Find lost element from a duplicated array

Given two arrays that are duplicates of each other except one element, that is one element from one of the array is missing, we need to find that missing element.

Examples:

Input:  arr1[] = {1, 4, 5, 7, 9}
        arr2[] = {4, 5, 7, 9}
Output: 1
1 is missing from second array.

Input: arr1[] = {2, 3, 4, 5}
       arr2[] = {2, 3, 4, 5, 6}
Output: 6
6 is missing from first array.

One simple solution is to iterate over arrays and check element by element and flag the missing element when an unmatched element is found, but this solution requires linear time oversize of the array.

Another efficient solution is based on a binary search approach. Algorithm steps are as follows:

1. Start a binary search in a bigger array and get mid as (lo + hi) / 2
2. If the value from both arrays is the same then the missing element must be in the right part so set lo as mid
3. Else set hi as mid because the missing element must be in the left part of the bigger array if mid-elements are not equal.
4. A special case is handled separately as for single element and zero elements array, the single element itself will be the missing element. 
   If the first element itself is not equal then that element will be the missing element./li> 

Below is the implementation of the above steps 

C++

// C++ program to find missing element from same
// arrays (except one missing element)
#include <bits/stdc++.h>
using namespace std;

// Function to find missing element based on binary
// search approach.  arr1[] is of larger size and
// N is size of it.  arr1[] and arr2[] are assumed
// to be in same order.
int findMissingUtil(int arr1[], int arr2[], int N)
{
    // special case, for only element which is
    // missing in second array
    if (N == 1)
        return arr1[0];

    // special case, for first element missing
    if (arr1[0] != arr2[0])
        return arr1[0];

    // Initialize current corner points
    int lo = 0,  hi = N - 1;

    // loop until lo < hi
    while (lo < hi)
    {
        int mid = (lo + hi) / 2;

        // If element at mid indices are equal
        // then go to right subarray
        if (arr1[mid] == arr2[mid])
            lo = mid;
        else
            hi = mid;

        // if lo, hi becomes contiguous,  break
        if (lo == hi - 1)
            break;
    }

    // missing element will be at hi index of
    // bigger array
    return arr1[hi];
}

// This function mainly does basic error checking
// and calls findMissingUtil
void findMissing(int arr1[], int arr2[], int M, int N)
{
    if (N == M-1)
        cout << "Missing Element is "
        << findMissingUtil(arr1, arr2, M) << endl;
    else if (M == N-1)
        cout << "Missing Element is "
        << findMissingUtil(arr2, arr1, N) << endl;
    else
        cout << "Invalid Input";
}

// Driver Code
int main()
{
    int arr1[] = {1, 4, 5, 7, 9};
    int arr2[] = {4, 5, 7, 9};

    int M = sizeof(arr1) / sizeof(int);
    int N = sizeof(arr2) / sizeof(int);

    findMissing(arr1, arr2, M, N);

    return 0;
}

Java

// Java program to find missing element
// from same arrays
// (except one missing element)

import java.io.*;
class MissingNumber {

    /* Function to find missing element based
     on binary search approach. arr1[] is of
     larger size and N is size of it.arr1[] and
     arr2[] are assumed to be in same order. */
    int findMissingUtil(int arr1[], int arr2[],
                        int N)
    {
        // special case, for only element
        // which is missing in second array
        if (N == 1)
            return arr1[0];

        // special case, for first
        // element missing
        if (arr1[0] != arr2[0])
            return arr1[0];

        // Initialize current corner points
        int lo = 0, hi = N - 1;

        // loop until lo < hi
        while (lo < hi) {
            int mid = (lo + hi) / 2;

            // If element at mid indices are
            // equal then go to right subarray
            if (arr1[mid] == arr2[mid])
                lo = mid;
            else
                hi = mid;

            // if lo, hi becomes
            // contiguous, break
            if (lo == hi - 1)
                break;
        }

        // missing element will be at hi
        // index of bigger array
        return arr1[hi];
    }

    // This function mainly does basic error
    // checking and calls findMissingUtil
    void findMissing(int arr1[], int arr2[],
                              int M, int N)
    {
        if (N == M - 1)
        System.out.println("Missing Element is "
        + findMissingUtil(arr1, arr2, M) + "\n");
        else if (M == N - 1)
        System.out.println("Missing Element is "
        + findMissingUtil(arr2, arr1, N) + "\n");
        else
        System.out.println("Invalid Input");
    }

    // Driver Code
    public static void main(String args[])
    {
        MissingNumber obj = new MissingNumber();
        int arr1[] = { 1, 4, 5, 7, 9 };
        int arr2[] = { 4, 5, 7, 9 };
        int M = arr1.length;
        int N = arr2.length;
        obj.findMissing(arr1, arr2, M, N);
    }
}

// This code is contributed by Anshika Goyal.

