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https://github.com/TheAlgorithms/Java.git
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Add Yen’s K-shortest loopless paths with tests [GRAPHS] (#6773)
* Add Yen’s K-shortest loopless paths with tests and index update * style: fix Checkstyle in Yens algorithm and tests * fix: resolve SpotBugs in Yens algorithm * fix (PMD): rename short variables in the code * (pmd): code fixes * fix(bloomfilter): hash arrays by content to satisfy array membership tests * style(pmd): fix EmptyControlStatement in validate() by returning early when src==dst * style(pmd): remove unnecessary return in validate()
This commit is contained in:
Sameer Prajapati
@@ -1,5 +1,6 @@
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package com.thealgorithms.datastructures.bloomfilter;
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import java.util.Arrays;
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import java.util.BitSet;
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/**
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@@ -115,7 +116,7 @@ public class BloomFilter<T> {
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* @return the computed hash value
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*/
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public int compute(T key) {
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return index * asciiString(String.valueOf(key));
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return index * contentHash(key);
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}
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/**
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@@ -135,5 +136,31 @@ public class BloomFilter<T> {
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}
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return sum;
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}
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/**
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* Computes a content-based hash for arrays; falls back to ASCII-sum of String value otherwise.
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*/
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private int contentHash(Object key) {
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if (key instanceof int[]) {
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return Arrays.hashCode((int[]) key);
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} else if (key instanceof long[]) {
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return Arrays.hashCode((long[]) key);
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} else if (key instanceof byte[]) {
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return Arrays.hashCode((byte[]) key);
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} else if (key instanceof short[]) {
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return Arrays.hashCode((short[]) key);
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} else if (key instanceof char[]) {
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return Arrays.hashCode((char[]) key);
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} else if (key instanceof boolean[]) {
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return Arrays.hashCode((boolean[]) key);
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} else if (key instanceof float[]) {
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return Arrays.hashCode((float[]) key);
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} else if (key instanceof double[]) {
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return Arrays.hashCode((double[]) key);
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} else if (key instanceof Object[]) {
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return Arrays.deepHashCode((Object[]) key);
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}
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return asciiString(String.valueOf(key));
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}
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}
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}
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263
src/main/java/com/thealgorithms/graph/YensKShortestPaths.java
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263
src/main/java/com/thealgorithms/graph/YensKShortestPaths.java
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@@ -0,0 +1,263 @@
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package com.thealgorithms.graph;
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import java.util.ArrayList;
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import java.util.Arrays;
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import java.util.HashSet;
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import java.util.List;
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import java.util.Objects;
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import java.util.PriorityQueue;
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import java.util.Set;
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/**
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* Yen's algorithm for finding K loopless shortest paths in a directed graph with non-negative edge weights.
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*
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* <p>Input is an adjacency matrix of edge weights. A value of -1 indicates no edge.
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* All existing edge weights must be non-negative. Zero-weight edges are allowed.</p>
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*
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* <p>References:
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* - Wikipedia: Yen's algorithm (https://en.wikipedia.org/wiki/Yen%27s_algorithm)
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* - Dijkstra's algorithm for the base shortest path computation.</p>
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*/
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public final class YensKShortestPaths {
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private YensKShortestPaths() {
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}
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private static final int NO_EDGE = -1;
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private static final long INF_COST = Long.MAX_VALUE / 4;
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/**
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* Compute up to k loopless shortest paths from src to dst using Yen's algorithm.
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*
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* @param weights adjacency matrix; weights[u][v] = -1 means no edge; otherwise non-negative edge weight
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* @param src source vertex index
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* @param dst destination vertex index
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* @param k maximum number of paths to return (k >= 1)
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* @return list of paths, each path is a list of vertex indices in order from src to dst
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* @throws IllegalArgumentException on invalid inputs (null, non-square, negatives on existing edges, bad indices, k < 1)
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*/
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public static List<List<Integer>> kShortestPaths(int[][] weights, int src, int dst, int k) {
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validate(weights, src, dst, k);
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final int n = weights.length;
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// Make a defensive copy to avoid mutating caller's matrix
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int[][] weightsCopy = new int[n][n];
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for (int i = 0; i < n; i++) {
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weightsCopy[i] = Arrays.copyOf(weights[i], n);
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}
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List<Path> shortestPaths = new ArrayList<>();
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PriorityQueue<Path> candidates = new PriorityQueue<>(); // min-heap by cost then lexicographic nodes
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Set<String> seen = new HashSet<>(); // deduplicate candidate paths by node sequence key
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Path first = dijkstra(weightsCopy, src, dst, new boolean[n]);
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if (first == null) {
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return List.of();
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}
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shortestPaths.add(first);
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for (int kIdx = 1; kIdx < k; kIdx++) {
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Path lastPath = shortestPaths.get(kIdx - 1);
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List<Integer> lastNodes = lastPath.nodes;
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for (int i = 0; i < lastNodes.size() - 1; i++) {
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int spurNode = lastNodes.get(i);
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List<Integer> rootPath = lastNodes.subList(0, i + 1);
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// Build modified graph: remove edges that would recreate same root + next edge as any A path
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int[][] modifiedWeights = cloneMatrix(weightsCopy);
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for (Path p : shortestPaths) {
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if (startsWith(p.nodes, rootPath) && p.nodes.size() > i + 1) {
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int u = p.nodes.get(i);
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int v = p.nodes.get(i + 1);
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modifiedWeights[u][v] = NO_EDGE; // remove edge
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}
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}
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// Prevent revisiting nodes in rootPath (loopless constraint), except spurNode itself
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boolean[] blocked = new boolean[n];
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for (int j = 0; j < rootPath.size() - 1; j++) {
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blocked[rootPath.get(j)] = true;
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}
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Path spurPath = dijkstra(modifiedWeights, spurNode, dst, blocked);
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if (spurPath != null) {
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// concatenate rootPath (excluding spurNode at end) + spurPath
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List<Integer> totalNodes = new ArrayList<>(rootPath);
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// spurPath.nodes starts with spurNode; avoid duplication
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for (int idx = 1; idx < spurPath.nodes.size(); idx++) {
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totalNodes.add(spurPath.nodes.get(idx));
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}
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long rootCost = pathCost(weightsCopy, rootPath);
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long totalCost = rootCost + spurPath.cost; // spurPath.cost covers from spurNode to dst
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Path candidate = new Path(totalNodes, totalCost);
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String key = candidate.key();
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if (seen.add(key)) {
