diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html index 55756583c..801982ad0 100644 --- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html +++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html @@ -236,6 +236,7 @@ Graph
  • Hamiltons Cycle
  • Hopcroft Karp
  • Is Graph Bipartite
    • +
  • Is Graph Bipartite2
  • Kosaraju
  • Kruskal
  • Lowest Common Ancestor
    • diff --git a/df/dce/namespacegraph.html b/df/dce/namespacegraph.html index 8ed34f6c9..1d18e2454 100644 --- a/df/dce/namespacegraph.html +++ b/df/dce/namespacegraph.html @@ -138,16 +138,26 @@ Functions int dijkstra (std::vector< std::vector< std::pair< int, int > > > *adj, int s, int t)  Function runs the dijkstra algorithm for some source vertex and target vertex in the graph and returns the shortest distance of target from the source. More...
      +bool checkBipartite (const std::vector< std::vector< int64_t > > &graph, int64_t index, std::vector< int64_t > *visited) + function to check whether the passed graph is bipartite or not More...
    +  +bool isBipartite (const std::vector< std::vector< int64_t > > &graph) + returns true if the given graph is bipartite else returns false More...
    +  int TravellingSalesmanProblem (std::vector< std::vector< uint32_t > > *cities, int32_t src, uint32_t V)  Function calculates the minimum path distance that will cover all the cities starting from the source. More...
     

    Detailed Description

    Graph Algorithms.

    +

    Check whether a given graph is bipartite or not.

    for std::vector

    Graph algorithms.

    for IO operations for std::set

    Graph Algorithms

    +

    A bipartite graph is the one whose nodes can be divided into two disjoint sets in such a way that the nodes in a set are not connected to each other at all, i.e. no intra-set connections. The only connections that exist are that of inter-set, i.e. the nodes from one set are connected to a subset of nodes in the other set. In this implementation, using a graph in the form of adjacency list, check whether the given graph is a bipartite or not.

    +

    References used: GeeksForGeeks

    Author
    tushar2407 for IO operations for queue data structure for vector data structure for assert
    +

    Graphical algorithms

    for std::min for assert for IO operations for limits of integral types for std::vector

    Function Documentation

    @@ -311,6 +321,91 @@ Here is the call graph for this function: + + + +

    ◆ checkBipartite()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    bool graph::checkBipartite (const std::vector< std::vector< int64_t > > & graph,
    int64_t index,
    std::vector< int64_t > * visited 
    )
    +
    + +

    function to check whether the passed graph is bipartite or not

    +
    Parameters
    + + + + +
    graphis a 2D matrix whose rows or the first index signify the node and values in that row signify the nodes it is connected to
    indexis the valus of the node currently under observation
    visitedis the vector which stores whether a given node has been traversed or not yet
    +
    +
    +
    Returns
    boolean
    +

    < stores the neighbouring node indexes in squence of being reached

    +

    insert the current node into the queue

    +

    mark the current node as travelled

    +

    < stores the neighbour of the current node

    +

    check whether the neighbour node is travelled already or not

    +

    colour the neighbouring node with different colour than the current node

    +

    insert the neighbouring node into the queue

    +

    if both the current node and its neighbour has the same state then it is not a bipartite graph

    +

    return true when all the connected nodes of the current nodes are travelled and satisify all the above conditions