Python3

# Python3 program to find missing
# element from same arrays
# (except one missing element)

# Function to find missing element based
# on binary search approach. arr1[] is
# of larger size and N is size of it.
# arr1[] and arr2[] are assumed
# to be in same order.
def findMissingUtil(arr1, arr2, N):

    # special case, for only element
    # which is missing in second array
    if N == 1:
        return arr1[0];

    # special case, for first
    # element missing
    if arr1[0] != arr2[0]:
        return arr1[0]

    # Initialize current corner points
    lo = 0
    hi = N - 1

    # loop until lo < hi
    while (lo < hi):

        mid = (lo + hi) / 2

        # If element at mid indices
        # are equal then go to
        # right subarray
        if arr1[mid] == arr2[mid]:
            lo = mid
        else:
            hi = mid

        # if lo, hi becomes
        # contiguous, break
        if lo == hi - 1:
            break

    # missing element will be at
    # hi index of bigger array
    return arr1[hi]

# This function mainly does basic
# error checking and calls
# findMissingUtil
def findMissing(arr1, arr2, M, N):

    if N == M-1:
        print("Missing Element is",
            findMissingUtil(arr1, arr2, M))
    elif M == N-1:
        print("Missing Element is",
            findMissingUtil(arr2, arr1, N))
    else:
        print("Invalid Input")

# Driver Code
arr1 = [1, 4, 5, 7, 9]
arr2 = [4, 5, 7, 9]
M = len(arr1)
N = len(arr2)
findMissing(arr1, arr2, M, N)

# This code is contributed by Smitha Dinesh Semwal

C#

// C# program to find missing element from
// same arrays (except one missing element)
using System;

class GFG {

    /* Function to find missing element based
    on binary search approach. arr1[] is of
    larger size and N is size of it.arr1[] and
    arr2[] are assumed to be in same order. */
    static int findMissingUtil(int []arr1,
                            int []arr2, int N)
    {

        // special case, for only element
        // which is missing in second array
        if (N == 1)
            return arr1[0];

        // special case, for first
        // element missing
        if (arr1[0] != arr2[0])
            return arr1[0];

        // Initialize current corner points
        int lo = 0, hi = N - 1;

        // loop until lo < hi
        while (lo < hi) {
            int mid = (lo + hi) / 2;

            // If element at mid indices are
            // equal then go to right subarray
            if (arr1[mid] == arr2[mid])
                lo = mid;
            else
                hi = mid;

            // if lo, hi becomes
            // contiguous, break
            if (lo == hi - 1)
                break;
        }

        // missing element will be at hi
        // index of bigger array
        return arr1[hi];
    }

    // This function mainly does basic error
    // checking and calls findMissingUtil
    static void findMissing(int []arr1, int []arr2,
                            int M, int N)
    {
        if (N == M - 1)
            Console.WriteLine("Missing Element is "
            + findMissingUtil(arr1, arr2, M) + "\n");
        else if (M == N - 1)
            Console.WriteLine("Missing Element is "
            + findMissingUtil(arr2, arr1, N) + "\n");
        else
            Console.WriteLine("Invalid Input");
    }

    // Driver Code
    public static void Main()
    {
        int []arr1 = { 1, 4, 5, 7, 9 };
        int []arr2 = { 4, 5, 7, 9 };
        int M = arr1.Length;
        int N = arr2.Length;
        findMissing(arr1, arr2, M, N);
    }
}

// This code is contributed by anuj_67.

PHP

<?php
// PHP program to find missing
// element from same arrays
// (except one missing element)

// Function to find missing
// element based on binary
// search approach. arr1[]
// is of larger size and
// N is size of it. arr1[]
// and arr2[] are assumed
// to be in same order.
function findMissingUtil($arr1, $arr2, $N)
{

    // special case, for only
    // element which is
    // missing in second array
    if ($N == 1)
        return $arr1[0];

    // special case, for first
    // element missing
    if ($arr1[0] != $arr2[0])
        return $arr1[0];

    // Initialize current
    // corner points
    $lo = 0;
    $hi = $N - 1;

    // loop until lo < hi
    while ($lo < $hi)
    {
        $mid = ($lo + $hi) / 2;

