# Recent questions tagged data-structures

1 vote
1
A recursive function $h$, is defined as follows: $\begin{array} {} h(m) & =k, \text{if } m=0 \\ &=1, \text{if } m=1 \\ &= 2 h(m-1)+4h(m-2), \text{if } m \geq 2 \end{array}$ If the value of $h(4)$ is $88$ then the value of $k$ is: $0$ $1$ $2$ $-1$
2
Let $C$ be a binary linear code with minimum distance $2t+1$ then it can correct upto _______ bits of error $t+1$ $t$ $t-2$ $\frac{t}{2}$
3
The seven elements $A, B, C, D, E,F$ and $G$ are pushed onto a stack in reverse order, i.e., starting from $G$. The stack is popped five times and each element is inserted into a queue. Two elements are deleted from the queue and pushed back onto the stack. Now, one element is popped from the stack. The popped item is ___________. $A$ $B$ $F$ $G$
4
Which of the following is a valid heap? $a$ $b$ $c$ $d$
1 vote
5
If $h$ is chosen from a universal collection of hash functions and is used to hash $n$ keys into a table of size $m$, where $n \leq m$, the expected number of collisions involving a particular key $x$ is less than __________. $1$ $1/n$ $1/m$ $n/m$
6
In a balanced binary search tree with $n$ elements, what is the worst case time complexity of reporting all elements in range $[a,b]$? Assume that the number of reported elements is $k$. $\Theta (\log n)$ $\Theta (\log n +k)$ $\Theta (k \log n)$ $\Theta ( n \log k)$
7
Consider a $2$-dimensional array $x$ with $10$ rows and $4$ columns, with each element storing a value equivalent to the product of row number and column number. The array is stored in row-major format. If the first element $x[0][0]$ occupies the memory location with ... location, which all locations (in decimal) will be holding a value of $10$? $1018,1019$ $1022,1041$ $1013,1014$ $1000,1399$
1 vote
8
$G$ is an undirected graph with vertex set $\{v1, \ v2, \ v3, \ v4, \ v5, \ v6, \ v7\}$ and edge set $\{v1v2,\ v1v3,\ v1v4\ ,v2v4,\ v2v5,\ v3v4,\ v4v5,\ v4v6,\ v5v6,\ v6v7\ \}$. A breadth first search of the graph is performed with $v1$ as the root node. Which of the following is a tree edge? $v2v4$ $v1v4$ $v4v5$ $v3v4$
9
Of the following, which best approximates the ratio of the number of nonterminal nodes in the total number of nodes in a complete $K$-ary tree of depth $N$ ? $1/N$ $N-1/N$ $1/K$ $K-1/K$
10
Convert the pre-fix expression to in-fix $- ^{\ast} +ABC^{\ast} – DE+FG$ $(A-B)^{\ast}C+(D^{\ast}E)-(F+G)$ $(A+B)^{\ast}C-(D-E)^{\ast}(F-G)$ $(A+B-C)^{\ast}(D-E)^{\ast}(F+G)$ $(A+B)^{\ast}C-(D^{\ast}E)-(F+G)$
11
The minimum height of an AVL tree with $n$ nodes is $\text{Ceil } (\log_2(n+1))$ $1.44\ \log_2n$ $\text{Floor } (\log_2(n+1))$ $1.64\ \log_2n$
12
What is the in-order successor of $15$ in the given binary search tree? $18$ $6$ $17$ $20$
13
A stack is implemented with an array of $'A[0...N-1]'$ and a variable $pos$'. The push and pop operations are defined by the following code. push (x) A[pos] <- x pos <- pos -1 end push pop() pos <- pos+1 return A[pos] end pop Which of the ... initialize an empty stack with capacity $N$ for the above implementation $pos \leftarrow -1$ $pos\leftarrow 0$ $pos\leftarrow 1$ $pos\leftarrow N-1$
1 vote
14
In linear hashing, if blocking factor $bfr$, loading factor $i$ and file buckets $N$ are known, the number of records will be $cr= i+bfr+N$ $r=i-bfr-N$ $r=i+bfr-N$ $r=i ^{\ast} bfr ^{\ast} N$
15
The post-order traversal of binary tree is $ACEDBHIGF$. The pre-order traversal is $\text{A B C D E F G H I}$ $\text{F B A D C E G I H}$ $\text{F A B C D E G H I}$ $\text{A B D C E F G I H}$
16
Suppose that the figure to the right is a binary search tree. The letters indicate the names of the nodes, not the values that are stored. What is the predecessor node, in terms of value, of the root node $A?$ $D$ $H$ $I$ $M$
17
A First In First Out queue is a data structure supporting the operation Enque, Deque, Print, Enque(x) adds the item $x$ to the tail of the queue. Deque removes the element at the head of the queue and returns its value. Print prints the head of the queue. You ... in reverse order. If the queue had $n$ elements to begin with, how many statements would you need to print the queue in reverse order?
