chore: relocate backend into apps/api ahead of monorepo merge

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

apps/api/utils/courses/taskPrerequisites.util.js

@@ -0,0 +1,63 @@
+"use strict";
+
+/***********************************************************************************************************************************************************************
+ * File Name: taskPrerequisites.util.js
+ * Type of Program: Utility
+ * Description: Cycle detection for the explicit Task ↔ Task prerequisite graph
+ *              (task_prerequisites junction table). A task's prerequisite set is
+ *              only meaningful if the graph stays a DAG — this checks whether
+ *              persisting a proposed edge set would introduce a cycle.
+ *
+ * Author: Kenneth Obsequio (@lash0000)
+ * Date Created: Jul. 17, 2026
+ ***********************************************************************************************************************************************************************/
+
+const { TaskPrerequisite } = require("../../models/task/task.mdl");
+
+/**
+ * Would setting `taskId`'s prerequisites to `newPrereqIds` introduce a cycle?
+ *
+ * Loads every existing task_prerequisites edge for the task list, overlays the
+ * proposed edges for `taskId` (replacing whatever it currently points to), then
+ * DFS from `taskId` looking for a path back to itself.
+ */
+async function wouldCreateCycle(taskId, newPrereqIds, taskListId, transaction) {
+  const { Task } = require("../../models/task/task.mdl");
+
+  const siblingTasks = await Task.findAll({
+    where: { task_list_id: taskListId },
+    attributes: ["task_id"],
+    transaction,
+  });
+  const siblingIds = siblingTasks.map((t) => t.task_id);
+
+  const existingEdges = await TaskPrerequisite.findAll({
+    where: { task_id: siblingIds },
+    attributes: ["task_id", "prerequisite_task_id"],
+    transaction,
+  });
+
+  // adjacency: task_id -> Set(prerequisite_task_id)  ("depends on")
+  const adjacency = new Map();
+  for (const { task_id, prerequisite_task_id } of existingEdges) {
+    if (task_id === taskId) continue; // overlay taskId's edges with the proposed set below
+    if (!adjacency.has(task_id)) adjacency.set(task_id, new Set());
+    adjacency.get(task_id).add(prerequisite_task_id);
+  }
+  adjacency.set(taskId, new Set(newPrereqIds));
+
+  // DFS from taskId looking for a path back to taskId
+  const visited = new Set();
+  const stack = [...adjacency.get(taskId)];
+  while (stack.length) {
+    const current = stack.pop();
+    if (current === taskId) return true;
+    if (visited.has(current)) continue;
+    visited.add(current);
+    for (const next of adjacency.get(current) ?? []) stack.push(next);
+  }
+
+  return false;
+}
+
+module.exports = { wouldCreateCycle };