Add example of min-heap and max-heap working together (gh-137251)

rhettinger · web-flow · commit dc05d475c149 · 2025-07-30T15:53:33.000-05:00
diff --git a/Doc/library/heapq.rst b/Doc/library/heapq.rst
@@ -231,6 +231,42 @@ Heap elements can be tuples.  This is useful for assigning comparison values
     (1, 'write spec')
 
 
+Other Applications
+------------------
+
+`Medians <https://en.wikipedia.org/wiki/Median>`_ are a measure of
+central tendency for a set of numbers.  In distributions skewed by
+outliers, the median provides a more stable estimate than an average
+(arithmetic mean).  A running median is an `online algorithm
+<https://en.wikipedia.org/wiki/Online_algorithm>`_ that updates
+continuously as new data arrives.
+
+A running median can be efficiently implemented by balancing two heaps,
+a max-heap for values at or below the midpoint and a min-heap for values
+above the midpoint.  When the two heaps have the same size, the new
+median is the average of the tops of the two heaps; otherwise, the
+median is at the top of the larger heap::
+
+    def running_median(iterable):
+        "Yields the cumulative median of values seen so far."
+
+        lo = []  # max-heap
+        hi = []  # min-heap (same size as or one smaller than lo)
+
+        for x in iterable:
+            if len(lo) == len(hi):
+                heappush_max(lo, heappushpop(hi, x))
+                yield lo[0]
+            else:
+                heappush(hi, heappushpop_max(lo, x))
+                yield (lo[0] + hi[0]) / 2
+
+For example::
+
+    >>> list(running_median([5.0, 9.0, 4.0, 12.0, 8.0, 9.0]))
+    [5.0, 7.0, 5.0, 7.0, 8.0, 8.5]
+
+
 Priority Queue Implementation Notes
 -----------------------------------
 
