1. Introduction
Coding tests are an important step in evaluating essential skills for modern technology jobs. In particular, graph theory is a common topic required in algorithm problems, and among these, the Bellman-Ford algorithm is widely used to solve the problem of finding the shortest path from a single source. In this article, we will implement the Bellman-Ford algorithm using Kotlin and explain the process of solving the problem in detail.
2. Introduction to the Bellman-Ford Algorithm
The Bellman-Ford algorithm is an algorithm for finding the shortest path from one vertex to all other vertices in a given graph. This algorithm is especially useful when there are edges with negative weights. The Bellman-Ford algorithm operates in the following steps:
- Initialize the distance value of the starting vertex to 0 and set the distance values of the other vertices to infinity.
- Repeat for all edges |V| – 1 times, performing distance[v] = min(distance[v], distance[u] + weight(u, v)) for each edge (u, v).
- Finally, check all edges one more time to see if there is a negative weight cycle.
3. Problem Statement
Problem: Finding the Shortest Path
There is a graph as follows. The vertices and edges are given below. The weights of each edge are indicated.
Vertices:
0, 1, 2, 3, 4
Edges:
0 -> 1 (4)
0 -> 2 (1)
1 -> 2 (2)
1 -> 3 (5)
2 -> 3 (8)
3 -> 4 (3)
2 -> 4 (7)
Calculate the shortest path from vertex 0 to all other vertices.
4. Problem Solving Process
4.1 Input Data Design
First, to represent the graph above in code, we need to define vertices and edges as data structures. In Kotlin, this can be easily implemented using lists and data classes.
4.2 Defining Kotlin Data Class
data class Edge(val u: Int, val v: Int, val weight: Int)
4.3 Implementing the Bellman-Ford Algorithm
fun bellmanFord(edges: List, vertexCount: Int, startVertex: Int): IntArray {
val distance = IntArray(vertexCount) { Int.MAX_VALUE }
distance[startVertex] = 0
for (i in 1 until vertexCount) {
for (edge in edges) {
if (distance[edge.u] != Int.MAX_VALUE && distance[edge.u] + edge.weight < distance[edge.v]) {
distance[edge.v] = distance[edge.u] + edge.weight
}
}
}
// Validate negative weight cycle
for (edge in edges) {
if (distance[edge.u] != Int.MAX_VALUE && distance[edge.u] + edge.weight < distance[edge.v]) {
throw IllegalArgumentException("Negative weight cycle exists")
}
}
return distance
}
5. Complete Implementation
fun main() {
val edges = listOf(
Edge(0, 1, 4),
Edge(0, 2, 1),
Edge(1, 2, 2),
Edge(1, 3, 5),
Edge(2, 3, 8),
Edge(3, 4, 3),
Edge(2, 4, 7)
)
val result = bellmanFord(edges, 5, 0)
println("Shortest distance from vertex 0 to other vertices: ${result.joinToString(", ")}")
}
6. Output Result
When the above code is executed, you can find out the shortest distances from vertex 0 to all other vertices. The expected result is as follows:
Shortest distance from vertex 0 to other vertices: 0, 3, 1, 11, 10
7. Conclusion
We have looked at the process of solving the shortest path problem using the Bellman-Ford algorithm. This algorithm provides a simple yet powerful functionality. I want to emphasize that it can be particularly useful when there are negative weights. While implementing it using Kotlin, you would have gained a better understanding of how the algorithm works. Practice the Bellman-Ford algorithm as you prepare for coding tests!