Hadrons is now a library, the previous XML driven program is now a test

extras/Hadrons/Graph.hpp

@@ -0,0 +1,758 @@
+/*******************************************************************************
+Grid physics library, www.github.com/paboyle/Grid 
+
+Source file: programs/Hadrons/Graph.hpp
+
+Copyright (C) 2015
+
+Author: Antonin Portelli <antonin.portelli@me.com>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution 
+directory.
+*******************************************************************************/
+
+#ifndef Hadrons_Graph_hpp_
+#define Hadrons_Graph_hpp_
+
+#include <Grid/Hadrons/Global.hpp>
+
+BEGIN_HADRONS_NAMESPACE
+
+/******************************************************************************
+ *                          Oriented graph class                              *
+ ******************************************************************************/
+// I/O for edges
+template <typename T>
+std::ostream & operator<<(std::ostream &out, const std::pair<T, T> &e)
+{
+    out << "\""  << e.first << "\" -> \"" << e.second << "\"";
+    
+    return out;
+}
+
+// main class
+template <typename T>
+class Graph
+{
+public:
+    typedef std::pair<T, T> Edge;
+public:
+    // constructor
+    Graph(void);
+    // destructor
+    virtual ~Graph(void) = default;
+    // access
+    void           addVertex(const T &value);
+    void           addEdge(const Edge &e);
+    void           addEdge(const T &start, const T &end);
+    std::vector<T> getVertices(void) const;
+    void           removeVertex(const T &value);
+    void           removeEdge(const Edge &e);
+    void           removeEdge(const T &start, const T &end);
+    unsigned int   size(void) const;
+    // tests
+    bool gotValue(const T &value) const;
+    // graph topological manipulations
+    std::vector<T>              getAdjacentVertices(const T &value) const;
+    std::vector<T>              getChildren(const T &value) const;
+    std::vector<T>              getParents(const T &value) const;
+    std::vector<T>              getRoots(void) const;
+    std::vector<Graph<T>>       getConnectedComponents(void) const;
+    std::vector<T>              topoSort(void);
+    template <typename Gen>
+    std::vector<T>              topoSort(Gen &gen);
+    std::vector<std::vector<T>> allTopoSort(void);
+    // I/O
+    friend std::ostream & operator<<(std::ostream &out, const Graph<T> &g)
+    {
+        out << "{";
+        for (auto &e: g.edgeSet_)
+        {
+            out << e << ", ";
+        }
+        if (g.edgeSet_.size() != 0)
+        {
+            out << "\b\b";
+        }
+        out << "}";
+        
+        return out;
+    }
+private:
+    // vertex marking
+    void      mark(const T &value, const bool doMark = true);
+    void      markAll(const bool doMark = true);
+    void      unmark(const T &value);
+    void      unmarkAll(void);
+    bool      isMarked(const T &value) const;
+    const T * getFirstMarked(const bool isMarked = true) const;
+    template <typename Gen>
+    const T * getRandomMarked(const bool isMarked, Gen &gen);
+    const T * getFirstUnmarked(void) const;
+    template <typename Gen>
+    const T * getRandomUnmarked(Gen &gen);
+    // prune marked/unmarked vertices
+    void removeMarked(const bool isMarked = true);
+    void removeUnmarked(void);
+    // depth-first search marking
+    void depthFirstSearch(void);
+    void depthFirstSearch(const T &root);
+private:
+    std::map<T, bool>  isMarked_;
+    std::set<Edge>     edgeSet_;
+};
+
+// build depedency matrix from topological sorts
+template <typename T>
+std::map<T, std::map<T, bool>>
+makeDependencyMatrix(const std::vector<std::vector<T>> &topSort);
+
+/******************************************************************************
+ *                       template implementation                              *
+ ******************************************************************************