    +
    40{
    +
    41 std::queue<int64_t> q; ///< stores the neighbouring node indexes in squence
    +
    42 /// of being reached
    +
    43 q.push(index); /// insert the current node into the queue
    +
    44 (*visited)[index] = 1; /// mark the current node as travelled
    +
    45 while(q.size())
    +
    46 {
    +
    47 int64_t u = q.front();
    +
    48 q.pop();
    +
    49 for(uint64_t i=0;i<graph[u].size();i++)
    +
    50 {
    +
    51 int64_t v = graph[u][i]; ///< stores the neighbour of the current node
    +
    52 if(!(*visited)[v]) /// check whether the neighbour node is
    +
    53 /// travelled already or not
    +
    54 {
    +
    55 (*visited)[v] = ((*visited)[u]==1)?-1:1; /// colour the neighbouring node with
    +
    56 /// different colour than the current node
    +
    57 q.push(v); /// insert the neighbouring node into the queue
    +
    58 }
    +
    59 else if((*visited)[v] == (*visited)[u]) /// if both the current node and its neighbour
    +
    60 /// has the same state then it is not a bipartite graph
    +
    61 {
    +
    62 return false;
    +
    63 }
    +
    64 }
    +
    65 }
    +
    66 return true; /// return true when all the connected nodes of the current
    +
    67 /// nodes are travelled and satisify all the above conditions
    +
    68}
    +
    graph
    Graph Algorithms.
    + +
    @@ -632,6 +727,59 @@ Here is the call graph for this function: + + + +

    ◆ isBipartite()

    + +
    +
    + + + + + + + + +
    bool graph::isBipartite (const std::vector< std::vector< int64_t > > & graph)
    +
    + +

    returns true if the given graph is bipartite else returns false

    +
    Parameters
    + + +
    graphis a 2D matrix whose rows or the first index signify the node and values in that row signify the nodes it is connected to
    +
    +
    +
    Returns
    booleans
    +

    < stores boolean values which signify whether that node had been visited or not

    +

    if the current node is not visited then check whether the sub-graph of that node is a bipartite or not

    +
    76{
    +
    77 std::vector<int64_t> visited(graph.size()); ///< stores boolean values
    +
    78 /// which signify whether that node had been visited or not
    +
    79
    +
    80 for(uint64_t i=0;i<graph.size();i++)
    +
    81 {
    +
    82 if(!visited[i]) /// if the current node is not visited then check
    +
    83 /// whether the sub-graph of that node is a bipartite or not
    +
    84 {
    +
    85 if(!checkBipartite(graph, i, &visited))
    +
    86 {
    +
    87 return false;
    +
    88 }
    +
    89 }
    +
    90 }
    +
    91 return true;
    +
    92}
    +
    graph::checkBipartite
    bool checkBipartite(const std::vector< std::vector< int64_t > > &graph, int64_t index, std::vector< int64_t > *visited)
    function to check whether the passed graph is bipartite or not
    Definition: is_graph_bipartite2.cpp:35
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    +
    diff --git a/df/dce/namespacegraph.js b/df/dce/namespacegraph.js index 0f4f1723e..e9f46c998 100644 --- a/df/dce/namespacegraph.js +++ b/df/dce/namespacegraph.js @@ -25,10 +25,12 @@ var namespacegraph = [ "addEdge", "df/dce/namespacegraph.html#a9125ceb66bfbec3093bba64c2c1e99e2", null ], [ "addEdge", "df/dce/namespacegraph.html#ad4016cfc80485a43748895a2c26c7d08", null ], [ "addEdge", "df/dce/namespacegraph.html#a0e30e0dca68cb6e4f671440819b35b6a", null ], + [ "checkBipartite", "df/dce/namespacegraph.html#a8e1b547cd407c0774e63f0dc95cda9e7", null ], [ "depth_first_search", "df/dce/namespacegraph.html#ab5428a3519267a28bba4b4310cfbb6ae", null ], [ "dijkstra", "df/dce/namespacegraph.html#adc68cbc8ba09eb1142265935c0d45b84", null ], [ "explore", "df/dce/namespacegraph.html#a3ae80bc4c6a79d041b4f3a6589eb7fb8", null ], [ "explore", "df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463", null ], [ "getConnectedComponents", "df/dce/namespacegraph.html#a83ab16e96cec644109a58dfc9329bc2b", null ], + [ "isBipartite", "df/dce/namespacegraph.html#a84b0551489c613a681cc83b34450da4b", null ], [ "TravellingSalesmanProblem", "df/dce/namespacegraph.html#ab7706341d006e20d1ae58274187a3346", null ] ]; \ No newline at end of file diff --git a/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.map b/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.map new file mode 100644 index 000000000..11e99bf1c --- /dev/null +++ b/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.map @@ -0,0 +1,4 @@ + + + + diff --git a/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.md5 b/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.md5 new file mode 100644 index 000000000..13cb60dfa --- /dev/null +++ b/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.md5 @@ -0,0 +1 @@ +e3f582d9ab69da1c47da2c7486ee57b6 \ No newline at end of file diff --git a/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.svg b/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.svg new file mode 100644 index 000000000..ea42b411b --- /dev/null +++ b/df/dce/namespacegraph_a84b0551489c613a681cc83b34450da4b_cgraph.svg @@ -0,0 +1,37 @@ + + + + + + +graph::isBipartite + + + +Node1 + + +graph::isBipartite + + + + + +Node2 + + +graph::checkBipartite + + + + + +Node1->Node2 + + + + + diff --git a/globals_func_i.html b/globals_func_i.html index 7ce39a9c8..eaac1ff58 100644 --- a/globals_func_i.html +++ b/globals_func_i.html @@ -104,8 +104,8 @@ $(document).ready(function(){initNavTree('globals_func_i.html',''); initResizabl
  • is_happy() : happy_number.cpp
  • is_prime() : check_prime.cpp
  • is_square() : ordinary_least_squares_regressor.cpp
    • -
  • isPrime() : modular_inverse_fermat_little_theorem.cpp
  • IsPrime() : primality_test.cpp
    • +
  • isPrime() : modular_inverse_fermat_little_theorem.cpp
  • it_ternary_search() : ternary_search.cpp
    • diff --git a/globals_i.html b/globals_i.html index 56e3b39f1..dc9209aef 100644 --- a/globals_i.html +++ b/globals_i.html @@ -105,9 +105,9 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
  • is_happy() : happy_number.cpp
  • is_prime() : check_prime.cpp
  • is_square() : ordinary_least_squares_regressor.cpp
    • -
  • isPrime() : modular_inverse_fermat_little_theorem.cpp
  • isprime : prime_factorization.cpp
  • IsPrime() : primality_test.cpp
    • +
  • isPrime() : modular_inverse_fermat_little_theorem.cpp
  • it_ternary_search() : ternary_search.cpp
    • diff --git a/namespacemembers.html b/namespacemembers.html index 5ce6f60e0..23357552c 100644 --- a/namespacemembers.html +++ b/namespacemembers.html @@ -110,6 +110,7 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza

