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The Heapify Algorithm

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  • At each step, the index of the largest of the elements A[i], A[Left(i)], and A[Right(i)] is stored in the variable largest.
  • If A[i] is largest, then the subtree rooted at node i is a heap and the procedure ends.
  • Otherwise, one of the two children has the largest element, and A[i] is swapped with A[largest], which causes node i and its children to satisfy the heap property.
  • The node largest, however, now has the original value A[i], and thus the subtree rooted at largest may violate the heap property.
  • Therefore, Heapify must be called recursively on that subtree.

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