        // If element at mid indices are
        // equal then go to right subarray
        if ($arr1[$mid] == $arr2[$mid])
            $lo = $mid;
        else
            $hi = $mid;

        // if lo, hi becomes
        // contiguous, break
        if ($lo == $hi - 1)
            break;
    }

    // missing element will be
    // at hi index of
    // bigger array
    return $arr1[$hi];
}

// This function mainly
// does basic error checking
// and calls findMissingUtil
function findMissing($arr1, $arr2,
                           $M, $N)
{
    if ($N == $M - 1)
        echo "Missing Element is "
             , findMissingUtil($arr1,
                         $arr2, $M) ;
    else if ($M == $N - 1)
        echo "Missing Element is "
             , findMissingUtil($arr2,
                           $arr1, $N);
    else
        echo "Invalid Input";
}

    // Driver Code
    $arr1 = array(1, 4, 5, 7, 9);
    $arr2 = array(4, 5, 7, 9);
    $M = count($arr1);
    $N = count($arr2);
    findMissing($arr1, $arr2, $M, $N);

// This code is contributed by anuj_67.
?>

Javascript

<script>
    // Javascript program to find missing element from
    // same arrays (except one missing element)

    /* Function to find missing element based
    on binary search approach. arr1[] is of
    larger size and N is size of it.arr1[] and
    arr2[] are assumed to be in same order. */
    function findMissingUtil(arr1, arr2, N)
    {

        // special case, for only element
        // which is missing in second array
        if (N == 1)
            return arr1[0];

        // special case, for first
        // element missing
        if (arr1[0] != arr2[0])
            return arr1[0];

        // Initialize current corner points
        let lo = 0, hi = N - 1;

        // loop until lo < hi
        while (lo < hi) {
            let mid = parseInt((lo + hi) / 2, 10);

            // If element at mid indices are
            // equal then go to right subarray
            if (arr1[mid] == arr2[mid])
                lo = mid;
            else
                hi = mid;

            // if lo, hi becomes
            // contiguous, break
            if (lo == hi - 1)
                break;
        }

        // missing element will be at hi
        // index of bigger array
        return arr1[hi];
    }

    // This function mainly does basic error
    // checking and calls findMissingUtil
    function findMissing(arr1, arr2, M, N)
    {
        if (N == M - 1)
            document.write("Missing Element is "
            + findMissingUtil(arr1, arr2, M) + "</br>");
        else if (M == N - 1)
            document.write("Missing Element is "
            + findMissingUtil(arr2, arr1, N) + "</br>");
        else
            document.write("Invalid Input" + "</br>");
    }

    let arr1 = [ 1, 4, 5, 7, 9 ];
    let arr2 = [ 4, 5, 7, 9 ];
    let M = arr1.length;
    let N = arr2.length;
    findMissing(arr1, arr2, M, N);

</script>

Output

Missing Element is 1

Time Complexity: O(logM + logN), where M and N represents the size of the given two arrays.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

What if input arrays are not in the same order?
In this case, the missing element is simply XOR of all elements of both arrays. Thanks to Yolo Song for suggesting this. 

CPP

// C++ program to find missing element from one array
// such that it has all elements of other array except
// one.  Elements in two arrays can be in any order.
#include <bits/stdc++.h>
using namespace std;

// This function mainly does XOR of all elements
// of arr1[] and arr2[]
void findMissing(int arr1[], int arr2[], int M,
                 int N)
{
    if (M != N-1 && N != M-1)
    {
        cout << "Invalid Input";
        return;
    }

    // Do XOR of all element
    int res = 0;
    for (int i=0; i<M; i++)
       res = res^arr1[i];
    for (int i=0; i<N; i++)
       res = res^arr2[i];

    cout << "Missing element is " << res;
}

// Driver Code
int main()
{
    int arr1[] = {4, 1, 5, 9, 7};
    int arr2[] = {7, 5, 9, 4};

    int M = sizeof(arr1) / sizeof(int);
    int N = sizeof(arr2) / sizeof(int);

    findMissing(arr1, arr2, M, N);

    return 0;
}

Java

// Java program to find missing element
// from one array such that it has all
// elements of other array except one.
// Elements in two arrays can be in any order.

import java.io.*;
class Missing {

    // This function mainly does XOR of
    // all elements of arr1[] and arr2[]
    void findMissing(int arr1[], int arr2[],
                              int M, int N)
    {
        if (M != N - 1 && N != M - 1) {
        System.out.println("Invalid Input");
            return;
        }

        // Do XOR of all element
        int res = 0;
        for (int i = 0; i < M; i++)
            res = res ^ arr1[i];
        for (int i = 0; i < N; i++)
            res = res ^ arr2[i];

        System.out.println("Missing element is "
                                          + res);
    }

    // Driver Code
    public static void main(String args[])
    {
        Missing obj = new Missing();
        int arr1[] = { 4, 1, 5, 9, 7 };
        int arr2[] = { 7, 5, 9, 4 };
        int M = arr1.length;
        int N = arr2.length;
        obj.findMissing(arr1, arr2, M, N);
    }
}

// This code is contributed by Anshika Goyal.

