What is min heap? Create the min heap for the given data set: 6, 15, 50, 3, 33, 45, 40, 80, 10

Min Heap:

A min heap is a complete binary tree where the value of each node is less than or equal to the values of its children. This property is also known as the "heap property." Min heaps are often used in priority queues, where elements are retrieved in ascending order of their values.

Creating a Min Heap:

To create a min heap from a given set of data, we can use the following steps:

1. Initialization: Create an empty min heap.

2. Insertion:

   • Start from the first element of the given data set.
   • Add the element to the min heap by inserting it at the next available position, which is always the rightmost leaf node.
   • Restore the heap property by comparing the new node with its parent node and swapping them if necessary to maintain the min heap property.

3. Continue Insertion:

   • Repeat step 2 for all remaining elements in the data set.

Example:

Let's create a min heap for the given data set: 6, 15, 50, 3, 33, 45, 40, 80, 10

1. Initialization:

      null

2. Insertion:

Step 1: Add the first element, 6, to the min heap:

        6

Step 2: Add the second element, 15, to the min heap:

        6
      /   \
    15    null

Step 3: Add the third element, 50, to the min heap:

        6
      /   \
    15    50

Step 4: Add the fourth element, 3, to the min heap:

        3
      /   \
    6    50
   /   \
15     null

Step 5: Add the fifth element, 33, to the min heap:

        3
      /   \
    6    50
   / \   / \
15  null 33 null

Step 6: Add the sixth element, 45, to the min heap:

        3
      /   \
    6    50
   / \   / \
15  null 33 45

Step 7: Add the seventh element, 40, to the min heap:

        3
      /   \
    6    50
   / \   / \
15  null 33 45
         /
       40

Step 8: Add the eighth element, 80, to the min heap:

        3
      /   \
    6    50
   / \   / \
15  null 33 45
         / \
       40  80

Step 9: Add the ninth element, 10, to the min heap:

        3
      /   \
    6    50
   / \   / \
15 10  33 45
         / \
       40  80

This completes the creation of the min heap for the given data set.

Conclusion:

Min heaps are a versatile data structure that can be used to efficiently store and retrieve data in ascending order. They are often used in priority queues, where the highest priority element is always at the root of the heap.