1
GATE CSE 2016 Set 1
Numerical
+2
-0
Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given by the entry $${W_{ij}}$$ in the matrix $$W.$$ $$W = \left[ {\matrix{ 0 & 2 & 8 & 5 \cr 2 & 0 & 5 & 8 \cr 8 & 5 & 0 & X \cr 5 & 8 & X & 0 \cr } } \right]$$\$

The largest possible integer value of $$x,$$ for which at least one shortest path between some pair of vertices will contain the edge with weight $$x$$ is _________________.

2
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 $$O\left( {{2^d}} \right)$$
3
GATE CSE 2016 Set 1
Numerical
+1
-0
Consider the following code segment.
x = u - t;
y = x * v;
x = y + w;
y = t - z;
y = x * y;
The minimum number of total variables required to convert the above code segment to static single assignment form is .
4
GATE CSE 2016 Set 1
Numerical
+2
-0
The attributes of three arithmetic operators in some programming language are given below.

Operator Precedence Associativity Arity
+ High Left Binary
_ Medium Right Binary
* Low Left Binary

The value of the expression $$2 - 5 + 1 - 7 * 3$$ in this language is _______________.

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