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43 * @file priority_queue_dijkstra_example.cpp
44 * A basic example showing how to cross reference a vector and a
45 * priority-queue for modify.
49 * This example shows how to cross-reference priority queues
50 * and a vector. I.e., using a vector to
51 * map keys to entries in a priority queue, and using the priority
52 * queue to map entries to the vector. The combination
53 * can be used for fast modification of keys.
55 * As an example, a very simple form of Diskstra's algorithm is used. The graph
56 * is represented by an adjacency matrix. Nodes and vertices are size_ts, and
57 * it is assumed that the minimal path between any two nodes is less than 1000.
64 #include <ext/pb_ds/priority_queue.hpp>
67 using namespace __gnu_pbds
;
69 // The value type of the priority queue.
70 // The first entry is the node's id, and the second is the distance.
71 typedef std::pair
<size_t, size_t> pq_value
;
73 // Comparison functor used to compare priority-queue value types.
74 struct pq_value_cmp
: public binary_function
<pq_value
, pq_value
, bool>
77 operator()(const pq_value
& r_lhs
, const pq_value
& r_rhs
) const
79 // Note that a value is considered smaller than a different value
80 // if its distance is* larger*. This is because by STL
81 // conventions, "larger" entries are nearer the top of the
83 return r_rhs
.second
< r_lhs
.second
;
91 // Number of vertices is hard-coded in this example.
97 // The edge-distance matrix.
98 // For example, the distance from node 0 to node 1 is 5, and the
99 // distance from node 1 to node 0 is 2.
100 const size_t a_a_edge_legnth
[num_vertices
][num_vertices
] =
109 // The priority queue type.
110 typedef __gnu_pbds::priority_queue
< pq_value
, pq_value_cmp
> pq_t
;
112 // The priority queue object.
115 // This vector contains for each node, a find-iterator into the
117 vector
<pq_t::point_iterator
> a_it
;
119 // First we initialize the data structures.
121 // For each node, we push into the priority queue a value
122 // identifying it with a distance of infinity.
123 for (size_t i
= 0; i
< num_vertices
; ++i
)
124 a_it
.push_back(p
.push(pq_value(i
, graph_inf
)));
126 // Now we take the initial node, in this case 0, and modify its
128 p
.modify(a_it
[0], pq_value(0, 0));
130 // The priority queue contains all vertices whose final distance has
131 // not been determined, so to finish the algorithm, we must loop
132 // until it is empty.
135 // First we find the node whose distance is smallest.
136 const pq_value
& r_v
= p
.top();
137 const size_t node_id
= r_v
.first
;
138 const size_t dist
= r_v
.second
;
140 // This is the node's final distance, so we can print it out.
141 cout
<< "The distance from 0 to " << node_id
142 << " is " << dist
<< endl
;
144 // Now we go over the node's neighbors and "relax" the
145 // distances, if applicable.
146 for (size_t neighbor_i
= 0; neighbor_i
< num_vertices
; ++neighbor_i
)
148 // Potentially, the distance to the neighbor is the distance
149 // to the currently-considered node + the distance from this
150 // node to the neighbor.
151 const size_t pot_dist
= dist
+ a_a_edge_legnth
[node_id
][neighbor_i
];
153 if (a_it
[neighbor_i
] == a_it
[0])
156 // "Relax" the distance (if appropriate) through modify.
157 if (pot_dist
< a_it
[neighbor_i
]->second
)
158 p
.modify(a_it
[neighbor_i
], pq_value(neighbor_i
, pot_dist
));
161 // Done with the node, so we pop it.
162 a_it
[node_id
] = a_it
[0];