Add KCenters algorithm (#5806)

Author: Hardvan

DIRECTORY.md

@@ -325,6 +325,7 @@
             * [FractionalKnapsack](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/FractionalKnapsack.java)
             * [GaleShapley](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/GaleShapley.java)
             * [JobSequencing](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/JobSequencing.java)
+            * [KCenters](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/KCenters.java)
             * [MergeIntervals](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/MergeIntervals.java)
             * [MinimizingLateness](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/MinimizingLateness.java)
             * [MinimumWaitingTime](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/MinimumWaitingTime.java)
@@ -954,6 +955,7 @@
             * [FractionalKnapsackTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/FractionalKnapsackTest.java)
             * [GaleShapleyTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/GaleShapleyTest.java)
             * [JobSequencingTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/JobSequencingTest.java)
+            * [KCentersTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/KCentersTest.java)
             * [MergeIntervalsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/MergeIntervalsTest.java)
             * [MinimizingLatenessTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/MinimizingLatenessTest.java)
             * [MinimumWaitingTimeTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/MinimumWaitingTimeTest.java)

src/main/java/com/thealgorithms/greedyalgorithms/KCenters.java

@@ -0,0 +1,62 @@
+package com.thealgorithms.greedyalgorithms;
+
+import java.util.Arrays;
+
+/**
+ * Given a set of points and a number k.
+ * The goal is to minimize the maximum distance between any point and its nearest center.
+ * Each point is assigned to the nearest center.
+ * The distance between two points is the Euclidean distance.
+ * The problem is NP-hard.
+ *
+ * @author Hardvan
+ */
+public final class KCenters {
+    private KCenters() {
+    }
+
+    /**
+     * Finds the maximum distance to the nearest center given k centers.
+     * Steps:
+     * 1. Initialize an array {@code selected} of size n and an array {@code maxDist} of size n.
+     * 2. Set the first node as selected and update the maxDist array.
+     * 3. For each center, find the farthest node from the selected centers.
+     * 4. Update the maxDist array.
+     * 5. Return the maximum distance to the nearest center.
+     *
+     * @param distances matrix representing distances between nodes
+     * @param k         the number of centers
+     * @return the maximum distance to the nearest center
+     */
+    public static int findKCenters(int[][] distances, int k) {
+        int n = distances.length;
+        boolean[] selected = new boolean[n];
+        int[] maxDist = new int[n];
+
+        Arrays.fill(maxDist, Integer.MAX_VALUE);
+
+        selected[0] = true;
+        for (int i = 1; i < n; i++) {
+            maxDist[i] = Math.min(maxDist[i], distances[0][i]);
+        }
+
+        for (int centers = 1; centers < k; centers++) {
+            int farthest = -1;
+            for (int i = 0; i < n; i++) {
+                if (!selected[i] && (farthest == -1 || maxDist[i] > maxDist[farthest])) {
+                    farthest = i;
+                }
+            }
+            selected[farthest] = true;
+            for (int i = 0; i < n; i++) {
+                maxDist[i] = Math.min(maxDist[i], distances[farthest][i]);
+            }
+        }
+
+        int result = 0;
+        for (int dist : maxDist) {
+            result = Math.max(result, dist);
+        }
+        return result;
+    }
+}

src/test/java/com/thealgorithms/greedyalgorithms/KCentersTest.java

@@ -0,0 +1,15 @@
+package com.thealgorithms.greedyalgorithms;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+public class KCentersTest {
+
+    @Test
+    public void testFindKCenters() {
+        int[][] distances = {{0, 2, 3, 4}, {2, 0, 5, 1}, {3, 5, 0, 7}, {4, 1, 7, 0}};
+        assertEquals(4, KCenters.findKCenters(distances, 2));
+        assertEquals(2, KCenters.findKCenters(distances, 4));
+    }
+}