package com.github.btrekkie.connectivity;

/**
 * Represents an edge in a ConnGraph, at the level of the edge (i.e. at the lowest level i for which G_i contains the
 * edge). Every graph edge has exactly one corresponding ConnEdge object, regardless of the number of levels it appears
 * in. See the comments for the implementation of ConnGraph.
 *
 * ConnEdges are stored in the linked lists suggested by EulerTourVertex.graphListHead and
 * EulerTourVertex.forestListHead. Each ConnEdge is in two linked lists, so care must be taken when traversing the
 * linked lists. prev1 and next1 are the links for the list starting at vertex1.graphListHead or vertex1.forestListHead,
 * while prev2 and next2 are the links for vertex2. But the vertex1 and vertex2 fields of a given edge are different
 * from the vertex1 and vertex2 fields of the linked edges. For example, the edge after next1 is not necessarily
 * next1.next1. It depends on whether next1.vertex1 is the same as vertex1. If next1.vertex1 == vertex1, then the edge
 * after next1 is next1.next1, but otherwise, it is next1.next2.
 */
class ConnEdge {
    /** The edge's first endpoint (at the same level as the edge). */
    public EulerTourVertex vertex1;

    /** The edge's second endpoint (at the same level as the edge). */
    public EulerTourVertex vertex2;

    /**
     * The EulerTourEdge object describing the edge's presence in an Euler tour tree, at the same level as the edge, or
     * null if the edge is not in the Euler tour forest F_i.
     */
    public EulerTourEdge eulerTourEdge;

    /**
     * The edge preceding this in a linked list of same-level edges adjacent to vertex1, if any. The edge is either part
     * of a list of non-forest edges starting with vertex1.graphListHead, or part of a list of forest edges starting
     * with vertex1.forestListHead. Note that this list excludes any edges that also appear in lower levels.
     */
    public ConnEdge prev1;

    /**
     * The edge succeeding this in a linked list of same-level edges adjacent to vertex1, if any. The edge is either
     * part of a list of non-forest edges starting with vertex1.graphListHead, or part of a list of forest edges
     * starting with vertex1.forestListHead. Note that this list excludes any edges that also appear in lower levels.
     */
    public ConnEdge next1;

    /**
     * The edge preceding this in a linked list of same-level edges adjacent to vertex2, if any. The edge is either part
     * of a list of non-forest edges starting with vertex2.graphListHead, or part of a list of forest edges starting
     * with vertex2.forestListHead. Note that this list excludes any edges that also appear in lower levels.
     */
    public ConnEdge prev2;

    /**
     * The edge succeeding this in a linked list of same-level edges adjacent to vertex2, if any. The edge is either
     * part of a list of non-forest edges starting with vertex2.graphListHead, or part of a list of forest edges
     * starting with vertex2.forestListHead. Note that this list excludes any edges that also appear in lower levels.
     */
    public ConnEdge next2;

    public ConnEdge(EulerTourVertex vertex1, EulerTourVertex vertex2) {
        this.vertex1 = vertex1;
        this.vertex2 = vertex2;
    }
}