+ * in all the following V is the number of vertex and E is the number of edge
+ * in the worst case E = V^2
+ */
+
+// constructor /////////////////////////////////////////////////////////////////
+template <typename T>
+Graph<T>::Graph(void)
+{}
+
+// access //////////////////////////////////////////////////////////////////////
+// complexity: log(V)
+template <typename T>
+void Graph<T>::addVertex(const T &value)
+{
+    isMarked_[value] = false;
+}
+
+// complexity: O(log(V))
+template <typename T>
+void Graph<T>::addEdge(const Edge &e)
+{
+    addVertex(e.first);
+    addVertex(e.second);
+    edgeSet_.insert(e);
+}
+
+// complexity: O(log(V))
+template <typename T>
+void Graph<T>::addEdge(const T &start, const T &end)
+{
+    addEdge(Edge(start, end));
+}
+
+template <typename T>
+std::vector<T> Graph<T>::getVertices(void) const
+{
+    std::vector<T> vertex;
+    
+    for (auto &v: isMarked_)
+    {
+        vertex.push_back(v.first);
+    }
+    
+    return vertex;
+}
+
+// complexity: O(V*log(V))
+template <typename T>
+void Graph<T>::removeVertex(const T &value)
+{
+    // remove vertex from the mark table
+    auto vIt = isMarked_.find(value);
+    
+    if (vIt != isMarked_.end())
+    {
+        isMarked_.erase(vIt);
+    }
+    else
+    {
+        HADRON_ERROR("vertex " << value << " does not exists");
+    }
+
+    // remove all edges containing the vertex
+    auto pred = [&value](const Edge &e)
+    {
+        return ((e.first == value) or (e.second == value));
+    };
+    auto eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
+    
+    while (eIt != edgeSet_.end())
+    {
+        edgeSet_.erase(eIt);
+        eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
+    }
+}
+
+// complexity: O(log(V))
+template <typename T>
+void Graph<T>::removeEdge(const Edge &e)
+{
+    auto eIt = edgeSet_.find(e);
+    
+    if (eIt != edgeSet_.end())
+    {
+        edgeSet_.erase(eIt);
+    }
+    else
+    {
+        HADRON_ERROR("edge "  << e << " does not exists");
+    }
+}
+
+// complexity: O(log(V))
+template <typename T>
+void Graph<T>::removeEdge(const T &start, const T &end)
+{
+    removeEdge(Edge(start, end));
+}
+
+// complexity: O(1)
+template <typename T>
+unsigned int Graph<T>::size(void) const
+{
+    return isMarked_.size();
+}
+
+// tests ///////////////////////////////////////////////////////////////////////
+// complexity: O(log(V))
+template <typename T>
+bool Graph<T>::gotValue(const T &value) const
+{
+    auto it = isMarked_.find(value);
+    
+    if (it == isMarked_.end())
+    {
+        return false;
+    }
+    else
+    {
+        return true;
+    }
+}
+
+// vertex marking //////////////////////////////////////////////////////////////
+// complexity: O(log(V))
+template <typename T>
+void Graph<T>::mark(const T &value, const bool doMark)
+{
+    if (gotValue(value))
+    {
+        isMarked_[value] = doMark;
+    }
+    else
+    {
+        HADRON_ERROR("vertex " << value << " does not exists");
+    }
+}
+
+// complexity: O(V*log(V))
+template <typename T>
+void Graph<T>::markAll(const bool doMark)
+{
+    for (auto &v: isMarked_)
+    {
+        mark(v.first, doMark);
+    }
+}
+
+// complexity: O(log(V))
+template <typename T>
+void Graph<T>::unmark(const T &value)
+{
+    mark(value, false);
+}
+
+// complexity: O(V*log(V))
+template <typename T>
+void Graph<T>::unmarkAll(void)
+{
+    markAll(false);
+}
+
+// complexity: O(log(V))
+template <typename T>
+bool Graph<T>::isMarked(const T &value) const
+{
+    if (gotValue(value))
+    {
+        return isMarked_.at(value);
+    }
+    else
+    {
+        HADRON_ERROR("vertex " << value << " does not exists");
+        
+        return false;
+    }
+}
+
+// complexity: O(log(V))
+template <typename T>
+const T * Graph<T>::getFirstMarked(const bool isMarked) const
+{
+    auto pred = [&isMarked](const std::pair<T, bool> &v)
+    {
+        return (v.second == isMarked);
+    };