Python3

# Python 3 program to find
# missing element from one array
# such that it has all elements
# of other array except
# one. Elements in two arrays
# can be in any order.

# This function mainly does XOR of all elements
# of arr1[] and arr2[]
def findMissing(arr1,arr2, M, N):
    if (M != N-1 and N != M-1):

        print("Invalid Input")
        return


    # Do XOR of all element
    res = 0
    for i in range(0,M):
        res = res^arr1[i];
    for i in range(0,N):
        res = res^arr2[i]

    print("Missing element is",res)

# Driver Code
arr1 = [4, 1, 5, 9, 7]
arr2 = [7, 5, 9, 4]
M = len(arr1)
N = len(arr2)
findMissing(arr1, arr2, M, N)

# This code is contributed
# by Smitha Dinesh Semwal

C#

// C# program to find missing element
// from one array such that it has all
// elements of other array except one.
// Elements in two arrays can be in
// any order.
using System;
class GFG {

    // This function mainly does XOR of
    // all elements of arr1[] and arr2[]
    static void findMissing(int []arr1,
                            int []arr2,
                            int M, int N)
    {
        if (M != N - 1 && N != M - 1)
        {
            Console.WriteLine("Invalid Input");
            return;
        }

        // Do XOR of all element
        int res = 0;
        for (int i = 0; i < M; i++)
            res = res ^ arr1[i];
        for (int i = 0; i < N; i++)
            res = res ^ arr2[i];

        Console.WriteLine("Missing element is "
                                        + res);
    }

    // Driver Code
    public static void Main()
    {

        int []arr1 = {4, 1, 5, 9, 7};
        int []arr2 = {7, 5, 9, 4};
        int M = arr1.Length;
        int N = arr2.Length;
        findMissing(arr1, arr2, M, N);
    }
}

// This code is contributed by anuj_67.

PHP

<?php
// PHP program to find missing
// element from one array
// such that it has all elements
// of other array except
// one. Elements in two arrays
// can be in any order.

// This function mainly does
// XOR of all elements
// of arr1[] and arr2[]
function findMissing($arr1, $arr2,
                           $M, $N)
{
    if ($M != $N - 1 && $N != $M - 1)
    {
        echo "Invalid Input";
        return;
    }

    // Do XOR of all element
    $res = 0;
    for ($i = 0; $i < $M; $i++)
        $res = $res ^ $arr1[$i];

    for ($i = 0; $i < $N; $i++)
    $res = $res ^ $arr2[$i];
    echo "Missing element is ", $res;
}

    // Driver Code
    $arr1 = array(4, 1, 5, 9, 7);
    $arr2 = array(7, 5, 9, 4);
    $M = sizeof($arr1);
    $N = sizeof($arr2);

    findMissing($arr1, $arr2, $M, $N);

// This code is contributed by aj_36
?>

Javascript

<script>

    // Javascript program to find
    // missing element from one array
    // such that it has all elements
    // of other array except one.
    // Elements in two arrays
    // can be in any order.

    // This function mainly does XOR
    // of all elements
    // of arr1[] and arr2[]
    function findMissing(arr1, arr2, M, N)
    {
        if (M != N-1 && N != M-1)
        {
            document.write("Invalid Input");
            return;
        }

        // Do XOR of all element
        let res = 0;
        for (let i=0; i<M; i++)
           res = res^arr1[i];
        for (let i=0; i<N; i++)
           res = res^arr2[i];

        document.write("Missing element is " + res);
    }

    let arr1 = [4, 1, 5, 9, 7];
    let arr2 = [7, 5, 9, 4];

    let M = arr1.length;
    let N = arr2.length;

    findMissing(arr1, arr2, M, N);

</script>

Output

Missing element is 1

Time Complexity: O(M + N), where M and N represents the size of the given two arrays.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

This article is contributed by Utkarsh Trivedi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.