    - c -

    diff --git a/namespacemembers_func.html b/namespacemembers_func.html index 699109822..2892f83c3 100644 --- a/namespacemembers_func.html +++ b/namespacemembers_func.html @@ -110,6 +110,7 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR

    - c -

    diff --git a/navtreedata.js b/navtreedata.js index 849b021ad..eaf573829 100644 --- a/navtreedata.js +++ b/navtreedata.js @@ -144,7 +144,7 @@ var NAVTREEINDEX = "db/d9a/classuint128__t.html#a1ee2f1ffbd9984faad34883eb45e9705", "dd/d1c/classhash__chain.html#a6b4b4de1a8c96f98a63a77f650a9dcff", "de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0", -"dir_19b2bf9199a15c634a08b1ede1dd896a.html" +"dir_0eaa691bd54ab0922ca7f50599de6d22.html" ]; var SYNCONMSG = 'click to disable panel synchronisation'; diff --git a/navtreeindex0.js b/navtreeindex0.js index cfc607e09..61e2b67c1 100644 --- a/navtreeindex0.js +++ b/navtreeindex0.js @@ -5,23 +5,23 @@ var NAVTREEINDEX0 = "cpp/algorithm/accumulate.html":[9,0,97,14], "cpp/algorithm/adjacent_difference.html":[9,0,97,18], "cpp/algorithm/adjacent_find.html":[9,0,97,19], -"cpp/algorithm/all_any_none_of.html":[9,0,97,24], -"cpp/algorithm/all_any_none_of.html":[9,0,97,22], "cpp/algorithm/all_any_none_of.html":[9,0,97,299], 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