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Given an array of element 0, 5, 9, 1, 3, 10, 8, 6,11. Which of the following is the correct sequence when we pop the elements 1 by 1, after inserting all the elements in a min-heap?

Question

Given an array of element 0, 5, 9, 1, 3, 10, 8, 6,11. Which of the following is the correct sequence when we pop the elements 1 by 1, after inserting all the elements in a min-heap?

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Solution

To answer this question, we first need to understand what a min-heap is. A min-heap is a complete binary tree in which the value in each node is less than or equal to the values in the children of that node.

So, when we insert the elements 0, 5, 9, 1, 3, 10, 8, 6, 11 into a min-heap, the heap will automatically arrange itself so that the smallest element is at the root.

The min-heap would look like this after inserting all elements:

       0
     /   \
    1     5
   / \   / \
  9   3 10  8
 / \
6   11

Now, when we pop the elements one by one, we always remove the smallest element, which is the root of the heap. After removing an element, the heap will rearrange itself to maintain the min-heap property.

So, the sequence of elements when we pop them one by one from the min-heap is: 0, 1, 3, 5, 6, 8, 9, 10, 11.

This problem has been solved

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Consider an array arr of size 5, initially filled with elements [2, 4, 6, 8, 10]. You want to insert the element 5 at position 2 in the array. What would be the array after the insertion?

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