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What is the time complexity of Build Heap operation. Build Heap is used to build a max(or min) binary heap from a given array. Build Heap is used in Heap Sort as a first step for sorting.
- a)O(nLogn)
- b)O(n^2)
- c)O(Logn)
- d)O(n)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the time complexity of Build Heap operation. Build Heap is use...
Following is algorithm for building a Heap of an input array A.
BUILD-HEAP(A)
heapsize := size(A);
for i := floor(heapsize/2) downto 1
do HEAPIFY(A, i);
end for
END
heapsize := size(A);
for i := floor(heapsize/2) downto 1
do HEAPIFY(A, i);
end for
END
Although the worst case complexity looks like O(nLogn), upper bound of time complexity is O(n).
Most Upvoted Answer
What is the time complexity of Build Heap operation. Build Heap is use...
Explanation:
Build Heap operation is used to build a max or min binary heap from a given array. The time complexity of this operation is O(n), where n is the number of elements in the array.
1. Building a binary tree from an array:
- The first step in building a binary heap from an array is to create a binary tree from the array.
- This step requires visiting each element in the array once and adding it to the binary tree.
- The time complexity of this step is O(n).
2. Heapifying the binary tree:
- Once the binary tree is created, the next step is to heapify it.
- Heapifying a binary tree involves ensuring that the root node of each subtree is the maximum(or minimum) value within that subtree.
- This step requires visiting each node in the binary tree once and swapping values to ensure that the heap property is maintained.
- The time complexity of this step is O(n).
3. Conclusion:
- The time complexity of building a max(or min) binary heap from an array is the sum of the time complexities of the two steps above.
- Therefore, the time complexity of build heap operation is O(n).
Therefore, the correct answer is option 'D', O(n).
Build Heap operation is used to build a max or min binary heap from a given array. The time complexity of this operation is O(n), where n is the number of elements in the array.
1. Building a binary tree from an array:
- The first step in building a binary heap from an array is to create a binary tree from the array.
- This step requires visiting each element in the array once and adding it to the binary tree.
- The time complexity of this step is O(n).
2. Heapifying the binary tree:
- Once the binary tree is created, the next step is to heapify it.
- Heapifying a binary tree involves ensuring that the root node of each subtree is the maximum(or minimum) value within that subtree.
- This step requires visiting each node in the binary tree once and swapping values to ensure that the heap property is maintained.
- The time complexity of this step is O(n).
3. Conclusion:
- The time complexity of building a max(or min) binary heap from an array is the sum of the time complexities of the two steps above.
- Therefore, the time complexity of build heap operation is O(n).
Therefore, the correct answer is option 'D', O(n).
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