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BreadthFirstPaths.kt
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BreadthFirstPaths.kt
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class BreadthFirstPaths {
private var marked: BooleanArray? = null // marked[v] = is there an s-v path
private var edgeTo: IntArray? = null // edgeTo[v] = previous edge on shortest s-v path
private var distTo: IntArray? = null // distTo[v] = number of edges shortest s-v path
/**
* Computes the shortest path between the source vertex `s`
* and every other vertex in the graph `G`.
* @param G the graph
* @param s the source vertex
*/
constructor(G: Graph, s: Int) {
marked = BooleanArray(G.V())
distTo = IntArray(G.V())
edgeTo = IntArray(G.V())
bfs(G, s)
assert(check(G, s))
}
/**
* Computes the shortest path between any one of the source vertices in `sources`
* and every other vertex in graph `G`.
* @param G the graph
* @param sources the source vertices
*/
constructor(G: Graph, sources: Iterable<Integer>) {
marked = BooleanArray(G.V())
distTo = IntArray(G.V())
edgeTo = IntArray(G.V())
for (v in 0 until G.V())
distTo[v] = INFINITY
bfs(G, sources)
}
// breadth-first search from a single source
private fun bfs(G: Graph, s: Int) {
val q = Queue<Integer>()
for (v in 0 until G.V())
distTo[v] = INFINITY
distTo[s] = 0
marked[s] = true
q.enqueue(s)
while (!q.isEmpty()) {
val v = q.dequeue()
for (w in G.adj(v)) {
if (!marked!![w]) {
edgeTo[w] = v
distTo[w] = distTo!![v] + 1
marked[w] = true
q.enqueue(w)
}
}
}
}
// breadth-first search from multiple sources
private fun bfs(G: Graph, sources: Iterable<Integer>) {
val q = Queue<Integer>()
for (s in sources) {
marked[s] = true
distTo[s] = 0
q.enqueue(s)
}
while (!q.isEmpty()) {
val v = q.dequeue()
for (w in G.adj(v)) {
if (!marked!![w]) {
edgeTo[w] = v
distTo[w] = distTo!![v] + 1
marked[w] = true
q.enqueue(w)
}
}
}
}
/**
* Is there a path between the source vertex `s` (or sources) and vertex `v`?
* @param v the vertex
* @return `true` if there is a path, and `false` otherwise
*/
fun hasPathTo(v: Int): Boolean {
return marked!![v]
}
/**
* Returns the number of edges in a shortest path between the source vertex `s`
* (or sources) and vertex `v`?
* @param v the vertex
* @return the number of edges in a shortest path
*/
fun distTo(v: Int): Int {
return distTo!![v]
}
/**
* Returns a shortest path between the source vertex `s` (or sources)
* and `v`, or `null` if no such path.
* @param v the vertex
* @return the sequence of vertices on a shortest path, as an Iterable
*/
fun pathTo(v: Int): Iterable<Integer>? {
if (!hasPathTo(v)) return null
val path = Stack<Integer>()
var x: Int
x = v
while (distTo!![x] != 0) {
path.push(x)
x = edgeTo!![x]
}
path.push(x)
return path
}
// check optimality conditions for single source
private fun check(G: Graph, s: Int): Boolean {
// check that the distance of s = 0
if (distTo!![s] != 0) {
StdOut.println("distance of source " + s + " to itself = " + distTo!![s])
return false
}
// check that for each edge v-w dist[w] <= dist[v] + 1
// provided v is reachable from s
for (v in 0 until G.V()) {
for (w in G.adj(v)) {
if (hasPathTo(v) != hasPathTo(w)) {
StdOut.println("edge $v-$w")
StdOut.println("hasPathTo(" + v + ") = " + hasPathTo(v))
StdOut.println("hasPathTo(" + w + ") = " + hasPathTo(w))
return false
}
if (hasPathTo(v) && distTo!![w] > distTo!![v] + 1) {
StdOut.println("edge $v-$w")
StdOut.println("distTo[" + v + "] = " + distTo!![v])
StdOut.println("distTo[" + w + "] = " + distTo!![w])
return false
}
}
}
// check that v = edgeTo[w] satisfies distTo[w] = distTo[v] + 1
// provided v is reachable from s
for (w in 0 until G.V()) {
if (!hasPathTo(w) || w == s) continue
val v = edgeTo!![w]
if (distTo!![w] != distTo!![v] + 1) {
StdOut.println("shortest path edge $v-$w")
StdOut.println("distTo[" + v + "] = " + distTo!![v])
StdOut.println("distTo[" + w + "] = " + distTo!![w])
return false
}
}
return true
}
companion object {
private val INFINITY = Integer.MAX_VALUE
/**
* Unit tests the `BreadthFirstPaths` data type.
*
* @param args the command-line arguments
*/
fun main(args: Array<String>) {
val `in` = In(args[0])
val G = Graph(`in`)
// StdOut.println(G);
val s = Integer.parseInt(args[1])
val bfs = BreadthFirstPaths(G, s)
for (v in 0 until G.V()) {
if (bfs.hasPathTo(v)) {
StdOut.printf("%d to %d (%d): ", s, v, bfs.distTo(v))
for (x in bfs.pathTo(v)!!) {
if (x == s)
StdOut.print(x)
else
StdOut.print("-$x")
}
StdOut.println()
} else {
StdOut.printf("%d to %d (-): not connected\n", s, v)
}
}
}
}
}