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Given an array of element 5, 7, 9, 1, 3, 10, 8, 4. Which of the following are the correct sequences of elements after inserting all the elements in a min-heap?*2 points1,3,4,5,7,8,9,101,4,3,9,8,5,7,101,3,4,5,8,7,9,101,3,7,4,8,5,9,10

Question

Given an array of element 5, 7, 9, 1, 3, 10, 8, 4. Which of the following are the correct sequences of elements after inserting all the elements in a min-heap?*2 points1,3,4,5,7,8,9,101,4,3,9,8,5,7,101,3,4,5,8,7,9,101,3,7,4,8,5,9,10

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Solution

The correct sequence of elements after inserting all the elements in a min-heap is 1,3,4,5,7,8,9,10.

Here's the step by step process:

  1. Start with the first element of the array, which is 5. This becomes the root of our min-heap.

  2. Next, insert the second element, 7. Since 7 is greater than 5, it becomes the right child of 5.

  3. Insert the third element, 9. As 9 is greater than 5, it becomes the right child of 7.

  4. Insert the fourth element, 1. Since 1 is less than 5, it becomes the new root and 5 is moved down to become its child.

  5. Continue this process with the remaining elements. The goal is to always maintain the property of the min-heap, where the parent node is smaller than its child nodes.

  6. After inserting all the elements, the min-heap looks like this:

        1
       / \
      3   4
     / \ / \
    5  7 8  9
   /
  10
  1. Reading the elements from top to bottom, left to right gives us the sequence 1,3,4,5,7,8,9,10.

This problem has been solved

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