adding comments to heapify code

leetcode/p912_heapsort_array_heapify.cpp

@@ -1,5 +1,24 @@
 class Solution {
 public:
+/* The heapify function is designed to ensure that a subtree rooted at a given index i 
+ * in an array representation of a heap maintains the heap property. 
+ * While the function doesn't have an explicit base case like some recursive functions, 
+ * it inherently terminates due to the following conditions:
+ *  
+ * Leaf Node Condition: If the node at index i is a leaf node (i.e., it has no children), 
+ * the function reaches a point where both left and right indices are greater than or equal to n (the size of the heap). 
+ * In this scenario, the conditions left < n and right < n in the if statements evaluating the children will both be false, 
+ * preventing further recursive calls.
+ * 
+ * Heap Property Satisfaction: If the node at index i is greater than or equal to its children (or if it has no children), 
+ * the heap property is already satisfied. Consequently, the variable largest remains equal to i, 
+ * and the condition largest != i evaluates to false. 
+ * This prevents the swap operation and the subsequent recursive call, leading to termination. 
+ * In essence, the function will return when:
+ * The node is a leaf node. 
+ * The node's value is greater than or equal to its children's values, maintaining the heap property.
+ * These implicit conditions ensure that the recursion does not continue indefinitely.
+ * */
     void heapify(vector<int>& nums, int n, int i){
         int largest = i; // assuming i is the largest
         int left = 2*i+1;    // i's left child is at this location
@@ -24,10 +43,14 @@ public:
     // heap sort: O(nlogn)
     vector<int> sortArray(vector<int>& nums) {
         int n = nums.size();
-        // build the heap, starting from the last non-leaf node
+        // build the heap, starting from the last non-leaf node.
+	// why we start from the last non-leaf node? because leaf nodes inherently satisfy the heap property, as they have no children.
+	// By beginning the heapify process from the last non-leaf node and moving upwards:
+	// We ensure that when we heapify a node, its children are already heapified.
+	// This bottom-up approach guarantees that each subtree satisfies the heap property before moving to the next node.
         for(int i=n/2-1; i>=0; i--){
             // heapify the subtree whose root is at i
-            // i.e., build a max heap, with i being the root.
+            // i.e., build a max heap, with i being the root; and this heap contains nodes from i to n-1;
             heapify(nums, n, i);
         }