So there is a way to do prioq general node removal in log(n)

But it doesn't improve the overall speed of the algorithm much.
Meaning most of the time was not spent in that function.

main.go

@@ -386,6 +386,11 @@ func (pq *prioq) Add(car *Car) {
 
 	// Rebalance tree to respect invariant
 	var i = len(pq.bintree) - 1
+	pq.percolateUp(i)
+}
+
+func (pq *prioq) percolateUp(k int) {
+	var i = k
 	var p = (i - 1) / 2
 	for p >= 0 && pq.bintree[p].greater(pq.bintree[i]) {
 		pq.bintree[p], pq.bintree[i] = pq.bintree[i], pq.bintree[p]
@@ -396,25 +401,31 @@ func (pq *prioq) Add(car *Car) {
 	}
 }
 
-func (pq *prioq) Pop() *Car {
+func (pq *prioq) RemoveAtIndex(k int) *Car {
 	if len(pq.bintree) == 0 {
 		return nil
 	}
 
-	if len(pq.bintree) == 1 {
-		elem := pq.bintree[0]
-		pq.bintree = pq.bintree[:0]
+	if k == len(pq.bintree)-1 {
+		elem := pq.bintree[k]
+		pq.bintree = pq.bintree[:k]
 		return elem
 	}
 
-	pq.bintree[0].pqindex = -1
-	elem := pq.bintree[0]
-	// Put last element at root
-	pq.bintree[0] = pq.bintree[len(pq.bintree)-1]
-	pq.bintree[0].pqindex = 0
+	pq.bintree[k].pqindex = -1
+	elem := pq.bintree[k]
+	// Put last element at hole
+	pq.bintree[k] = pq.bintree[len(pq.bintree)-1]
+	pq.bintree[k].pqindex = k
 	// Remove last element
 	pq.bintree = pq.bintree[:len(pq.bintree)-1]
 
+	// Oops! might need to go up
+	if k != 0 && !pq.bintree[k].greater(pq.bintree[(k-1)/2]) {
+		pq.percolateUp(k)
+		return elem
+	}
+
 	//        1                  9
 	//    10     9	         10     12
 	//  11 12   13 14  ->  11 12   13 14
@@ -422,7 +433,8 @@ func (pq *prioq) Pop() *Car {
 
 	// Rebalance tree to respect invariant
 	len := len(pq.bintree)
-	i, left, right := 0, 0, 0
+	i := k
+	left, right := 0, 0
 	for {
 		left = 2*i + 1
 		right = 2*i + 2
@@ -463,18 +475,8 @@ func (pq *prioq) Pop() *Car {
 	return elem
 }
 
-func (pq *prioq) RemoveAtIndex(k int) *Car {
-	if k == 0 {
-		return pq.Pop()
-	}
-	pq.bintree[k].pqindex = -1
-	elem := pq.bintree[k]
-	reassign := pq.bintree[k+1:]
-	pq.bintree = pq.bintree[:k]
-	for _, c := range reassign {
-		pq.Add(c)
-	}
-	return elem
+func (pq *prioq) Pop() *Car {
+	return pq.RemoveAtIndex(0)
 }
 
 func (pq *prioq) empty() bool {