# Find the missing and repeating number

Given an unsorted array of size n. Array elements are in the range of 1 to n. One number from set {1, 2, …n} is missing and one number occurs twice in the array. Find these two numbers.

Examples:

Input: arr[] = {3, 1, 3}
Output: Missing = 2, Repeating = 3
Explanation: In the array, 2 is missing and 3 occurs twice

Input: arr[] = {4, 3, 6, 2, 1, 1}
Output: Missing = 5, Repeating = 1

Below are various methods to solve the problems:

Method 1 (Use count array)
Approach:

• Create a temp array temp[] of size n with all initial values as 0.
• Traverse the input array arr[], and do the following for each arr[i]
• if(temp[arr[i]-1] == 0), set temp[arr[i]-1] = 1;
• if(temp[arr[i]-1] == 1) output “arr[i]” //repeating number
• Traverse temp[] and output ‘i+1’ corresponding to the element of array temp[] having value as 0. (This is the missing number)

Note that, we use ‘arr[i]-1’ as the corresponding element to the ‘arr[i]’ in temp[] array, as indexing in an array starts from 0 to n-1 and the input array arr[] has numbers from 1 to n.

## C++

 `#include ``using` `namespace` `std;` `void` `printTwoElements(``int` `arr[], ``int` `n)``{``    ``int` `temp[n] = {}; ``// Creating temp array of size n with``                      ``// initial values as 0.``    ``int` `repeatingNumber=-1;``    ``int` `missingNumber=-1;``  ` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``temp[arr[i]-1]++;``        ``if` `(temp[arr[i] - 1] > 1) {``            ``repeatingNumber = arr[i];``        ``}``    ``}``    ``for` `(``int` `i = 0; i < n; i++) {``        ``if` `(temp[i] == 0) {``            ``missingNumber = i + 1;``            ``break``;``        ``}``    ``}``  ` `    ``cout << ``"The repeating number is "` `<< repeatingNumber<<``"."``         ``<< endl;``    ``cout << ``"The missing number is "` `<< missingNumber<<``"."``         ``<< endl;``  ` `}` `int` `main()``{` `    ``int` `arr[] = { 7, 3, 4, 5, 5, 6, 2 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``printTwoElements(arr, n);``    ``return` `0;``}``//  This code is contributed by vivek1208`

## Java

 `import` `java.io.*;` `class` `Main {` `    ``static` `void` `printTwoElements(``int``[] arr, ``int` `n)``    ``{``        ``int``[] temp``            ``= ``new` `int``[n]; ``// Creating temp array of size n``                          ``// with initial values as 0.``        ``int` `repeatingNumber = -``1``;``        ``int` `missingNumber = -``1``;` `        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``temp[arr[i] - ``1``]++;``            ``if` `(temp[arr[i] - ``1``] > ``1``) {``                ``repeatingNumber = arr[i];``            ``}``        ``}``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``if` `(temp[i] == ``0``) {``                ``missingNumber = i + ``1``;``                ``break``;``            ``}``        ``}` `        ``System.out.println(``"The repeating number is "``                           ``+ repeatingNumber + ``"."``);``        ``System.out.println(``"The missing number is "``                           ``+ missingNumber + ``"."``);``    ``}` `    ``public` `static` `void` `main(String[] args)``    ``{``        ``int``[] arr = { ``7``, ``3``, ``4``, ``5``, ``5``, ``6``, ``2` `};``        ``int` `n = arr.length;``        ``printTwoElements(arr, n);``    ``}``}` `// This code is contributed by vivek1208`

## Python3

 `def` `printTwoElements(arr):``    ``n ``=` `len``(arr)``    ``temp ``=` `[``0``] ``*` `n  ``# Creating temp array of size n with initial values as 0.``    ``repeatingNumber ``=` `-``1``    ``missingNumber ``=` `-``1` `    ``for` `i ``in` `range``(n):``        ``temp[arr[i] ``-` `1``] ``+``=` `1``        ``if` `temp[arr[i] ``-` `1``] > ``1``:``            ``repeatingNumber ``=` `arr[i]``    ``for` `i ``in` `range``(n):``        ``if` `temp[i] ``=``=` `0``:``            ``missingNumber ``=` `i ``+` `1``            ``break` `    ``print``(``"The repeating number is"``, repeatingNumber, ``"."``)``    ``print``(``"The missing number is"``, missingNumber, ``"."``)`  `arr ``=` `[``7``, ``3``, ``4``, ``5``, ``5``, ``6``, ``2``]``printTwoElements(arr)` `# This code is contributed by vivek1208`