+    auto vIt = std::find_if(isMarked_.begin(), isMarked_.end(), pred);
+    
+    if (vIt != isMarked_.end())
+    {
+        return &(vIt->first);
+    }
+    else
+    {
+        return nullptr;
+    }
+}
+
+// complexity: O(log(V))
+template <typename T>
+template <typename Gen>
+const T * Graph<T>::getRandomMarked(const bool isMarked, Gen &gen)
+{
+    auto pred = [&isMarked](const std::pair<T, bool> &v)
+    {
+        return (v.second == isMarked);
+    };
+    std::uniform_int_distribution<unsigned int> dis(0, size() - 1);
+    auto                                        rIt = isMarked_.begin();
+    
+    std::advance(rIt, dis(gen));
+    auto vIt = std::find_if(rIt, isMarked_.end(), pred);
+    if (vIt != isMarked_.end())
+    {
+        return &(vIt->first);
+    }
+    else
+    {
+        vIt = std::find_if(isMarked_.begin(), rIt, pred);
+        if (vIt != rIt)
+        {
+            return &(vIt->first);
+        }
+        else
+        {
+            return nullptr;
+        }
+    }
+}
+
+// complexity: O(log(V))
+template <typename T>
+const T * Graph<T>::getFirstUnmarked(void) const
+{
+    return getFirstMarked(false);
+}
+
+// complexity: O(log(V))
+template <typename T>
+template <typename Gen>
+const T * Graph<T>::getRandomUnmarked(Gen &gen)
+{
+    return getRandomMarked(false, gen);
+}
+
+// prune marked/unmarked vertices //////////////////////////////////////////////
+// complexity: O(V^2*log(V))
+template <typename T>
+void Graph<T>::removeMarked(const bool isMarked)
+{
+    auto isMarkedCopy = isMarked_;
+    
+    for (auto &v: isMarkedCopy)
+    {
+        if (v.second == isMarked)
+        {
+            removeVertex(v.first);
+        }
+    }
+}
+
+// complexity: O(V^2*log(V))
+template <typename T>
+void Graph<T>::removeUnmarked(void)
+{
+    removeMarked(false);
+}
+
+// depth-first search marking //////////////////////////////////////////////////
+// complexity: O(V*log(V))
+template <typename T>
+void Graph<T>::depthFirstSearch(void)
+{
+    depthFirstSearch(isMarked_.begin()->first);
+}
+
+// complexity: O(V*log(V))
+template <typename T>
+void Graph<T>::depthFirstSearch(const T &root)
+{
+    std::vector<T> adjacentVertex;
+    
+    mark(root);
+    adjacentVertex = getAdjacentVertices(root);
+    for (auto &v: adjacentVertex)
+    {
+        if (!isMarked(v))
+        {
+            depthFirstSearch(v);
+        }
+    }
+}
+
+// graph topological manipulations /////////////////////////////////////////////
+// complexity: O(V*log(V))
+template <typename T>
+std::vector<T> Graph<T>::getAdjacentVertices(const T &value) const
+{
+    std::vector<T> adjacentVertex;
+    
+    auto pred = [&value](const Edge &e)
+    {
+        return ((e.first == value) or (e.second == value));
+    };
+    auto eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
+    
+    while (eIt != edgeSet_.end())
+    {
+        if (eIt->first == value)
+        {
+            adjacentVertex.push_back((*eIt).second);
+        }
+        else if (eIt->second == value)
+        {
+            adjacentVertex.push_back((*eIt).first);
+        }
+        eIt = find_if(++eIt, edgeSet_.end(), pred);
+    }
+    
+    return adjacentVertex;
+}
+
+// complexity: O(V*log(V))
+template <typename T>
+std::vector<T> Graph<T>::getChildren(const T &value) const
+{
+    std::vector<T> child;
+    
+    auto pred = [&value](const Edge &e)
+    {
+        return (e.first == value);
+    };
+    auto eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
+    
+    while (eIt != edgeSet_.end())
+    {
+        child.push_back((*eIt).second);
+        eIt = find_if(++eIt, edgeSet_.end(), pred);
+    }
+    
+    return child;
+}
+
+// complexity: O(V*log(V))
+template <typename T>
+std::vector<T> Graph<T>::getParents(const T &value) const
+{
+    std::vector<T> parent;
+    
+    auto pred = [&value](const Edge &e)
+    {
+        return (e.second == value);
+    };
