refactor: use Nuxt 4 directory structure

app/utils/tree-node.ts

@@ -0,0 +1,28 @@
+export function isChildNode(parentId: string, childId: string) {
+  return childId.length > parentId.length && childId.startsWith(parentId)
+}
+
+export function isParentNode(parentId: string, childId: string) {
+  return childId.length < parentId.length && childId.startsWith(parentId)
+}
+
+export function isRootNode(nodeId: string) {
+  return nodeId === '0' // equal to `nodeDepth(nodeId) === 1`
+}
+
+export function parentNodeId(nodeId: string) {
+  return nodeId.split('-').shift()
+}
+
+export function nodeIndex(nodeId: string) {
+  return parseInt(nodeId.split('-').pop()!)
+}
+
+export function nodeDepth(nodeId: string) {
+  return nodeId.split('-').length
+}
+
+/** Returns the next search breadth at a given node */
+export function searchBreadth(initialBreadth: number, nodeId: string) {
+  return Math.ceil(initialBreadth / Math.pow(2, nodeDepth(nodeId) - 1))
+}