## C#

 `using` `System;` `public` `class` `Program``{``    ``public` `static` `void` `printTwoElements(``int``[] arr, ``int` `n)``    ``{``        ``int``[] temp = ``new` `int``[n]; ``// Creating temp array of size n with initial values as 0.``        ``int` `repeatingNumber = -1;``        ``int` `missingNumber = -1;` `        ``for` `(``int` `i = 0; i < n; i++)``        ``{``            ``temp[arr[i] - 1]++;``            ``if` `(temp[arr[i] - 1] > 1)``            ``{``                ``repeatingNumber = arr[i];``            ``}``        ``}``        ``for` `(``int` `i = 0; i < n; i++)``        ``{``            ``if` `(temp[i] == 0)``            ``{``                ``missingNumber = i + 1;``                ``break``;``            ``}``        ``}` `        ``Console.WriteLine(``"The repeating number is "` `+ repeatingNumber + ``"."``);``        ``Console.WriteLine(``"The missing number is "` `+ missingNumber + ``"."``);``    ``}` `    ``public` `static` `void` `Main()``    ``{``        ``int``[] arr = { 7, 3, 4, 5, 5, 6, 2 };``        ``int` `n = arr.Length;``        ``printTwoElements(arr, n);``    ``}``}`

## Javascript

 `function` `printTwoElements(arr) {``    ``const n = arr.length;``    ``const temp = Array(n).fill(0); ``// Creating temp array of size n with initial values as 0.``    ``let repeatingNumber = -1;``    ``let missingNumber = -1;` `    ``for` `(let i = 0; i < n; i++) {``        ``temp[arr[i] - 1]++;``        ``if` `(temp[arr[i] - 1] > 1) {``            ``repeatingNumber = arr[i];``        ``}``    ``}``    ``for` `(let i = 0; i < n; i++) {``        ``if` `(temp[i] === 0) {``            ``missingNumber = i + 1;``            ``break``;``        ``}``    ``}` `    ``console.log(`The repeating number is \${repeatingNumber}.`);``    ``console.log(`The missing number is \${missingNumber}.`);``}` `const arr = [7, 3, 4, 5, 5, 6, 2];``printTwoElements(arr);` `// This code is contributed by vivek1208`

Output
```The repeating number is 5.
The missing number is 1.

```

Time Complexity: O(n)
Auxiliary Space: O(n)

Method 2 (Use elements as Index and mark the visited places)
Approach:
Traverse the array. While traversing, use the absolute value of every element as an index and make the value at this index negative to mark it visited. If something is already marked negative then this is the repeating element. To find the missing, traverse the array again and look for a positive value.

## C++

 `// C++ program to Find the repeating``// and missing elements` `#include ``using` `namespace` `std;` `void` `printTwoElements(``int` `arr[], ``int` `size)``{``    ``int` `i;``    ``cout << ``"The repeating element is "``;` `    ``for` `(i = 0; i < size; i++) {``        ``if` `(arr[``abs``(arr[i]) - 1] > 0)``            ``arr[``abs``(arr[i]) - 1] = -arr[``abs``(arr[i]) - 1];``        ``else``            ``cout << ``abs``(arr[i]) << ``"\n"``;``    ``}` `    ``cout << ``"and the missing element is "``;``    ``for` `(i = 0; i < size; i++) {``        ``if` `(arr[i] > 0)``            ``cout << (i + 1);``    ``}``}` `/* Driver code */``int` `main()``{``    ``int` `arr[] = { 7, 3, 4, 5, 5, 6, 2 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``printTwoElements(arr, n);``}` `// This code is contributed by Shivi_Aggarwal`

