A priority queue is implemented as a max-heap initially, it has five elements. The level-order traversal of theheap is as follows: 20, 18, 15, 13, 12. Suppose two new elements ‘10’ and ‘17’ are inserted in the heap inthat order. Find the level-order traversal of the heap after the insertion of the element.
Question
A priority queue is implemented as a max-heap initially, it has five elements. The level-order traversal of theheap is as follows: 20, 18, 15, 13, 12. Suppose two new elements ‘10’ and ‘17’ are inserted in the heap inthat order. Find the level-order traversal of the heap after the insertion of the element.
Solution
Sure, let's go through this step by step.
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We start with the initial max-heap: 20, 18, 15, 13, 12.
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The first element to be inserted is '10'. Since this is a max-heap, we add the element to the next available spot, which is the left child of '15'. Now the heap looks like this: 20, 18, 15, 13, 12, 10.
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Next, we insert '17'. We add it to the next available spot, which is the right child of '15'. Now the heap looks like this: 20, 18, 15, 13, 12, 10, 17.
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However, '17' is larger than its parent '15', so we need to swap them to maintain the max-heap property. The heap now looks like this: 20, 18, 17, 13, 12, 10, 15.
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But '17' is still larger than its new parent '18', so we swap them as well. The final max-heap, after inserting '10' and '17', is: 20, 17, 18, 13, 12, 10, 15.
So, the level-order traversal of the heap after the insertion of the elements '10' and '17' is: 20, 17, 18, 13, 12, 10, 15.
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