diff --git a/src/ruptures/detection/bottomup.py b/src/ruptures/detection/bottomup.py
index d00cfb91..ec4656ec 100644
--- a/src/ruptures/detection/bottomup.py
+++ b/src/ruptures/detection/bottomup.py
@@ -37,11 +37,11 @@ def __init__(self, model="l2", custom_cost=None, min_size=2, jump=5, params=None
 
     def _grow_tree(self):
         """Grow the entire binary tree."""
-        partition = [(0, self.n_samples)]
+        partition = [(-self.n_samples, (0, self.n_samples))]
         stop = False
         while not stop:  # recursively divide the signal
             stop = True
-            start, end = max(partition, key=lambda t: t[1] - t[0])
+            _, (start, end) = partition[0]
             mid = (start + end) * 0.5
             bkps = list()
             for bkp in range(start, end):
@@ -50,15 +50,15 @@ def _grow_tree(self):
                         bkps.append(bkp)
             if len(bkps) > 0:  # at least one admissible breakpoint was found
                 bkp = min(bkps, key=lambda x: abs(x - mid))
-                partition.remove((start, end))
-                partition.append((start, bkp))
-                partition.append((bkp, end))
+                heapq.heappop(partition)
+                heapq.heappush(partition, (-bkp + start, (start, bkp)))
+                heapq.heappush(partition, (-end + bkp, (bkp, end)))
                 stop = False
 
-        partition.sort()
+        partition.sort(key=lambda x: x[1])
         # compute segment costs
         leaves = list()
-        for start, end in partition:
+        for _, (start, end) in partition:
             val = self.cost.error(start, end)
             leaf = Bnode(start, end, val)
             leaves.append(leaf)
@@ -87,6 +87,7 @@ def _seg(self, n_bkps=None, pen=None, epsilon=None):
             dict: partition dict {(start, end): cost value,...}
         """
         leaves = sorted(self.leaves)
+        keys = [leaf.start for leaf in leaves]
         removed = set()
         merged = []
         for left, right in pairwise(leaves):
@@ -121,10 +122,13 @@ def _seg(self, n_bkps=None, pen=None, epsilon=None):
             if not stop:
                 # updates the list of leaves (i.e. segments of the partitions)
                 # find the merged segments indexes
-                keys = [leaf.start for leaf in leaves]
                 left_idx = bisect_left(keys, leaf.left.start)
-                leaves[left_idx] = leaf  # replace leaf.left
-                del leaves[left_idx + 1]  # remove leaf.right
+                # replace leaf.left
+                leaves[left_idx] = leaf
+                keys[left_idx] = leaf.start
+                # remove leaf.right
+                del leaves[left_idx + 1]
+                del keys[left_idx + 1]
                 # add to the set of removed segments.
                 removed.add(leaf.left)
                 removed.add(leaf.right)