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Find the Missing Number in a sorted array

  • Difficulty Level : Medium
  • Last Updated : 29 Apr, 2021

Given a list of n-1 integers and these integers are in the range of 1 to n. There are no duplicates in list. One of the integers is missing in the list. Write an efficient code to find the missing integer. 
Examples: 

Input : arr[] = [1, 2, 3, 4, 6, 7, 8]
Output : 5

Input : arr[] = [1, 2, 3, 4, 5, 6, 8, 9]
Output : 7

One Simple solution is to apply methods discussed for finding the missing element in an unsorted array. Time complexity of this solution is O(n).
An efficient solution is based on the divide and conquer algorithm that we have seen in binary search, the concept behind this solution is that the elements appearing before the missing element will have ar[i] – i = 1 and those appearing after the missing element will have ar[i] – i = 2.
This solution has a time complexity of O(log n) 

C++




// A binary search based program to find the
// only missing number in a sorted array of
// distinct elements within limited range.
#include <iostream>
using namespace std;
 
int search(int ar[], int size)
{
    int a = 0, b = size - 1;
    int mid;
    while ((b - a) > 1) {
        mid = (a + b) / 2;
        if ((ar[a] - a) != (ar[mid] - mid))
            b = mid;
        else if ((ar[b] - b) != (ar[mid] - mid))
            a = mid;
    }
    return (ar[a] + 1);
}
 
int main()
{
    int ar[] = { 1, 2, 3, 4, 5, 6, 8 };
    int size = sizeof(ar) / sizeof(ar[0]);
    cout << "Missing number:" << search(ar, size);
}

Java




// A binary search based program
// to find the only missing number
// in a sorted array of distinct
// elements within limited range.
import java.io.*;
 
class GFG
{
static int search(int ar[],
                  int size)
{
    int a = 0, b = size - 1;
    int mid = 0;
    while ((b - a) > 1)
    {
        mid = (a + b) / 2;
        if ((ar[a] - a) != (ar[mid] - mid))
            b = mid;
        else if ((ar[b] - b) != (ar[mid] - mid))
            a = mid;
    }
    return (ar[a] + 1);
}
 
// Driver Code
public static void main (String[] args)
{
    int ar[] = { 1, 2, 3, 4, 5, 6, 8 };
    int size = ar.length;
    System.out.println("Missing number: " +
                        search(ar, size));
}
}
 
// This code is contributed
// by inder_verma.

Python3




# A binary search based program to find
# the only missing number in a sorted
# in a sorted array of distinct elements
# within limited range
def search(ar, size):
    a = 0
    b = size - 1
    mid = 0
    while b > a + 1:
        mid = (a + b) // 2
        if (ar[a] - a) != (ar[mid] - mid):
            b = mid
        elif (ar[b] - b) != (ar[mid] - mid):
            a = mid
    return ar[a] + 1
 
# Driver Code
a = [1, 2, 3, 4, 5, 6, 8]
n = len(a)
 
print("Missing number:", search(a, n))
 
# This code is contributed
# by Mohit Kumar

C#




// A binary search based program
// to find the only missing number
// in a sorted array of distinct
// elements within limited range.
using System;
 
class GFG
{
static int search(int []ar,
                  int size)
{
    int a = 0, b = size - 1;
    int mid = 0;
    while ((b - a) > 1)
    {
        mid = (a + b) / 2;
        if ((ar[a] - a) != (ar[mid] - mid))
            b = mid;
        else if ((ar[b] - b) != (ar[mid] - mid))
            a = mid;
    }
    return (ar[a] + 1);
}
 
// Driver Code
static public void Main (String []args)
{
    int []ar = { 1, 2, 3, 4, 5, 6, 8 };
    int size = ar.Length;
    Console.WriteLine("Missing number: " +
                        search(ar, size));
}
}
 
// This code is contributed
// by Arnab Kundu

PHP




<?php
// A binary search based program to find the
// only missing number in a sorted array of
// distinct elements within limited range.
 
function search($ar, $size)
{
    $a = 0;
    $b = $size - 1;
    $mid;
    while (($b - $a) > 1)
    {
        $mid = (int)(($a + $b) / 2);
        if (($ar[$a] - $a) != ($ar[$mid] -
                                   $mid))
            $b = $mid;
        else if (($ar[$b] - $b) != ($ar[$mid] -
                                        $mid))
            $a = $mid;
    }
    return ($ar[$a] + 1);
}
 
// Driver Code
$ar = array(1, 2, 3, 4, 5, 6, 8 );
$size = sizeof($ar);
echo "Missing number: ",
     search($ar, $size);
 
// This code is contributed by ajit.
?>

Javascript




<script>
// A binary search based program
// to find the only missing number
// in a sorted array of distinct
// elements within limited range.
 
function search(ar, size)
{
    let a = 0, b = size - 1;
    let mid = 0;
    while ((b - a) > 1)
    {
        mid = (a + b) / 2;
        if ((ar[a] - a) != (ar[mid] - mid))
            b = mid;
        else if ((ar[b] - b) != (ar[mid] - mid))
            a = mid;
    }
    return (ar[a] + 3);
}
 
// Driver Code
 
let ar = [1, 2, 3, 4, 5, 6, 8];
let size = ar.length;
document.write("Missing number: " +search(ar, size));
 
// This code is contributed by mohit kumar 29.
</script>

Output: 

Missing number: 7

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