Add methods for efficient counting of paths between vertices.

Sources/SwiftGraph/Graph.swift

@@ -303,3 +303,91 @@ extension Graph {
     }
 }
 
+extension Graph {
+    /// Find all of the neighbors of a vertex at a given index.
+    ///
+    /// - parameter index: The index for the vertex to find the neighbors of.
+    /// - returns: An array of the neighbor vertex indices.
+    public func neighborIndicesForIndex(_ index: Int) -> [Int] {
+        return edges[index].map({$0.v})
+    }
+
+    /// Find out if a route exists from one vertex to another, using a DFS.
+    ///
+    /// - parameter fromIndex: The index of the starting vertex.
+    /// - parameter toIndex: The index of the ending vertex.
+    /// - returns: `true` if a path exists
+    func pathExists(fromIndex: Int, toIndex: Int) -> Bool {
+        var visited: [Bool] = [Bool](repeating: false, count: vertexCount)
+        var stack: [Int] = []
+        stack.append(fromIndex)
+        while !stack.isEmpty {
+            if let v: Int = stack.popLast() {
+                if (visited[v]) {
+                    continue
+                }
+                visited[v] = true
+                if v == toIndex {
+                    // we've found the destination
+                    return true
+                }
+                for e in edgesForIndex(v) {
+                    if !visited[e.v] {
+                        stack.append(e.v)
+                    }
+                }
+            }
+        }
+        return false // no solution found
+    }
+
+    /// This is an exhaustive search to find out how many paths there are between two vertices.
+    ///
+    /// - parameter fromIndex: the index of the starting vertex
+    /// - parameter toIndex: the index of the destination vertex
+    /// - parameter visited: a set of vertex indices which will be considered to have been visited already
+    /// - returns: the number of paths that exist going from the start to the destinatin
+    func countPaths(fromIndex startIndex: Int, toIndex endIndex: Int, visited: inout Set<Int>) -> Int {
+        if startIndex == endIndex { return 1 }
+        visited.insert(startIndex)
+        var total = 0
+        for n in neighborIndicesForIndex(startIndex) where !visited.contains(n) {
+            total += countPaths(fromIndex: n, toIndex: endIndex, visited: &visited)
+        }
+        visited.remove(startIndex)
+        return total
+    }
+
+    /// This is an exhaustive search to find out how many paths there are between two vertices.
+    /// The search is optimized by not bothering to compute paths for known dead ends.
+    ///
+    /// - parameter fromIndex: the index of the starting vertex
+    /// - parameter toIndex: the index of the destination vertex
+    /// - parameter visited: a set of vertex indices which will be considered to have been visited already
+    /// - parameter reachability: a dictionary where the key is a vertex index and the value is whether or not a path exists from that vertex to the destination
+    /// - returns: the number of paths that exist going from the start to the destinatin
+    func countPaths(fromIndex startIndex: Int,
+                    toIndex endIndex: Int,
+                    visited: inout Set<Int>,
+                    reachability: [Int: Bool]) -> Int {
+        if startIndex == endIndex { return 1 }
+        guard reachability[startIndex] ?? false else { return 0 }
+        visited.insert(startIndex)
+        var total = 0
+        for n in neighborIndicesForIndex(startIndex) where !visited.contains(n) && (reachability[n] ?? false) {
+            total += countPaths(fromIndex: n, toIndex: endIndex, visited: &visited, reachability: reachability)
+        }
+        visited.remove(startIndex)
+        return total
+    }
+
+    /// Computes whether or not a given vertex (by index) is reachable, for every vertex in the graph.
+    func reachabilityOf(_ index: Int) -> [Int: Bool] {
+        var answers: [Int: Bool] = [:]
+        for vi in vertices.indices {
+            answers[vi] = pathExists(fromIndex: vi, toIndex: index)
+        }
+        return answers
+    }
+
+}

Tests/SwiftGraphTests/SwiftGraphTests.swift

@@ -16,6 +16,7 @@
 //  See the License for the specific language governing permissions and
 //  limitations under the License.
 
+import Foundation
 import XCTest
 @testable import SwiftGraph
 
@@ -132,4 +133,43 @@ class SwiftGraphTests: XCTestCase {
         XCTAssertFalse(graph.edgeExists(fromIndex: 2, toIndex: 3))
         XCTAssertFalse(graph.edgeExists(fromIndex: 3, toIndex: 2))
     }
+
+    // a trivial smoke test to exercise the methods added to Graph to
+    // perform exhaustive searches for paths.
+    func testExhaustivePathCounting() throws {
+        let graph = try getAoCGraph()
+        guard let fftIndex = graph.indexOfVertex("fft") else {
+            XCTFail("Bad graph, no fft")
+            return
+        }
+        guard let dacIndex = graph.indexOfVertex("dac") else {
+            XCTFail("Bad graph, no dac")
+            return
+        }
+        guard let outIndex = graph.indexOfVertex("out") else {
+            XCTFail("Bad graph, no out")
+            return
+        }
+        guard let svrIndex = graph.indexOfVertex( "svr" ) else {
+            XCTFail("Bad graph, no svr")
+            return
+        }
+        var visited: Set<Int> = [svrIndex, outIndex]
+        XCTAssertEqual(0, graph.countPaths(fromIndex: dacIndex, toIndex: fftIndex, visited: &visited))
+        let outReachability = graph.reachabilityOf(outIndex)
+        visited = [svrIndex, fftIndex]
+        XCTAssertEqual(2,
+                       graph.countPaths(fromIndex: dacIndex,
+                                        toIndex: outIndex,
+                                        visited: &visited,
+                                        reachability: outReachability))
+    }
+
+    fileprivate func getAoCGraph() throws -> UnweightedGraph<String> {
+        // this is the sample graph for part 2 of the 2025 Advent of Code challenge, day 11.
+        let serializedGraph = """
+            {"vertices":["hhh","ddd","fft","ccc","svr","fff","eee","aaa","bbb","hub","ggg","dac","tty","out"],"edges":[[{"u":0,"v":13,"directed":true}],[{"u":1,"v":9,"directed":true}],[{"u":2,"v":3,"directed":true}],[{"u":3,"v":1,"directed":true},{"u":3,"v":6,"directed":true}],[{"u":4,"v":7,"directed":true},{"u":4,"v":8,"directed":true}],[{"u":5,"v":10,"directed":true},{"u":5,"v":0,"directed":true}],[{"u":6,"v":11,"directed":true}],[{"u":7,"v":2,"directed":true}],[{"u":8,"v":12,"directed":true}],[{"u":9,"v":5,"directed":true}],[{"u":10,"v":13,"directed":true}],[{"u":11,"v":5,"directed":true}],[{"u":12,"v":3,"directed":true}],[]]}
+            """
+        return try JSONDecoder().decode(UnweightedGraph<String>.self, from: serializedGraph.data(using: .utf8)!)
+    }
 }