/DepthFirstPaths.h) | paths in a graph (DFS) | [4.2](https://algs4.cs.princeton.edu/41graph/index.php#4.2) | [BreadthFirstPaths.h](ch4/head/BreadthFirstPaths.h) | paths in a graph (BFS) |
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| REF | PROGRAM | DESCRIPTION / JAVADOC | REF | PROGRAM | DESCRIPTION / JAVADOC |
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| :---------------------------------------------------------: | :-----------------------------------------------: | :-----------------------------: | :---------------------------------------------------------: | :----------------------------------------------------------: | :---------------------------: |
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| [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [Graph.h](ch4/head/Graph.h) | undirected graph | [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [GraphGenerator.java](https://algs4.cs.princeton.edu/41graph/GraphGenerator.java.html) | generate random graphs |
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| [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [DepthFirstSearch.h](ch4/head/DepthFirstSearch.h) | depth-first search in a graph | [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [NonrecursiveDFS.h](ch4/head/NonrecursiveDFS.h) | DFS in a graph (nonrecursive) |
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| [4.1](https://algs4.cs.princeton.edu/41graph/index.php#4.1) | [DepthFirstPaths.h](ch4/head/DepthFirstPaths.h) | paths in a graph (DFS) | [4.2](https://algs4.cs.princeton.edu/41graph/index.php#4.2) | [BreadthFirstPaths.h](ch4/head/BreadthFirstPaths.h) | paths in a graph (BFS) |
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| [4.3](https://algs4.cs.princeton.edu/41graph/index.php#4.3) | [CC.h](ch4/head/CC.h) | connected components of a graph | [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [Bipartite.h](ch4/head/Bipartite.h) | bipartite or odd cycle (DFS) |
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| [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [BipartiteX.h](ch4/head/BipartiteX.h) | bipartite or odd cycle (BFS) | [-](https://algs4.cs.princeton.edu/41graph/index.php#-) | [Cycle.h](ch4/head/Cycle.h) | cycle in a graph |
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| | | | | | |
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‎ch4/10_Cycle/CMakeLists.txt

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cmake_minimum_required(VERSION 3.8)
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project(10_Cycle)
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set(CMAKE_CXX_STANDARD 14)
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set(SOURCE_FILES main.cpp ../head/Graph.h ../head/GraphGenerator.h ../head/DepthFirstSearch.h ../head/EulerianCycle.h)
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add_executable(10_Cycle ${SOURCE_FILES})

‎ch4/10_Cycle/main.cpp

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#include <iostream>
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#include "../head/Cycle.h"
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using namespace std;
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/**
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* Unit tests the {@code Cycle} data type.
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*
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* @param args the command-line arguments
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*/
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int main() {
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string filename = "/home/ace/AceDev/C++/algorithm/ch4/data/tinyG.txt";
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Graph G(filename);
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Cycle finder(G);
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if (finder.hasCycle()) {
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auto cyc = finder.getcycle();
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while (!cyc.empty()) {
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cout << cyc.top() << " ";
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cyc.pop();
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}
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cout << endl;
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} else
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cout << "Graph is acyclic" << endl;
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}

‎ch4/7_CC/CMakeLists.txt

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cmake_minimum_required(VERSION 3.8)
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project(7_CC)
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set(CMAKE_CXX_STANDARD 14)
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set(SOURCE_FILES main.cpp ../head/Graph.h ../head/GraphGenerator.h ../head/DepthFirstSearch.h)
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add_executable(7_CC ${SOURCE_FILES})

‎ch4/7_CC/main.cpp

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#include <iostream>
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#include <queue>
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#include "../head/CC.h"
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using namespace std;
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/**
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* Unit tests the {@code BreadthFirstPaths} data type.
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*
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* @param args the command-line arguments
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*/
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int main() {
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string filename = "/home/ace/AceDev/C++/algorithm/ch4/data/tinyG.txt";
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Graph g(filename);
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CC cc(g);
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int m = cc.getcount();
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cout << m << " components" << endl;
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vector<queue<int>> components(m);
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for (int v = 0; v < g.getV(); ++v) {
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components[cc.getid(v)].push(v);
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}
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// print results
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for (int i = 0; i < m; ++i) {
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while (!components[i].empty()) {
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auto v = components[i].front();
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components[i].pop();
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cout << v << " ";
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}
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cout << endl;
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}
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}

