All Programming & Data Structures questions

Let $n$ be an odd number greater than 100. Consider a binary minheap with $n$ elements stored in an array $P$ whose index starts from 1. Which of the following indices of $P$ do/does NOT correspond to any leaf node of the minheap?

Consider a hash table $P[0, 1, \ldots, 10]$ that is initially empty. The hash table is maintained using open addressing with linear probing. The hash function used is $h(x) = (x + 7) \bmod 11$. Consider the following sequence of insertions performed on $P$: $$1, 13, 22, 15, 11, 24$$ Which of the following positions in the hash table is/are empty after these insertions are performed?

The height of a binary tree is the number of edges in the longest path from the root to a leaf in the tree. The maximum possible height of a full binary tree with 23 nodes is _________. (*answer in integer*)

Consider the following program in C:

#include <stdio.h>

void func(int i, int j) {
  if(i < j) {
    int i = 0;
    while (i < 10) {
      j += 2;
      i++;
    }
  }
  printf("%d", i);
}

int main() {
  int i = 9, j = 10;
  func(i, j);
  return 0;
}

The output of the program is _________. (*answer in integer*) *Note*: Assume that the program compiles and runs successfully.

Consider the following code snippet in C language that computes the number of nodes in a non-empty singly linked list pointed to by the pointer variable head.

struct node{
  int elt;
  struct node *next;
};
int getListSize (struct node *head)
{
  if( E1 ) return 1;
  return E2;
}

Which one of the following options gives the correct replacements for the expressions E1 and E2?

Let $P$ be the set of all integers from 1 to 15. Consider any order of insertion of the elements of $P$ into a binary search tree that creates a complete binary tree. Which one of the following elements can NEVER be the third element that is inserted?

Consider the recursive functions represented by the following code segment:

int bar(int n){
     if (n == 1) return 0;
     else return 1 + bar(n/2);
}
int foo(int n){
     if (n == 1) return 1;
     else return 1 + foo(bar(n));
}

The smallest positive integer n for which foo(n) returns 5 is ______. (*answer in integer*) *Note:* Ignore syntax errors (if any) in the function.

The following sequence corresponds to the preorder traversal of a binary search tree $T$: $$50, 25, 13, 40, 30, 47, 75, 60, 70, 80, 77$$ The position of the element 60 in the postorder traversal of $T$ is ______. (*answer in integer*) *Note:* The position begins with 1.

Which of the following statement(s) is/are TRUE for any binary search tree (BST) having $n$ distinct integers?

#include <stdio.h>
void foo(int *p, int x){
    *p=x;
}
int main(){
    int *z;
    int a = 20, b = 25;
    z = &a;
    foo(z,b);
    printf("%d",a);
    return 0;
}

The output of the given C program is __________. (Answer in integer)

The height of any rooted tree is defined as the maximum number of edges in the path from the root node to any leaf node. Suppose a Min-Heap $T$ stores 32 keys. The height of $T$ is _____________. (Answer in integer)

#include <stdio.h>
int foo(int S[],int size){
    if(size == 0) return 0;
    if(size == 1) return 1;
    if(S[0] != S[1]) return 1+foo(S+1,size-1);
    return foo(S+1,size-1);
}
int main(){
    int A[]={0,1,2,2,2,0,0,1,1};
    printf("%d",foo(A,9));
    return 0;
}

The value printed by the given C program is _______. (Answer in integer)

Let LIST be a datatype for an implementation of linked list defined as follows:

typedef struct list {
    int data;
    struct list *next;
} LIST;

Suppose a program has created two linked lists, L1 and L2, whose contents are given in the figure below (code for creating L1 and L2 is not provided here). L1 contains 9 nodes, and L2 contains 7 nodes.

L1: 1 -> 7 -> 12 -> 3 -> 9 -> 5 -> 11 -> 15 -> 8 -> NULL
L2: 1 -> 11 -> 6 -> 9 -> 15 -> 12 -> 4 -> NULL

Consider the following C program segment that modifies the list L1. The number of nodes that will be there in L1 after the execution of the code segment is ________. (Answer in integer)

int find (int query, LIST *list) {
    while (list != NULL){
        if(list->data == query) return 1;
        list = list->next;
    }
    return 0;
}
int main () {
    … … …
    ptr1=L1; ptr2=L2;
    while (ptr1->next != NULL){
        query = ptr1->next->data;
        if (find (query, L2))
            ptr1->next = ptr1->next->next;
        else ptr1 = ptr1->next;
    }
    … … …
    return 0;
}

Consider the following C program:

#include <stdio.h>
int gate (int n) {
    int d, t, newnum, turn;
    newnum = turn = 0; t=1;
    while (n>=t) t *= 10;
    t /=10;
    while (t>0) {
        d = n/t;
        n = n%t;
        t /= 10;
        if (turn) newnum = 10*newnum + d;
        turn = (turn + 1) % 2;
    }
    return newnum;
}
int main () {
    printf ("%d", gate(14362));
    return 0;
}

The value printed by the given C program is _______. (Answer in integer)

In a double hashing scheme, $h_1(k) = k \bmod 11$ and $h_2(k) = 1 + (k \bmod 7)$ are the auxiliary hash functions. The size $m$ of the hash table is 11. The hash function for the $i$-th probe in the open address table is $[h_1(k) + i\, h_2(k)] \bmod m$. The following keys are inserted in the given order: 63, 50, 25, 79, 67, 24. The slot at which key 24 gets stored is ___________. (Answer in integer)

Consider the following C program:

#include <stdio.h>
int main(){
   int a = 6;
   int b = 0;
   while(a < 10) {
      a = a / 12 + 1;
      a += b;}
   printf("%d", a);
   return 0;}

Which one of the following statements is CORRECT?

Consider the following C program:

#include <stdio.h>
void fX();
int main(){
   fX();
   return 0;}
void fX(){
   char a;
   if((a=getchar()) != '\n')
       fX();
   if(a != '\n')
       putchar(a);}

Assume that the input to the program from the command line is 1234 followed by a newline character. Which one of the following statements is CORRECT?

An array [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one of the following options represents the first three elements in the heapified array?

Consider a binary min-heap containing 105 distinct elements. Let $k$ be the index (in the underlying array) of the maximum element stored in the heap. The number of possible values of $k$ is

Consider the following C function definition.

int f(int x, int y) {
  for (int i=0; i<y; i++) {
    x=x+x+y;
  }
  return x;
}

Which of the following statements is/are TRUE about the above function?