18
Explain how to implement doubly linked lists using only one pointer value $x.np$ per item instead of the usual two (next and prev). Assume that all pointer values can be interpreted as $k$-bit integers, and define $x.np$ to be $x.np=x.next$ $XOR$ $x.prev$, the $k$- ... to implement the $SEARCH$, $INSERT$, and $DELETE$ operations on such a list. Also, show how to reverse such a list in $O(1)$ time.
19
Give a $\Theta(n)$ time nonrecursive procedure that reverses a singly linked list of $n$ elements. The procedure should use no more than constant storage beyond that needed for the list itself.
20
The dynamic-set operation $UNION$ takes two disjoint sets $S_1$ and $S_2$ as input, and it returns a set $S=S_1 \cup S_2$ consisting of all the elements of $S_1$ and $S_2$.The sets $S_1$ and $S_2$ are usually destroyed by the operation. Show how to support $UNION$ in $O(1)$ time using a suitable list data structure.
21
Implement the dictionary operations $INSERT$, $DELETE$, and $SEARCH$ using singly linked, circular lists. What are the running times of your procedures?
22
LIST-SEARCH’(L, k) 1 x = L.nil.next 2 while x != L.nil and x.key != k 3 x = x.next 4 return x As written, each loop iteration in the LIST-SEARCH’ procedure requires two tests: one for $x\neq L.nil$ and one for $x.key\neq k$. Show how to eliminate the test for $x\neq L.nil$ in each iteration.
23
Implement a queue by a singly linked list $L$. The operations of $ENQUEUE$ and $DEQUEUE$ should still take $O(1)$ time.
24
Implement a stack using a singly linked list $L$. The operations $PUSH$ and $POP$ should still take $O(1)$ time.
25
Can you implement the dynamic-set operation $INSERT$ on a singly linked list in $O(1)$ time? How about $DELETE$?
26
Show how to implement a stack using two queues. Analyze the running time of the stack operations.
27
Show how to implement a queue using two stacks. Analyze the running time of the queue operations.
Whereas a stack allows insertion and deletion of elements at only one end, and a queue allows insertion at one end and deletion at the other end, a deque (double ended queue) allows insertion and deletion at both ends. Write four $O(1)$ time procedures to insert elements into and delete elements from both ends of a deque implemented by an array.
ENQUEUE(Q, x) 1 Q[Q.tail] = x 2 if Q.tail == Q.length 3 Q.tail = 1 4 else Q.tail = Q.tail + 1 DEQUEUE(Q) 1 x = Q[Q.head] 2 if Q.head == Q.length 3 Q.head = 1 4 else Q.head = Q.head + 1 5 return x illustrate the result of each operation in the sequence ENQUEUE(Q,4),ENQUEUE(Q,1),ENQUEUE(Q,3),DEQUEUE(Q),ENQUEUE(Q,8),DEQUEUE(Q) on an initially empty queue $Q$ stored in array $Q[1...6]$.