## C

 `// C program to Find the repeating``// and missing elements` `#include ``#include ` `void` `printTwoElements(``int` `arr[], ``int` `size)``{``    ``int` `i;``    ``printf``(``"\nThe repeating element is "``);` `    ``for` `(i = 0; i < size; i++) {``        ``if` `(arr[``abs``(arr[i]) - 1] > 0)``            ``arr[``abs``(arr[i]) - 1] = -arr[``abs``(arr[i]) - 1];``        ``else``            ``printf``(``" %d "``, ``abs``(arr[i]));``    ``}` `    ``printf``(``"\nand the missing element is "``);``    ``for` `(i = 0; i < size; i++) {``        ``if` `(arr[i] > 0)``            ``printf``(``"%d"``, i + 1);``    ``}``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 7, 3, 4, 5, 5, 6, 2 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``printTwoElements(arr, n);``    ``return` `0;``}`

## Java

 `// Java program to Find the repeating``// and missing elements` `import` `java.io.*;` `class` `GFG {` `    ``static` `void` `printTwoElements(``int` `arr[], ``int` `size)``    ``{``        ``int` `i;``        ``System.out.print(``"The repeating element is "``);` `        ``for` `(i = ``0``; i < size; i++) {``            ``int` `abs_val = Math.abs(arr[i]);``            ``if` `(arr[abs_val - ``1``] > ``0``)``                ``arr[abs_val - ``1``] = -arr[abs_val - ``1``];``            ``else``                ``System.out.println(abs_val);``        ``}` `        ``System.out.print(``"and the missing element is "``);``        ``for` `(i = ``0``; i < size; i++) {``            ``if` `(arr[i] > ``0``)``                ``System.out.println(i + ``1``);``        ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { ``7``, ``3``, ``4``, ``5``, ``5``, ``6``, ``2` `};``        ``int` `n = arr.length;``        ``printTwoElements(arr, n);``    ``}``}` `// This code is contributed by Gitanjali`

## Python3

 `# Python3 code to Find the repeating ``# and the missing elements` `def` `printTwoElements( arr, size):``    ``for` `i ``in` `range``(size):``        ``if` `arr[``abs``(arr[i])``-``1``] > ``0``:``            ``arr[``abs``(arr[i])``-``1``] ``=` `-``arr[``abs``(arr[i])``-``1``]``        ``else``:``            ``print``(``"The repeating element is "``, ``abs``(arr[i]))``            ` `    ``for` `i ``in` `range``(size):``        ``if` `arr[i]>``0``:``            ``print``(``"and the missing element is "``, i ``+` `1``)` `# Driver program to test above function */``arr ``=` `[``7``, ``3``, ``4``, ``5``, ``5``, ``6``, ``2``]``n ``=` `len``(arr)``printTwoElements(arr, n)` `# This code is contributed by "Abhishek Sharma 44"`

## C#

 `// C# program to Find the repeating``// and missing elements` `using` `System;` `class` `GFG {``    ``static` `void` `printTwoElements(``int``[] arr, ``int` `size)``    ``{``        ``int` `i;``        ``Console.Write(``"The repeating element is "``);` `        ``for` `(i = 0; i < size; i++) {``            ``int` `abs_val = Math.Abs(arr[i]);``            ``if` `(arr[abs_val - 1] > 0)``                ``arr[abs_val - 1] = -arr[abs_val - 1];``            ``else``                ``Console.WriteLine(abs_val);``        ``}` `        ``Console.Write(``"and the missing element is "``);``        ``for` `(i = 0; i < size; i++) {``            ``if` `(arr[i] > 0)``                ``Console.WriteLine(i + 1);``        ``}``    ``}` `    ``// Driver program``    ``public` `static` `void` `Main()``    ``{``        ``int``[] arr = { 7, 3, 4, 5, 5, 6, 2 };``        ``int` `n = arr.Length;``        ``printTwoElements(arr, n);``    ``}``}``// This code is contributed by Sam007`