‎ch4/8_Bipartite/CMakeLists.txt

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cmake_minimum_required(VERSION 3.8)
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project(8_Bipartite)
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set(CMAKE_CXX_STANDARD 14)
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set(SOURCE_FILES main.cpp ../head/Graph.h ../head/GraphGenerator.h ../head/DepthFirstSearch.h)
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add_executable(8_Bipartite ${SOURCE_FILES})

‎ch4/8_Bipartite/main.cpp

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#include <iostream>
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#include <queue>
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#include "../head/GraphGenerator.h"
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#include "../head/Bipartite.h"
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using namespace std;
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/**
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* Unit tests the {@code Bipartite} data type.
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*
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* @param args the command-line arguments
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*/
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int main() {
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int V1 = 5;
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int V2 = 8;
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int E = 4;
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int F = 6;
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// create random bipartite graph with V1 vertices on left side,
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// V2 vertices on right side, and E edges; then add F random edges
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Graph G = GraphGenerator::bipartite(V1, V2, E);
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uniform_int_distribution<> dis(0, V1 + V2 - 1);
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for (int i = 0; i < F; ++i) {
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int v = dis(g);
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int w = dis(g);
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G.addEdge(v, w);
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}
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cout << G << endl;
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Bipartite b(G);
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if (b.getisBipartite()) {
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cout << "Graph is bipartite" << endl;
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for (int v = 0; v < G.getV(); ++v) {
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cout << v << " : " << b.getcolor(v) << endl;
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}
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} else {
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cout << "Graph has an odd-length cycle: ";
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auto odd = b.oddCycle();
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while (!odd.empty()) {
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cout << odd.top() << " ";
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odd.pop();
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}
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}
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}

‎ch4/9_BipartiteX/CMakeLists.txt

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cmake_minimum_required(VERSION 3.8)
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project(9_BipartiteX)
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set(CMAKE_CXX_STANDARD 14)
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set(SOURCE_FILES main.cpp ../head/Graph.h ../head/GraphGenerator.h ../head/DepthFirstSearch.h)
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add_executable(9_BipartiteX ${SOURCE_FILES})

‎ch4/9_BipartiteX/main.cpp

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#include <iostream>
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#include <queue>
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#include "../head/GraphGenerator.h"
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#include "../head/BipartiteX.h"
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using namespace std;
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/**
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* Unit tests the {@code Bipartite} data type.
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*
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* @param args the command-line arguments
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*/
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int main() {
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int V1 = 5;
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int V2 = 8;
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int E = 4;
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int F = 6;
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// create random bipartite graph with V1 vertices on left side,
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// V2 vertices on right side, and E edges; then add F random edges
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Graph G = GraphGenerator::bipartite(V1, V2, E);
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uniform_int_distribution<> dis(0, V1 + V2 - 1);
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for (int i = 0; i < F; ++i) {
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int v = dis(g);
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int w = dis(g);
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G.addEdge(v, w);
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}
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cout << G << endl;
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BipartiteX b(G);
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if (b.getisBipartite()) {
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cout << "Graph is bipartite" << endl;
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for (int v = 0; v < G.getV(); ++v) {
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cout << v << " : " << b.getcolor(v) << endl;
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}
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} else {
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cout << "Graph has an odd-length cycle: ";
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auto odd = b.oddCycle();
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while (!odd.empty()) {
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cout << odd.front() << " ";
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odd.pop();
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}
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}
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}

‎ch4/CMakeLists.txt

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set(CMAKE_CXX_STANDARD 14)
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add_subdirectory(1_Graph)
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add_subdirectory(2_GraphGenerator)
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add_subdirectory(3_DepthFirstSearch)
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add_subdirectory(4_NonrecursiveDFS)
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add_subdirectory(5_DepthFirstPaths)
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add_subdirectory(6_BreadthFirstPaths)
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add_subdirectory(7_CC)
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add_subdirectory(8_Bipartite)
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add_subdirectory(9_BipartiteX)
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add_subdirectory(10_Cycle)
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add_subdirectory(temp)

