Swift port of an algorythm used to find all the cycles in a directed graph:
This is an implementation of an algorithm by Donald B. Johnson to find all elementary cycles in a directed graph (Donald B. Johnson: Finding All the Elementary Circuits of a Directed Graph. SIAM Journal on Computing. Volumne 4, Nr. 1 (1975), pp. 77-84).
Original Java implementation: http://normalisiert.de
import ElementaryCycles
// dictionary pairs represent node connections from the keys to their values
let graph = ["A": ["B", "C"], "B": ["A"], "C": ["D"], "D": ["C"]]
let cycles = ElementaryCycles.find(graph: graph, sort: { $0 < $1 })
// nodes order is determined by sort parameter
print(cycles) // [["A", "B"], ["C", "D"]]- Input: Directed graph
┌─────────┐
∨ │
┌───┐ ┌───┐ ┌───┐
┌> │ A │ ──> │ C │ ──> │ D │
│ └───┘ └───┘ └───┘
│ │
│ │
│ ∨
│ ┌───┐
└─ │ B │
└───┘
- Output: Elementary circuits
┌───┐ ┌───┐
│ A │ ──> │ B │
└───┘ └───┘
┌───┐ ┌───┐
│ C │ ──> │ D │
└───┘ └───┘
Alternatively, you can use ElementaryCyclesSearch library directly, which contains the actual algorythm implementation:
The implementation is pretty much generic, all it needs is a adjacency-matrix of your graph and the objects of your nodes. Then you get back the sets of node-objects which build a cycle.
Original Java implemnetation: http://normalisiert.de
import ElementaryCyclesSearch
let nodes = Vector(["A", "B", "C", "D"])
let matrix = AdjacencyMatrix(4, 4) { matrix in
matrix[0][1] = true
matrix[0][2] = true
matrix[1][0] = true
matrix[2][3] = true
matrix[3][2] = true
}
let cycles = getElementaryCycles(adjacencyMatrix: matrix, graphNodes: nodes)- Input: Node objects
| A | B | C | D |
|---|
- Input: Adjacency-matrix
| A | B | C | D | |
|---|---|---|---|---|
| A | false |
true |
false |
false |
| B | true |
false |
false |
false |
| C | true |
false |
false |
true |
| D | false |
false |
true |
false |
- Output: Elementary circuits
┌───┐ ┌───┐
│ A │ ──> │ B │
└───┘ └───┘
┌───┐ ┌───┐
│ C │ ──> │ D │
└───┘ └───┘
(BSD-2 license)
Original work Copyright (c) 2012, Frank Meyer
All rights reserved.
Swift port Copyright (c) 2018, Hèctor Marquès
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