## Javascript

 ``

## PHP

 ` 0)``            ``\$arr``[``abs``(``\$arr``[``\$i``]) - 1] = ``            ``- ``\$arr``[``abs``(``\$arr``[``\$i``]) - 1];``        ``else``            ``echo` `( ``abs``(``\$arr``[``\$i``]));``    ``}` `    ``echo` `"\nand the missing element is "``;``    ``for``(``\$i` `= 0; ``\$i` `< ``\$size``; ``\$i``++)``    ``{``        ``if``(``\$arr``[``\$i``] > 0)``            ``echo``(``\$i` `+ 1);``    ``}``}``    ` `    ``// Driver Code``    ``\$arr` `= ``array``(7, 3, 4, 5, 5, 6, 2);``    ``\$n` `= ``count``(``\$arr``);``    ``printTwoElements(``\$arr``, ``\$n``);` `// This code is contributed by anuj_67.``?>`

Output
```The repeating element is 5
and the missing element is 1

```

Time Complexity: O(n)
Auxiliary Space: O(1) as it is using constant variables
Thanks to Manish Mishra for suggesting this method.

Method 3 (Make two equations)
Approach:

• Let x be the missing and y be the repeating element.
• Get the sum of all numbers using formula S = n(n+1)/2 – x + y
• Get product of all numbers using formula P = 1*2*3*…*n * y / x
• The above two steps give us two equations, we can solve the equations and get the values of x and y.

Time Complexity: O(n)
Thanks to disappearedng for suggesting this solution.

Note: This method can cause arithmetic overflow as we calculate the product and sum of all array elements.

Method 4 (Use XOR)

Approach:

• Let x and y be the desired output elements.
• Calculate the XOR of all the array elements.

xor1 = arr[0]^arr[1]^arr[2]…..arr[n-1]

• XOR the result with all numbers from 1 to n

xor1 = xor1^1^2^…..^n

• In the result xor1, all elements would nullify each other except x and y. All the bits that are set in xor1 will be set in either x or y. So if we take any set bit (We have chosen the rightmost set bit in code) of xor1 and divide the elements of the array in two sets â€“ one set of elements with the same bit set and another set with the same bit not set. By doing so, we will get x in one set and y in another set. Now if we do XOR of all the elements in the first set, we will get x, and by doing the same in the other set we will get y.

Below is the implementation of the above approach:

## C++

 `#include ``#include ` `using` `namespace` `std;` `int` `x, y;` `// Function to find the repeating and missing elements in an``// array``void` `getTwoElements(vector<``int``>& arr, ``int` `n)``{``    ``int` `xor1 = 0; ``// Will hold xor of all elements and``                  ``// numbers from 1 to n``    ``int` `set_bit_no; ``// Will have only a single set bit of``                    ``// xor1``    ``x = 0;``    ``y = 0;` `    ``xor1 = arr[0];` `    ``// Get the xor of all array elements``    ``for` `(``int` `i = 1; i < n; i++)``        ``xor1 = xor1 ^ arr[i];` `    ``// XOR the previous result with numbers from 1 to n``    ``for` `(``int` `i = 1; i <= n; i++)``        ``xor1 = xor1 ^ i;` `    ``// Get the rightmost set bit in set_bit_no``    ``set_bit_no = xor1 & ~(xor1 - 1);` `    ``// Divide elements into two sets by comparing rightmost``    ``// set bit of xor1 with bit at the same position in each``    ``// element. Also, get XORs of two sets. The two XORs are``    ``// the output elements.``    ``for` `(``int` `i = 0; i < n; i++) {``        ``if` `((arr[i] & set_bit_no) != 0)``            ``x = x``                ``^ arr[i]; ``// arr[i] belongs to the first set``        ``else``            ``y = y ^ arr[i]; ``// arr[i] belongs to the second``                            ``// set``    ``}` `    ``for` `(``int` `i = 1; i <= n; i++) {``        ``if` `((i & set_bit_no) != 0)``            ``x = x ^ i; ``// i belongs to the first set``        ``else``            ``y = y ^ i; ``// i belongs to the second set``    ``}` `    ``// *x and *y hold the desired output elements``}` `int` `main()``{``    ``vector<``int``> arr = { 1, 3, 4, 5, 1, 6, 2 };``    ``int` `n = arr.size();``    ``getTwoElements(arr, n);``    ``cout << ``"The missing element is "` `<< x``         ``<< ``" and the repeating number is "` `<< y << endl;``    ``return` `0;``}`