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candidates.add(candidate);
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}
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}
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}
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if (candidates.isEmpty()) {
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break;
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}
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shortestPaths.add(candidates.poll());
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}
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// Map to list of node indices for output
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List<List<Integer>> result = new ArrayList<>(shortestPaths.size());
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for (Path p : shortestPaths) {
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result.add(new ArrayList<>(p.nodes));
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}
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return result;
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}
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private static void validate(int[][] weights, int src, int dst, int k) {
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if (weights == null || weights.length == 0) {
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throw new IllegalArgumentException("Weights matrix must not be null or empty");
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}
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int n = weights.length;
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for (int i = 0; i < n; i++) {
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if (weights[i] == null || weights[i].length != n) {
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throw new IllegalArgumentException("Weights matrix must be square");
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}
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for (int j = 0; j < n; j++) {
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int val = weights[i][j];
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if (val < NO_EDGE) {
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throw new IllegalArgumentException("Weights must be -1 (no edge) or >= 0");
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}
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}
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}
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if (src < 0 || dst < 0 || src >= n || dst >= n) {
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throw new IllegalArgumentException("Invalid src/dst indices");
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}
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if (k < 1) {
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throw new IllegalArgumentException("k must be >= 1");
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}
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}
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private static boolean startsWith(List<Integer> list, List<Integer> prefix) {
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if (prefix.size() > list.size()) {
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return false;
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}
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for (int i = 0; i < prefix.size(); i++) {
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if (!Objects.equals(list.get(i), prefix.get(i))) {
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return false;
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}
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}
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return true;
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}
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private static int[][] cloneMatrix(int[][] a) {
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int n = a.length;
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int[][] b = new int[n][n];
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for (int i = 0; i < n; i++) {
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b[i] = Arrays.copyOf(a[i], n);
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}
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return b;
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}
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private static long pathCost(int[][] weights, List<Integer> nodes) {
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long cost = 0;
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for (int i = 0; i + 1 < nodes.size(); i++) {
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int u = nodes.get(i);
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int v = nodes.get(i + 1);
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int edgeCost = weights[u][v];
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if (edgeCost < 0) {
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return INF_COST; // invalid
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}
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cost += edgeCost;
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}
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return cost;
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}
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private static Path dijkstra(int[][] weights, int src, int dst, boolean[] blocked) {
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int n = weights.length;
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final long inf = INF_COST;
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long[] dist = new long[n];
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int[] parent = new int[n];
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Arrays.fill(dist, inf);
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Arrays.fill(parent, -1);
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PriorityQueue<Node> queue = new PriorityQueue<>();
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if (blocked[src]) {
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return null;
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}
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dist[src] = 0;
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queue.add(new Node(src, 0));
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while (!queue.isEmpty()) {
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Node current = queue.poll();
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if (current.dist != dist[current.u]) {
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continue;
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}
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if (current.u == dst) {
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break;
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}
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for (int v = 0; v < n; v++) {
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int edgeWeight = weights[current.u][v];
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if (edgeWeight >= 0 && !blocked[v]) {
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long newDist = current.dist + edgeWeight;
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if (newDist < dist[v]) {
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dist[v] = newDist;
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parent[v] = current.u;
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queue.add(new Node(v, newDist));
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}
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}
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}
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}
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if (dist[dst] >= inf) {
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// If src==dst and not blocked, the path is trivial with cost 0
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if (src == dst) {
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List<Integer> nodes = new ArrayList<>();
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nodes.add(src);
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return new Path(nodes, 0);
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}
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return null;
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}
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// Reconstruct path
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List<Integer> nodes = new ArrayList<>();
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int cur = dst;
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while (cur != -1) {
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nodes.add(0, cur);
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cur = parent[cur];
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}
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return new Path(nodes, dist[dst]);
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}
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private static final class Node implements Comparable<Node> {
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final int u;
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final long dist;
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Node(int u, long dist) {
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this.u = u;
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this.dist = dist;
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}
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public int compareTo(Node o) {
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return Long.compare(this.dist, o.dist);
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}
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}
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private static final class Path implements Comparable<Path> {
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final List<Integer> nodes;
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final long cost;
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Path(List<Integer> nodes, long cost) {
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this.nodes = nodes;
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this.cost = cost;
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}
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String key() {
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return nodes.toString();
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}
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@Override
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public int compareTo(Path o) {
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int costCmp = Long.compare(this.cost, o.cost);
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if (costCmp != 0) {
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return costCmp;
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}
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// tie-break lexicographically on nodes
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int minLength = Math.min(this.nodes.size(), o.nodes.size());
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for (int i = 0; i < minLength; i++) {
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int aNode = this.nodes.get(i);
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int bNode = o.nodes.get(i);
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if (aNode != bNode) {
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return Integer.compare(aNode, bNode);
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}
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}
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return Integer.compare(this.nodes.size(), o.nodes.size());
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}
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}
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}
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