Searching

What is the output of following program?

#include <stdio.h>

void print(int n, int j)
{
   if (j >= n)
      return;
   if (n-j > 0 && n-j >= j)
       printf("%d %dn", j, n-j);
   print(n, j+1);
}

int main()
{
    int n = 8;
    print(n, 1);
}

Which of the following is correct recurrence for worst case of Binary Search?

Given a sorted array of integers, what can be the minimum worst case time complexity to find ceiling of a number x in given array? Ceiling of an element x is the smallest element present in array which is greater than or equal to x. Ceiling is not present if x is greater than the maximum element present in array. For example, if the given array is {12, 67, 90, 100, 300, 399} and x = 95, then output should be 100.

Consider the following C program that attempts to locate an element x in an array Y[] using binary search. The program is erroneous. (GATE CS 2008)

1.   f(int Y[10], int x) {
2.     int i, j, k;
3.     i = 0; j = 9;
4.     do {
5.             k =  (i + j) /2;
6.             if( Y[k] < x)  i = k; else j = k;
7.         } while(Y[k] != x && i < j);
8.     if(Y[k] == x) printf ("x is in the array ") ;
9.     else printf (" x is not in the array ") ;
10. }

On which of the following contents of Y and x does the program fail?

In the above question, the correction needed in the program to make it work properly is (GATE CS 2008)

You are given a list of 5 integers and these integers are in the range from 1 to 6. There are no duplicates in list. One of the integers is missing in the list. Which of the following expression would give the missing number. ^ is bitwise XOR operator. ~ is bitwise NOT operator. Let elements of list can be accessed as list[0], list[1], list[2], list[3], list[4]

Consider the C function given below. Assume that the array listA contains n (> 0) elements, sorted in ascending order.

int ProcessArray(int *listA, int x, int n)
{
    int i, j, k;
    i = 0;
    j = n-1;
    do
    {
        k = (i+j)/2;
        if (x <= listA[k])
            j = k-1;
        if (listA[k] <= x)
            i = k+1;
    }
    while (i <= j);
    if (listA[k] == x)
        return(k);
    else
        return -1;
}

Which one of the following statements about the function ProcessArray is CORRECT?

The function is iterative implementation of Binary Search.  

k keeps track of current middle element.

i and j keep track of left and right corners
of current subarray

Consider a sorted array of n numbers. What would be the time complexity of the best known algorithm to find a pair a and b such that |a-b| = k , k being a positive integer.

The average number of key comparisons done in a successful sequential search in a list of length it is

Consider the following program that attempts to locate an element x in a sorted array a[ ] using binary search. Assume N>1. The program is erroneous. Under what conditions does the program fail?

var i,j,k: integer;  x: integer;
    a: array; [1....N] of integer;
begin	i:= 1; j:= N;
repeat	
    k:(i+j) div 2;
    if a[k] < x then i:= k 
    else j:= k 
until (a[k] = x) or (i >= j);
    
if (a[k] = x) then
    writeln ('x is in the array')
else
    writeln ('x is not in the array')
end;