## C

 `// C program to Find the repeating``// and missing elements` `#include ``#include ` `/* The output of this function is stored at``   ``*x and *y */``void` `getTwoElements(``int` `arr[], ``int` `n, ``int``* x, ``int``* y)``{``    ``/* Will hold xor of all elements and numbers ``       ``from 1 to n */``    ``int` `xor1;` `    ``/* Will have only single set bit of xor1 */``    ``int` `set_bit_no;` `    ``int` `i;``    ``*x = 0;``    ``*y = 0;` `    ``xor1 = arr[0];` `    ``/* Get the xor of all array elements */``    ``for` `(i = 1; i < n; i++)``        ``xor1 = xor1 ^ arr[i];` `    ``/* XOR the previous result with numbers ``       ``from 1 to n*/``    ``for` `(i = 1; i <= n; i++)``        ``xor1 = xor1 ^ i;` `    ``/* Get the rightmost set bit in set_bit_no */``    ``set_bit_no = xor1 & ~(xor1 - 1);` `    ``/* Now divide elements in two sets by comparing ``    ``rightmost set bit of xor1 with bit at same ``    ``position in each element. Also, get XORs of two ``    ``sets. The two XORs are the output elements. The``    ``following two for loops serve the purpose */``    ``for` `(i = 0; i < n; i++) {``        ``if` `(arr[i] & set_bit_no)``            ``/* arr[i] belongs to first set */``            ``*x = *x ^ arr[i];` `        ``else``            ``/* arr[i] belongs to second set*/``            ``*y = *y ^ arr[i];``    ``}``    ``for` `(i = 1; i <= n; i++) {``        ``if` `(i & set_bit_no)``            ``/* i belongs to first set */``            ``*x = *x ^ i;` `        ``else``            ``/* i belongs to second set*/``            ``*y = *y ^ i;``    ``}` `    ``/* *x and *y hold the desired output elements */``}` `/* Driver program to test above function */``int` `main()``{``    ``int` `arr[] = { 1, 3, 4, 5, 5, 6, 2 };``    ``int``* x = (``int``*)``malloc``(``sizeof``(``int``));``    ``int``* y = (``int``*)``malloc``(``sizeof``(``int``));``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``getTwoElements(arr, n, x, y);``    ``printf``(``" The missing element is %d"``           ``" and the repeating number"``           ``" is %d"``,``           ``*x, *y);``    ``getchar``();``}`

## Java

 `// Java program to Find the repeating``// and missing elements` `import` `java.io.*;` `class` `GFG {``    ``static` `int` `x, y;` `    ``static` `void` `getTwoElements(``int` `arr[], ``int` `n)``    ``{``        ``/* Will hold xor of all elements``       ``and numbers from 1 to n  */``        ``int` `xor1;` `        ``/* Will have only single set bit of xor1 */``        ``int` `set_bit_no;` `        ``int` `i;``        ``x = ``0``;``        ``y = ``0``;` `        ``xor1 = arr[``0``];` `        ``/* Get the xor of all array elements  */``        ``for` `(i = ``1``; i < n; i++)``            ``xor1 = xor1 ^ arr[i];` `        ``/* XOR the previous result with numbers from ``       ``1 to n*/``        ``for` `(i = ``1``; i <= n; i++)``            ``xor1 = xor1 ^ i;` `        ``/* Get the rightmost set bit in set_bit_no */``        ``set_bit_no = xor1 & ~(xor1 - ``1``);` `        ``/* Now divide elements into two sets by comparing``    ``rightmost set bit of xor1 with the bit at the same ``    ``position in each element. Also, get XORs of two``    ``sets. The two XORs are the output elements. The ``    ``following two for loops serve the purpose */``        ``for` `(i = ``0``; i < n; i++) {``            ``if` `((arr[i] & set_bit_no) != ``0``)``                ``/* arr[i] belongs to first set */``                ``x = x ^ arr[i];` `            ``else``                ``/* arr[i] belongs to second set*/``                ``y = y ^ arr[i];``        ``}``        ``for` `(i = ``1``; i <= n; i++) {``            ``if` `((i & set_bit_no) != ``0``)``                ``/* i belongs to first set */``                ``x = x ^ i;` `            ``else``                ``/* i belongs to second set*/``                ``y = y ^ i;``        ``}` `        ``/* *x and *y hold the desired output elements */``    ``}``    ``/* Driver program to test above function */``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { ``1``, ``3``, ``4``, ``5``, ``1``, ``6``, ``2` `};` `        ``int` `n = arr.length;``        ``getTwoElements(arr, n);``        ``System.out.println(``" The missing element is  "``                           ``+ x + ``"and the "``                           ``+ ``"repeating number is "``                           ``+ y);``    ``}``}` `// This code is contributed by Gitanjali.`

