Making an adjacency list in C++ for a directed graph

Question

Hello all :) Today I am refining my skills on graph theory and data structures. I decided to do a small project in C++ because it\'s been a while since I\'ve worked in C++

Answer 1

You may use a vector in node, as a adjacency list.

class node {
  int value;
  vector neighbors;
 };

If the graph is known at compile time, you can use array, but it's "a little bit" harder. If you know just size of graph (at compile time) you can do something like that.

template
class graph {
  array nodes;
 }

To add a neighbor, you doing something like that (do not forget numbering from zero):

nodes[i].neighbors.push_back(nodes+j); //or &nodes[j]

Of course, you can do no-pointer adjacency list and work "above" a table. Than you have vector in node and you pushing number of neighbour. With both representation of the graph, you can realize all algorithms which use adjacency list.

And finally, I might add. Some use a list instead of a vector, because the removal is in O(1) time. Mistake. For most algorithms, the order in the adjacency list is not important. So you can erase any element from vector in O(1) time. Just swap it with last element, pop_back is O(1) complexity. Something like that:

if(i != number_of_last_element_in_list) //neighbors.size() - 1
 swap(neighbors[i], neighbor.back());
neighbors.pop_back();

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Specific example (you have vector in node, C++11 (!)):

//creation of nodes, as previously
constexpr unsigned int N = 3;
array nodes; //or array nodes;
//creating edge (adding neighbors), in the constructor, or somewhere
nodes[0].neighbors = {&nodes[1]};
nodes[1].neighbors = {&nodes[0], &nodes[1]};
//adding runtime, i,j from user, eg. i = 2, j = 0
nodes[i].neighbors.push_back(&nodes[j]); //nodes[2].neighbors = {&nodes[0]};

I believe it's clear. From 0 you can go to 1, from 1 to 0 and to itself, and (as in eg.) from 2 to 0. It's directed graph. If you want undirected, you should add to both nodes neighbour’s addresses. You can use numbers instead of pointers. vector in class node and pushing back numbers, no addresses.

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As we know, you do not need to use pointers. Here is an example of it, too.

When the number of vertexes may change, you can use vector of nodes (vector) instead array, and just resizing. The rest remains unchanged. For example:

vector nodes(n); //you have n nodes
nodes.emplace_back(); //you added new node, or .resize(n+1)
//here is place to runtime graph generate
//as previously, i,j from user, but now you have 'vector' in node
nodes[i].neighbors.push_back(j);

But you can't erase a node, this breaches numbering! If you want to erase something, you should use list (list) of pointers. Otherwise you must keep non-existent vertexes. Here, the order matters!

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Regarding the line nodes.emplace_back(); //adding node, It is safe with graph without pointers. If you want use pointers, you predominately shouldn't change size of graph. You can accidentally change address of some nodes, while adding vertex, when vector will be copied to new place (out of space).

One way to deal with it is using reserve, although you have to know maximal size of graph! But in fact I encourage you not to use vector to keep vertexes, when you are using pointers. If you don't know implementation, more safe could be self memory management (smart pointers eg. shared_ptr or just new).

node* const graph = new node[size]; //<-- It is your graph.
//Here no address change accidentally.

Using vector as adjacency list is always fine! There's no chance to change node's address.