Add min-heap (#68)

* Min-heap implementation

* Heap test cases

utilities/python/heap.py

@@ -0,0 +1,84 @@
+# Implements a min-heap. For max-heap, simply reverse all comparison orders.
+#
+# Note on alternate subroutine namings (used in some textbooks):
+#     - _bubble_up = siftdown
+#     - _bubble_down = siftup
+
+def _bubble_up(heap, i):
+    while i > 0:
+        parent_i = (i - 1) // 2
+        if heap[i] < heap[parent_i]:
+            heap[i], heap[parent_i] = heap[parent_i], heap[i]
+            i = parent_i
+            continue
+        break
+
+def _bubble_down(heap, i):
+    startpos = i
+    newitem = heap[i]
+    left_i = 2 * i + 1
+    while left_i < len(heap):
+        # Pick the smaller of the L and R children
+        right_i = left_i + 1
+        if right_i < len(heap) and not heap[left_i] < heap[right_i]:
+            child_i = right_i
+        else:
+            child_i = left_i
+
+        # Break if heap invariant satisfied
+        if heap[i] < heap[child_i]:
+            break
+        
+        # Move the smaller child up.
+        heap[i], heap[child_i] = heap[child_i], heap[i]
+        i = child_i
+        left_i = 2 * i + 1
+
+def heapify(lst):
+    for i in reversed(range(len(lst) // 2)):
+        _bubble_down(lst, i)
+
+def heappush(heap, item):
+    heap.append(item)
+    _bubble_up(heap, len(heap) - 1)
+
+def heappop(heap):
+    if len(heap) == 1:
+        return heap.pop()
+    min_value = heap[0]
+    heap[0] = heap[-1]
+    del heap[-1]
+    _bubble_down(heap, 0)
+    return min_value
+
+
+
+# Example usage
+heap = [3, 2, 1, 0]
+heapify(heap)
+print('Heap(0, 1, 2, 3):', heap)
+heappush(heap, 4)
+heappush(heap, 7)
+heappush(heap, 6)
+heappush(heap, 5)
+print('Heap(0, 1, 2, 3, 4, 5, 6, 7):', heap)
+
+sorted_list = [heappop(heap) for _ in range(8)]
+print('Heap-sorted list:', sorted_list)
+
+# Large test case, for randomized tests
+import random
+
+# Heapify 0 ~ 99
+heap = list(range(100))
+random.shuffle(heap)
+heapify(heap)
+
+# Push 100 ~ 199 in random order
+new_elems = list(range(100, 200))
+random.shuffle(new_elems)
+for elem in new_elems:
+    heappush(heap, elem)
+
+sorted_list = [heappop(heap) for _ in range(200)]
+print(sorted_list == sorted(sorted_list))