A min-heap is useful when we are interested in the minimum value of a set of numbers. Now, instead of the min, we are interested in the K-th smallest value. a.) Please design a data structure to allow the following two operations: push (insert a new number) and find_Kmin (return the value of the K-th smallest number without removing it). Both operations should be done in O(log K) time.
A min-heap is useful when we are interested in the minimum value of a
set of numbers. Now, instead of the min, we are interested in the K-th smallest value.
a.) Please design a data structure to allow the following two operations: push (insert a new
number) and find_Kmin (return the value of the K-th smallest number without removing it). Both
operations should be done in O(log K) time.
b.) In addition to push and find_Kmin, now we also want to support the pop operation to
return and remove the K-th smallest element. Please design a data structure to support these three
operations, and each operation should take O(log n) time with n being the size of the current set.
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I don't really follow this explanation. So we are modifying the heap in part a to contain the size of the left subtree as well. How does this help at all in maintaining the kth smallest value at the root of the heap? Suppose we push 1, 7, 8, and 11 in a min heap. We want to return the 3rd smallest element. It seems as if this explanation is suggesting 1 is returned not 8.
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