1
GATE CSE 2016 Set 1
+2
-0.6
An operator $$delete(i)$$ for a binary heap data structure is to be designed to delete the item in the $$i$$-th node. Assume that the heap is implemented in an array and i refers to the $$i$$-th index of the array. If the heap tree has depth $$d$$ (number of edges on the path from the root to the farthest leaf), then what is the time complexity to re-fix the heap efficiently after the removal of the element?
A
$$O\left( 1 \right)$$
B
$$O\left( d \right)$$ but not $$O\left( 1 \right)$$
C
$$O\left( {{2^d}} \right)$$ but not $$O\left( d \right)$$
D
$$O\left( {d{2^d}} \right)$$ but not $$O\left( {{2^d}} \right)$$
2
GATE CSE 2015 Set 1
+2
-0.6
Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4.
Array Index 1 2 3 4 5 6 7 8 9
Value 40 30 20 10 15 16 17 8 4

Now consider that a value 35 is inserted into this heap. After insertion, the new heap is

A
40, 30, 20, 10, 15, 16, 17, 8, 4, 35
B
40, 35, 20, 10, 30, 16, 17, 8, 4, 15
C
40, 30, 20, 10, 35, 16, 17, 8, 4, 15
D
40, 35, 20, 10, 15, 16, 17, 8, 4, 30
3
GATE CSE 2015 Set 2
+2
-0.6
Suppose you are provided with the following function declaration in the C programming language.
int partition(int a[], int n);
The function treats the first element of a[ ] as a pivot and rearranges the array so that all elements less than or equal to the pivot is in the left part of the array, and all elements greater than the pivot is in the right part. In addition, it moves the pivot so that the pivot is the last element of the left part. The return value is the number of elements in the left part. The following partially given function in the C programming language is used to find the kth smallest element in an array a[ ] of size n using the partition function. We assume k≤n.
int kth_smallest (int a[], int n, int k)
{
int left_end = partition (a, n);
if (left_end+1==k) {
return a[left_end];
}
if (left_end+1 > k) {
return kth_smallest (___________);
} else {
return kth_smallest (___________);
}
}
The missing arguments lists are respectively
A
(a, left_end, k) and (a + left_end + 1, n - left_end - 1, k - left_end - 1)
B
(a, left_end, k) and (a, n - left_end - 1, k - left_end-1)
C
(a + left_end + 1, n - left_end - 1, k - left_end - 1) and (a, left_end, k)
D
(a, n - left_end - 1, k - left_end - 1) and (a, left_end, k)
4
GATE CSE 2015 Set 3
+2
-0.6
Assume that a mergesort algorithm in the worst case takes $$30$$ seconds for an input of size $$64.$$ Which of the following most closely approximates the maximum input size of a problem that can be solved in $$6$$ minutes?
A
$$256$$
B
$$512$$
C
$$1024$$
D
$$2048$$
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