## Python3

 `# Python3 program to find the repeating ``# and missing elements ` `# The output of this function is stored ``# at x and y ``def` `getTwoElements(arr, n):``    ` `    ``global` `x, y``    ``x ``=` `0``    ``y ``=` `0``    ` `    ``# Will hold xor of all elements ``    ``# and numbers from 1 to n ``    ``xor1 ``=` `arr[``0``]``    ` `    ``# Get the xor of all array elements``    ``for` `i ``in` `range``(``1``, n):``        ``xor1 ``=` `xor1 ^ arr[i]``        ` `    ``# XOR the previous result with numbers ``    ``# from 1 to n``    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ``xor1 ``=` `xor1 ^ i``    ` `    ``# Will have only single set bit of xor1``    ``set_bit_no ``=` `xor1 & ~(xor1 ``-` `1``)``    ` `    ``# Now divide elements into two ``    ``# sets by comparing a rightmost set ``    ``# bit of xor1 with the bit at the same ``    ``# position in each element. Also, ``    ``# get XORs of two sets. The two ``    ``# XORs are the output elements. ``    ``# The following two for loops ``    ``# serve the purpose``    ``for` `i ``in` `range``(n):``        ``if` `(arr[i] & set_bit_no) !``=` `0``:``            ` `            ``# arr[i] belongs to first set``            ``x ``=` `x ^ arr[i]``        ``else``:``            ` `            ``# arr[i] belongs to second set``            ``y ``=` `y ^ arr[i]``            ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ``if` `(i & set_bit_no) !``=` `0``:``            ` `            ``# i belongs to first set``            ``x ``=` `x ^ i``        ``else``:``            ` `            ``# i belongs to second set``            ``y ``=` `y ^ i ``        ` `    ``# x and y hold the desired ``    ``# output elements ``    ` `# Driver code``arr ``=` `[ ``1``, ``3``, ``4``, ``5``, ``5``, ``6``, ``2` `]``n ``=` `len``(arr)``    ` `getTwoElements(arr, n)` `print``(``"The missing element is"``, x,``      ``"and the repeating number is"``, y)``    ` `# This code is contributed by stutipathak31jan`