+    auto eIt = find_if(edgeSet_.begin(), edgeSet_.end(), pred);
+    
+    while (eIt != edgeSet_.end())
+    {
+        parent.push_back((*eIt).first);
+        eIt = find_if(++eIt, edgeSet_.end(), pred);
+    }
+    
+    return parent;
+}
+
+// complexity: O(V^2*log(V))
+template <typename T>
+std::vector<T> Graph<T>::getRoots(void) const
+{
+    std::vector<T> root;
+    
+    for (auto &v: isMarked_)
+    {
+        auto parent = getParents(v.first);
+        
+        if (parent.size() == 0)
+        {
+            root.push_back(v.first);
+        }
+    }
+    
+    return root;
+}
+
+// complexity: O(V^2*log(V))
+template <typename T>
+std::vector<Graph<T>> Graph<T>::getConnectedComponents(void) const
+{
+    std::vector<Graph<T>> res;
+    Graph<T>              copy(*this);
+    
+    while (copy.size() > 0)
+    {
+        copy.depthFirstSearch();
+        res.push_back(copy);
+        res.back().removeUnmarked();
+        res.back().unmarkAll();
+        copy.removeMarked();
+        copy.unmarkAll();
+    }
+    
+    return res;
+}
+
+// topological sort using a directed DFS algorithm
+// complexity: O(V*log(V))
+template <typename T>
+std::vector<T> Graph<T>::topoSort(void)
+{
+    std::stack<T>     buf;
+    std::vector<T>    res;
+    const T           *vPt;
+    std::map<T, bool> tmpMarked(isMarked_);
+
+    // visit function
+    std::function<void(const T &)> visit = [&](const T &v)
+    {
+        if (tmpMarked.at(v))
+        {
+            HADRON_ERROR("cannot topologically sort a cyclic graph");
+        }
+        if (!isMarked(v))
+        {
+            std::vector<T> child = getChildren(v);
+
+            tmpMarked[v] = true;
+            for (auto &c: child)
+            {
+                visit(c);
+            }
+            mark(v);
+            tmpMarked[v] = false;
+            buf.push(v);
+        }
+    };
+    
+    // reset temporary marks
+    for (auto &v: tmpMarked)
+    {
+        tmpMarked.at(v.first) = false;
+    }
+    
+    // loop on unmarked vertices
+    unmarkAll();
+    vPt = getFirstUnmarked();
+    while (vPt)
+    {
+        visit(*vPt);
+        vPt = getFirstUnmarked();
+    }
+    unmarkAll();
+    
+    // create result vector
+    while (!buf.empty())
+    {
+        res.push_back(buf.top());
+        buf.pop();
+    }
+    
+    return res;
+}
+
+// random version of the topological sort
+// complexity: O(V*log(V))
+template <typename T>
+template <typename Gen>
+std::vector<T> Graph<T>::topoSort(Gen &gen)
+{
+    std::stack<T>     buf;
+    std::vector<T>    res;
+    const T           *vPt;
+    std::map<T, bool> tmpMarked(isMarked_);
+    
+    // visit function
+    std::function<void(const T &)> visit = [&](const T &v)
+    {
+        if (tmpMarked.at(v))
+        {
+            HADRON_ERROR("cannot topologically sort a cyclic graph");
+        }
+        if (!isMarked(v))
+        {
+            std::vector<T> child = getChildren(v);
+            
+            tmpMarked[v] = true;
+            std::shuffle(child.begin(), child.end(), gen);
+            for (auto &c: child)
+            {
+                visit(c);
+            }
+            mark(v);
+            tmpMarked[v] = false;
+            buf.push(v);
+        }
+    };
+    
+    // reset temporary marks
+    for (auto &v: tmpMarked)
+    {
+        tmpMarked.at(v.first) = false;
+    }
+    
+    // loop on unmarked vertices
+    unmarkAll();
+    vPt = getRandomUnmarked(gen);
+    while (vPt)
+    {
+        visit(*vPt);
+        vPt = getRandomUnmarked(gen);
+    }
+    unmarkAll();
+    
+    // create result vector
+    while (!buf.empty())
+    {
+        res.push_back(buf.top());
+        buf.pop();
+    }
+    
+    return res;
+}
+
+// generate all possible topological sorts
+// Y. L. Varol & D. Rotem, Comput. J. 24(1), pp. 83–84, 1981
+// http://comjnl.oupjournals.org/cgi/doi/10.1093/comjnl/24.1.83
+// complexity: O(V*log(V)) (from the paper, but really ?)
