diff --git a/regex/priorityQueue.go b/regex/priorityQueue.go
new file mode 100644
index 0000000..59592a9
--- /dev/null
+++ b/regex/priorityQueue.go
@@ -0,0 +1,76 @@
+package regex
+
+import "container/heap"
+
+// Implement a priority queue using container/heap
+
+const (
+	min_priority int = iota
+	zerostate_priority
+	alternation_priority
+	kleene_priority
+	char_priority
+	max_priority
+)
+
+func getPriority(state *nfaState) int {
+	if state.isKleene {
+		return kleene_priority
+	} else if state.isQuestion || state.isAlternation {
+		return alternation_priority
+	} else {
+		if state.isEmpty {
+			return zerostate_priority
+		} else {
+			return char_priority
+		}
+	}
+}
+
+type priorQueueItem struct {
+	state    *nfaState
+	priority int
+	index    int
+}
+
+type priorityQueue []*priorQueueItem
+
+func (pq priorityQueue) Len() int {
+	return len(pq)
+}
+
+func (pq priorityQueue) Less(i, j int) bool {
+	if pq[i].priority == pq[j].priority {
+		return pq[i].index > pq[j].index
+	}
+	return pq[i].priority > pq[j].priority // We want max-heap, so we use greater-than
+}
+
+func (pq priorityQueue) Swap(i, j int) {
+	pq[i], pq[j] = pq[j], pq[i]
+	pq[i].index = i
+	pq[j].index = j
+}
+
+func (pq *priorityQueue) Push(x any) {
+	length := len(*pq)
+	item := x.(*priorQueueItem)
+	item.index = length
+	*pq = append(*pq, item)
+}
+
+func (pq *priorityQueue) Pop() any {
+	old := *pq
+	n := len(old)
+	item := old[n-1]
+	old[n-1] = nil
+	item.index = -1
+	*pq = old[0 : n-1]
+	return item
+}
+
+func (pq *priorityQueue) update(item *priorQueueItem, value *nfaState, priority int) {
+	item.state = value
+	item.priority = priority
+	heap.Fix(pq, item.index)
+}