feat(graph): add DSU-based account merge algorithm (#7377)

* feat(graph): add DSU-based account merge algorithm

* test(graph): add null and transitive account merge cases

* Handle no-email accounts in account merge

* Apply clang-format style to account merge tests

Author: nickzerjeski

src/main/java/com/thealgorithms/graph/AccountMerge.java

@@ -0,0 +1,112 @@
+package com.thealgorithms.graph;
+
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.LinkedHashMap;
+import java.util.List;
+import java.util.Map;
+
+/**
+ * Merges account records using Disjoint Set Union (Union-Find) on shared emails.
+ *
+ * <p>Input format: each account is a list where the first element is the user name and the
+ * remaining elements are emails.
+ */
+public final class AccountMerge {
+    private AccountMerge() {
+    }
+
+    public static List<List<String>> mergeAccounts(List<List<String>> accounts) {
+        if (accounts == null || accounts.isEmpty()) {
+            return List.of();
+        }
+
+        UnionFind dsu = new UnionFind(accounts.size());
+        Map<String, Integer> emailToAccount = new HashMap<>();
+
+        for (int i = 0; i < accounts.size(); i++) {
+            List<String> account = accounts.get(i);
+            for (int j = 1; j < account.size(); j++) {
+                String email = account.get(j);
+                Integer previous = emailToAccount.putIfAbsent(email, i);
+                if (previous != null) {
+                    dsu.union(i, previous);
+                }
+            }
+        }
+
+        Map<Integer, List<String>> rootToEmails = new LinkedHashMap<>();
+        for (Map.Entry<String, Integer> entry : emailToAccount.entrySet()) {
+            int root = dsu.find(entry.getValue());
+            rootToEmails.computeIfAbsent(root, ignored -> new ArrayList<>()).add(entry.getKey());
+        }
+        for (int i = 0; i < accounts.size(); i++) {
+            if (accounts.get(i).size() <= 1) {
+                int root = dsu.find(i);
+                rootToEmails.computeIfAbsent(root, ignored -> new ArrayList<>());
+            }
+        }
+
+        List<List<String>> merged = new ArrayList<>();
+        for (Map.Entry<Integer, List<String>> entry : rootToEmails.entrySet()) {
+            int root = entry.getKey();
+            List<String> emails = entry.getValue();
+            Collections.sort(emails);
+
+            List<String> mergedAccount = new ArrayList<>();
+            mergedAccount.add(accounts.get(root).getFirst());
+            mergedAccount.addAll(emails);
+            merged.add(mergedAccount);
+        }
+
+        merged.sort((a, b) -> {
+            int cmp = a.getFirst().compareTo(b.getFirst());
+            if (cmp != 0) {
+                return cmp;
+            }
+            if (a.size() == 1 || b.size() == 1) {
+                return Integer.compare(a.size(), b.size());
+            }
+            return a.get(1).compareTo(b.get(1));
+        });
+        return merged;
+    }
+
+    private static final class UnionFind {
+        private final int[] parent;
+        private final int[] rank;
+
+        private UnionFind(int size) {
+            this.parent = new int[size];
+            this.rank = new int[size];
+            for (int i = 0; i < size; i++) {
+                parent[i] = i;
+            }
+        }
+
+        private int find(int x) {
+            if (parent[x] != x) {
+                parent[x] = find(parent[x]);
+            }
+            return parent[x];
+        }
+
+        private void union(int x, int y) {
+            int rootX = find(x);
+            int rootY = find(y);
+            if (rootX == rootY) {
+                return;
+            }
+
+            if (rank[rootX] < rank[rootY]) {
+                parent[rootX] = rootY;
+            } else if (rank[rootX] > rank[rootY]) {
+                parent[rootY] = rootX;
+            } else {
+                parent[rootY] = rootX;
+                rank[rootX]++;
+            }
+        }
+    }
+}

src/test/java/com/thealgorithms/graph/AccountMergeTest.java

@@ -0,0 +1,61 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+class AccountMergeTest {
+
+    @Test
+    void testMergeAccountsWithSharedEmails() {
+        List<List<String>> accounts = List.of(List.of("abc", "abc@mail.com", "abx@mail.com"), List.of("abc", "abc@mail.com", "aby@mail.com"), List.of("Mary", "mary@mail.com"), List.of("John", "johnnybravo@mail.com"));
+
+        List<List<String>> merged = AccountMerge.mergeAccounts(accounts);
+
+        List<List<String>> expected = List.of(List.of("John", "johnnybravo@mail.com"), List.of("Mary", "mary@mail.com"), List.of("abc", "abc@mail.com", "abx@mail.com", "aby@mail.com"));
+
+        assertEquals(expected, merged);
+    }
+
+    @Test
+    void testAccountsWithSameNameButNoSharedEmailStaySeparate() {
+        List<List<String>> accounts = List.of(List.of("Alex", "alex1@mail.com"), List.of("Alex", "alex2@mail.com"));
+
+        List<List<String>> merged = AccountMerge.mergeAccounts(accounts);
+        List<List<String>> expected = List.of(List.of("Alex", "alex1@mail.com"), List.of("Alex", "alex2@mail.com"));
+
+        assertEquals(expected, merged);
+    }
+
+    @Test
+    void testEmptyInput() {
+        assertEquals(List.of(), AccountMerge.mergeAccounts(List.of()));
+    }
+
+    @Test
+    void testNullInput() {
+        assertEquals(List.of(), AccountMerge.mergeAccounts(null));
+    }
+
+    @Test
+    void testTransitiveMergeAndDuplicateEmails() {
+        List<List<String>> accounts = List.of(List.of("A", "a1@mail.com", "a2@mail.com"), List.of("A", "a2@mail.com", "a3@mail.com"), List.of("A", "a3@mail.com", "a4@mail.com", "a4@mail.com"));
+
+        List<List<String>> merged = AccountMerge.mergeAccounts(accounts);
+
+        List<List<String>> expected = List.of(List.of("A", "a1@mail.com", "a2@mail.com", "a3@mail.com", "a4@mail.com"));
+
+        assertEquals(expected, merged);
+    }
+
+    @Test
+    void testAccountsWithNoEmailsArePreserved() {
+        List<List<String>> accounts = List.of(List.of("Alex"), List.of("Alex", "alex1@mail.com"), List.of("Bob"));
+
+        List<List<String>> merged = AccountMerge.mergeAccounts(accounts);
+        List<List<String>> expected = List.of(List.of("Alex"), List.of("Alex", "alex1@mail.com"), List.of("Bob"));
+
+        assertEquals(expected, merged);
+    }
+}