Day40: add brainstorm thoughts about O(n) heapify

Author: thatguyintech

day38/README.md

@@ -82,3 +82,60 @@ If some kind of ordering is required, i.e. max or min ordering, a heap is an
 efficient way to maintain that ordering even when elements are being deleted
 and added. The tree structure of the heap allows you to find elements in
 `O(logn)` time rather than `O(n)` time like in a normal array or linked list.
+
+Some more thinking around heapify, aka just cram an unsorted array into
+a binary tree, and then compare and swap unordered parent-children pairs:
+
+arr = [4, 5, 7, 3, 9, 6, 1]
+
+        4
+       / \
+      5   7 
+     / \ / \
+    3  9 6  1
+
+len = 7
+first parent = 7/2 = 3
+index = 3-1
+arr[index] == 7
+
+7's children: arr[2*index + 1], arr[2*index + 2] aka 6, 1
+1 < 6
+
+        4
+       / \
+      5   1 
+     / \ / \
+    3  9 6  7
+
+next parent -> index -= 1
+arr[index] = 5
+
+5's children: 3, 9
+3 < 9
+
+        4
+       / \
+      3   1 
+     / \ / \
+    5  9 6  7
+
+next parent -> index -= 1
+arr[index] = 4
+
+4's children: 3, 1
+1 < 3
+
+        1
+       / \
+      3   4 
+     / \ / \
+    5  9 6  7
+
+done.
+
+Need to do one comparison set for each parent node, and then done. So O(n) time!
+
+
+
+

day38/heap.py

@@ -7,6 +7,7 @@ def __init__(self, arr=[]):
         if len(arr) > 0:
             self.heapify(arr)
 
+    # runtime: O(logn) aka the height of the heap
     def getMin(self):
         if self.size > 0:
             ret = self.heap.popleft()
@@ -16,19 +17,23 @@ def getMin(self):
                 self.bubbleDown()
             return ret
 
+    # runtime: O(1) 
     def peek(self):
         if self.size > 0:
             return self.heap[0]
 
+    # runtime: O(logn) aka the height of the tree
     def push(self, val):
         self.size += 1
         self.heap.append(val)
         self.bubbleUp()
 
+    # runtime: O(nlogn)
     def heapify(self, arr):
         for item in arr:
             self.push(item)
 
+    # runtime: O(1)
     def isEmpty(self):
         return self.size == 0