## C#

 `// C# program to Find the repeating``// and missing elements` `using` `System;` `class` `GFG {``    ``static` `int` `x, y;` `    ``static` `void` `getTwoElements(``int``[] arr, ``int` `n)``    ``{``        ``/* Will hold xor of all elements``        ``and numbers from 1 to n */``        ``int` `xor1;` `        ``/* Will have only single set bit of xor1 */``        ``int` `set_bit_no;` `        ``int` `i;``        ``x = 0;``        ``y = 0;` `        ``xor1 = arr[0];` `        ``/* Get the xor of all array elements */``        ``for` `(i = 1; i < n; i++)``            ``xor1 = xor1 ^ arr[i];` `        ``/* XOR the previous result with numbers from ``        ``1 to n*/``        ``for` `(i = 1; i <= n; i++)``            ``xor1 = xor1 ^ i;` `        ``/* Get the rightmost set bit in set_bit_no */``        ``set_bit_no = xor1 & ~(xor1 - 1);` `        ``/* Now divide elements in two sets by comparing``        ``rightmost set bit of xor1 with bit at same ``        ``position in each element. Also, get XORs of two``        ``sets. The two XORs are the output elements.The ``        ``following two for loops serve the purpose */``        ``for` `(i = 0; i < n; i++) {``            ``if` `((arr[i] & set_bit_no) != 0)` `                ``/* arr[i] belongs to first set */``                ``x = x ^ arr[i];` `            ``else` `                ``/* arr[i] belongs to second set*/``                ``y = y ^ arr[i];``        ``}``        ``for` `(i = 1; i <= n; i++) {``            ``if` `((i & set_bit_no) != 0)` `                ``/* i belongs to first set */``                ``x = x ^ i;` `            ``else` `                ``/* i belongs to second set*/``                ``y = y ^ i;``        ``}` `        ``/* *x and *y hold the desired output elements */``    ``}` `    ``// Driver program``    ``public` `static` `void` `Main()``    ``{``        ``int``[] arr = { 1, 3, 4, 5, 1, 6, 2 };` `        ``int` `n = arr.Length;``        ``getTwoElements(arr, n);``        ``Console.Write(``" The missing element is "``                      ``+ x + ``"and the "``                      ``+ ``"repeating number is "``                      ``+ y);``    ``}``}` `// This code is contributed by Sam007`

## Javascript

 `// Javascript program to Find the repeating``// and missing elements``let x, y;` `    ``function` `getTwoElements(arr, n)``    ``{``        ``/* Will hold xor of all elements``       ``and numbers from 1 to n  */``        ``let xor1;` `        ``/* Will have only single set bit of xor1 */``        ``let set_bit_no;` `        ``let i;``        ``x = 0;``        ``y = 0;` `        ``xor1 = arr[0];` `        ``/* Get the xor of all array elements  */``        ``for` `(i = 1; i < n; i++)``            ``xor1 = xor1 ^ arr[i];` `        ``/* XOR the previous result with numbers from ``       ``1 to n*/``        ``for` `(i = 1; i <= n; i++)``            ``xor1 = xor1 ^ i;` `        ``/* Get the rightmost set bit in set_bit_no */``        ``set_bit_no = xor1 & ~(xor1 - 1);` `        ``/* Now divide elements into two sets by comparing``    ``rightmost set bit of xor1 with the bit at the same ``    ``position in each element. Also, get XORs of two``    ``sets. The two XORs are the output elements. The ``    ``following two for loops serve the purpose */``        ``for` `(i = 0; i < n; i++) {``            ``if` `((arr[i] & set_bit_no) != 0)``                ``/* arr[i] belongs to first set */``                ``x = x ^ arr[i];` `            ``else``                ``/* arr[i] belongs to second set*/``                ``y = y ^ arr[i];``        ``}``        ``for` `(i = 1; i <= n; i++) {``            ``if` `((i & set_bit_no) != 0)``                ``/* i belongs to first set */``                ``x = x ^ i;` `            ``else``                ``/* i belongs to second set*/``                ``y = y ^ i;``        ``}` `        ``/* *x and *y hold the desired output elements */``    ``}``   ` `        ``let arr = [ 1, 3, 4, 5, 1, 6, 2 ];` `        ``let n = arr.length;``        ``getTwoElements(arr, n);``        ``console.log(``" The missing element is  "``                           ``+ x + ``" and the "``                           ``+ ``"repeating number is "``                           ``+ y);``    ` `    ``// This code is contributed by garg28harsh.`

## PHP

 `

Output
``` The missing element is 7 and the repeating number is 5

```

Time Complexity: O(n)
Auxiliary Space: O(1) as it is using constant space if the input array is excluded
This method doesn’t cause overflow, but it doesn’t tell which one occurs twice and which one is missing. We can add one more step that checks which one is missing and which one is repeating. This can be easily done in O(n) time.