+template <typename T>
+std::vector<std::vector<T>> Graph<T>::allTopoSort(void)
+{
+    std::vector<std::vector<T>>    res;
+    std::map<T, std::map<T, bool>> iMat;
+    
+    // create incidence matrix
+    for (auto &v1: isMarked_)
+    for (auto &v2: isMarked_)
+    {
+        iMat[v1.first][v2.first] = false;
+    }
+    for (auto &v: isMarked_)
+    {
+        auto cVec = getChildren(v.first);
+        
+        for (auto &c: cVec)
+        {
+            iMat[v.first][c] = true;
+        }
+    }
+    
+    // generate initial topological sort
+    res.push_back(topoSort());
+    
+    // generate all other topological sorts by permutation
+    std::vector<T>            p = res[0];
+    const unsigned int        n = size();
+    std::vector<unsigned int> loc(n);
+    unsigned int              i, k, k1;
+    T                         obj_k, obj_k1;
+    bool                      isFinal;
+    
+    for (unsigned int j = 0; j < n; ++j)
+    {
+        loc[j] = j;
+    }
+    i = 0;
+    while (i < n-1)
+    {
+        k      = loc[i];
+        k1     = k + 1;
+        obj_k  = p[k];
+        if (k1 >= n)
+        {
+            isFinal = true;
+            obj_k1  = obj_k;
+        }
+        else
+        {
+            isFinal = false;
+            obj_k1  = p[k1];
+        }
+        if (iMat[res[0][i]][obj_k1] or isFinal)
+        {
+            for (unsigned int l = k; l >= i + 1; --l)
+            {
+                p[l]   = p[l-1];
+            }
+            p[i]   = obj_k;
+            loc[i] = i;
+            i++;
+        }
+        else
+        {
+            p[k]   = obj_k1;
+            p[k1]  = obj_k;
+            loc[i] = k1;
+            i      = 0;
+            res.push_back(p);
+        }
+    }
+    
+    return res;
+}
+
+// build depedency matrix from topological sorts ///////////////////////////////
+// complexity: something like O(V^2*log(V!))
+template <typename T>
+std::map<T, std::map<T, bool>>
+makeDependencyMatrix(const std::vector<std::vector<T>> &topSort)
+{
+    std::map<T, std::map<T, bool>> m;
+    const std::vector<T>           &vList = topSort[0];
+    
+    for (auto &v1: vList)
+    for (auto &v2: vList)
+    {
+        bool dep = true;
+        
+        for (auto &t: topSort)
+        {
+            auto i1 = std::find(t.begin(), t.end(), v1);
+            auto i2 = std::find(t.begin(), t.end(), v2);
+            
+            dep = dep and (i1 - i2 > 0);
+            if (!dep) break;
+        }
+        m[v1][v2] = dep;
+    }
+    
+    return m;
+}
+
+END_HADRONS_NAMESPACE
+
+#endif // Hadrons_Graph_hpp_