‎ch4/head/Bipartite.h

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#ifndef CH4_BIPARTITE_H
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#define CH4_BIPARTITE_H
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#include "../head/Graph.h"
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/**
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* The {@code Bipartite} class represents a data type for
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* determining whether an undirected graph is bipartite or whether
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* it has an odd-length cycle.
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* The <em>isBipartite</em> operation determines whether the graph is
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* bipartite. If so, the <em>color</em> operation determines a
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* bipartition; if not, the <em>oddCycle</em> operation determines a
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* cycle with an odd number of edges.
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* <p>
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* This implementation uses depth-first search.
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* The constructor takes time proportional to <em>V</em> + <em>E</em>
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* (in the worst case),
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* where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
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* Afterwards, the <em>isBipartite</em> and <em>color</em> operations
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* take constant time; the <em>oddCycle</em> operation takes time proportional
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* to the length of the cycle.
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* See {@link BipartiteX} for a nonrecursive version that uses breadth-first
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* search.
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* <p>
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* For additional documentation, see <a href="https://algs4.cs.princeton.edu/41graph">Section 4.1</a>
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* of <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
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*
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* @author Robert Sedgewick
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* @author Kevin Wayne
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*/
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class Bipartite {
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public:
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/**
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* Determines whether an undirected graph is bipartite and finds either a
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* bipartition or an odd-length cycle.
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*
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* @param G the graph
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*/
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Bipartite(Graph &G) : isBipartite(true), color(G.getV()), marked(G.getV()), edgeTo(G.getV()) {
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for (int v = 0; v < G.getV(); v++) {
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if (!marked[v]) {
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dfs(G, v);
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}
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}
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}
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/**
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* Returns true if the graph is bipartite.
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*
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* @return {@code true} if the graph is bipartite; {@code false} otherwise
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*/
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bool getisBipartite() {
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return isBipartite;
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}
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/**
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* Returns the side of the bipartite that vertex {@code v} is on.
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*
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* @param v the vertex
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* @return the side of the bipartition that vertex {@code v} is on; two vertices
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* are in the same side of the bipartition if and only if they have the
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* same color
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* @throws IllegalArgumentException unless {@code 0 <= v < V}
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* @throws UnsupportedOperationException if this method is called when the graph
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* is not bipartite
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*/
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bool getcolor(int v) {
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validateVertex(v);
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if (!isBipartite)
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throw runtime_error("graph is not bipartite");
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return color[v];
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}
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/**
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* Returns an odd-length cycle if the graph is not bipartite, and
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* {@code null} otherwise.
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*
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* @return an odd-length cycle if the graph is not bipartite
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* (and hence has an odd-length cycle), and {@code null}
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* otherwise
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*/
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stack<int> oddCycle() {
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return cycle;
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}
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private:
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// throw an IllegalArgumentException unless {@code 0 <= v < V}
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void validateVertex(int v) {
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int V = marked.size();
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if (v < 0 || v >= V)
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throw runtime_error("vertex " + to_string(v) + " is not between 0 and " + to_string(V - 1));
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}
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void dfs(Graph G, int v) {
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marked[v] = true;
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for (int w : G.getadj(v)) {
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// short circuit if odd-length cycle found
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if (!cycle.empty()) return;
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// found uncolored vertex, so recur
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if (!marked[w]) {
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edgeTo[w] = v;
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color[w] = !color[v];
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dfs(G, w);
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} // if v-w create an odd-length cycle, find it
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else if (color[w] == color[v]) {
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isBipartite = false;
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cycle.push(w); // don't need this unless you want to include start vertex twice
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for (int x = v; x != w; x = edgeTo[x]) {
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cycle.push(x);
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}
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cycle.push(w);
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}
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}
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}
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private:
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bool isBipartite; // is the graph bipartite?
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vector<bool> color; // color[v] gives vertices on one side of bipartition
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vector<bool> marked; // marked[v] = true iff v has been visited in DFS
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vector<int> edgeTo; // edgeTo[v] = last edge on path to v
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stack<int> cycle; // odd-length cycle
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};
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#endif //CH4_BIPARTITE_H

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