Bridges in a connected graph

Question

I have a programming task(not homework.) where I have to find the bridges in a graph. I worked on it a bit myself, but could not come up with anything satisfactory. So i goo

Answer 1

Not a new answer, but I needed this for the JVM/Kotlin. Here's a translation that relies upon com.google.common.graph.Graph.

/**
 * [T] The type of key held in the [graph].
 */
private class BridgeComputer(private val graph: ImmutableGraph) {
    /**
     * Counter.
     */
    private var count = 0
    /**
     * `low[v]` = Lowest preorder of any vertex connected to `v`.
     */
    private val low: MutableMap =
        graph.nodes().map { it to -1 }.toMap(mutableMapOf())
    /**
     * `pre[v]` = Order in which [depthFirstSearch] examines `v`.
     */
    private val pre: MutableMap =
        graph.nodes().map { it to -1 }.toMap(mutableMapOf())

    private val foundBridges = mutableSetOf>()

    init {
        graph.nodes().forEach { v ->
            // DO NOT PRE-FILTER!
            if (pre[v] == -1) {
                depthFirstSearch(v, v)
            }
        }
    }

    private fun depthFirstSearch(u: T, v: T) {
        pre[v] = count++
        low[v] = checkNotNull(pre[v]) { "pre[v]" }
        graph.adjacentNodes(v).forEach { w ->
            if (pre[w] == -1) {
                depthFirstSearch(v, w)
                low[v] =
                    Math.min(checkNotNull(low[v]) { "low[v]" }, checkNotNull(low[w]) { "low[w]" })
                if (low[w] == pre[w]) {
                    println("$v - $w is a bridge")
                    foundBridges += (v to w)
                }
            } else if (w != u) {
                low[v] =
                    Math.min(checkNotNull(low[v]) { "low[v]" }, checkNotNull(pre[w]) { "pre[w]" })
            }
        }
    }

    /**
     * Holds the computed bridges.
     */
    fun bridges() = ImmutableSet.copyOf(foundBridges)!!
}

Hopefully this makes someone's life easier.