In PS1, we worked with an Extract-Insert-Stable (EIS) min heap which was defined as a min heap with no duplicate elements where the result of calling ExtractMin and immediately re-inserting the same element was the original heap. In this question we want to consider a related concept Insert-Extract-Stability IES. The pair (H,x) is the combination of min heap H with no duplicate elements and an element x. The pair is together considered IES if the result of inserting x into H and immediately calling ExtractMin results in the original heap H. (a) Formally describe the relationship between the elements of H and also the new element x so that (H,x) is IES. (b) Prove that your description holds by showing that it applies to all IES (H,x) pairs and does not hold for any (H,x) which is not IES.

Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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3. Неаps
In PS1, we worked with an Extract-Insert-Stable (EIS) min heap which was defined as a min heap
with no duplicate elements where the result of calling ExtractMin and immediately re-inserting
the same element was the original heap.
In this question we want to consider a related concept Insert-Extract-Stability IES. The pair (H, x)
is the combination of min heap H with no duplicate elements and an element x. The pair is
together considered IES if the result of inserting x into H and immediately calling ExtractMin
results in the original heap H.
(a) Formally describe the relationship between the elements of H and also the new element x so
that (H, x) is IES.
(b) Prove that your description holds by showing that it applies to all IES (H,x) pairs and does
not hold for any (H, x) which is not IES.
Transcribed Image Text:3. Неаps In PS1, we worked with an Extract-Insert-Stable (EIS) min heap which was defined as a min heap with no duplicate elements where the result of calling ExtractMin and immediately re-inserting the same element was the original heap. In this question we want to consider a related concept Insert-Extract-Stability IES. The pair (H, x) is the combination of min heap H with no duplicate elements and an element x. The pair is together considered IES if the result of inserting x into H and immediately calling ExtractMin results in the original heap H. (a) Formally describe the relationship between the elements of H and also the new element x so that (H, x) is IES. (b) Prove that your description holds by showing that it applies to all IES (H,x) pairs and does not hold for any (H, x) which is not IES.
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