Method 5 (Use a Map)
Approach:
This method involves creating a Hashtable with the help of Map. In this, the elements are mapped to their natural index. In this process, if an element is mapped twice, then it is the repeating element. And if an element’s mapping is not there, then it is the missing element.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the repeating``// and missing elements using Maps ``#include ``#include ``using` `namespace` `std;` `int` `main()``{``    ``int` `arr[] = { 4, 3, 6, 2, 1, 1 };``    ``int` `n = 6;``    ` `    ``unordered_map<``int``, ``bool``> numberMap;``    ` `    ``for``(``int` `i : arr) ``    ``{``        ``if` `(numberMap.find(i) == ``            ``numberMap.end())``        ``{``            ``numberMap[i] = ``true``;``        ``}``        ``else``        ``{``            ``cout << ``"Repeating = "` `<< i;``              ``break``;``        ``}``    ``}``    ``cout << endl;``    ` `    ``for``(``int` `i = 1; i <= n; i++)``    ``{``        ``if` `(numberMap.find(i) == ``            ``numberMap.end()) ``        ``{``            ``cout << ``"Missing = "` `<< i;``              ``break``;``        ``}``    ``}``    ``return` `0;``}` `// This code is contributed by RohitOberoi`

## Java

 `// Java program to find the``// repeating and missing elements``// using Maps` `import` `java.util.*;` `public` `class` `Test1 {` `    ``public` `static` `void` `main(String[] args)``    ``{` `        ``int``[] arr = { ``4``, ``3``, ``6``, ``2``, ``1``, ``1` `};` `        ``Map numberMap``            ``= ``new` `HashMap<>();` `        ``int` `max = arr.length;` `        ``for` `(Integer i : arr) {` `            ``if` `(numberMap.get(i) == ``null``) {``                ``numberMap.put(i, ``true``);``            ``}``            ``else` `{``                ``System.out.println(``"Repeating = "` `+ i);``            ``}``        ``}``        ``for` `(``int` `i = ``1``; i <= max; i++) {``            ``if` `(numberMap.get(i) == ``null``) {``                ``System.out.println(``"Missing = "` `+ i);``            ``}``        ``}``    ``}``}`

## Python3

 `# Python3 program to find the ``# repeating and missing elements ``# using Maps``def` `main():``    ` `    ``arr ``=` `[ ``4``, ``3``, ``6``, ``2``, ``1``, ``1` `]``    ` `    ``numberMap ``=` `{}``    ` `    ``max` `=` `len``(arr)``    ``for` `i ``in` `arr:``        ``if` `not` `i ``in` `numberMap:``            ``numberMap[i] ``=` `True``            ` `        ``else``:``            ``print``(``"Repeating ="``, i)``    ` `    ``for` `i ``in` `range``(``1``, ``max` `+` `1``):``        ``if` `not` `i ``in` `numberMap:``            ``print``(``"Missing ="``, i)``main()` `# This code is contributed by stutipathak31jan`

## C#

 `// C# program to find the``// repeating and missing elements``// using Maps``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int``[] arr = { 4, 3, 6, 2, 1, 1 };` `        ``Dictionary<``int``, Boolean> numberMap =``                   ``new` `Dictionary<``int``, Boolean>();` `        ``int` `max = arr.Length;` `        ``foreach` `(``int` `i ``in` `arr) ``        ``{``            ``if` `(!numberMap.ContainsKey(i)) ``            ``{``                ``numberMap.Add(i, ``true``);``            ``}``            ``else``            ``{``                ``Console.WriteLine(``"Repeating = "` `+ i);``            ``}``        ``}``        ``for` `(``int` `i = 1; i <= max; i++) ``        ``{``            ``if` `(!numberMap.ContainsKey(i)) ``            ``{``                ``Console.WriteLine(``"Missing = "` `+ i);``            ``}``        ``}``    ``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output
```Repeating = 1
Missing = 5

```

Time Complexity: O(N)
Auxiliary Space: O(N)

Method 6 (Make two equations using sum and sum of squares)
Approach:

• Let x be the missing and y be the repeating element.
• Let N is the size of the array.
• Get the sum of all numbers using the formula S = N(N+1)/2
• Get the sum of square of all numbers using formula Sum_Sq = N(N+1)(2N+1)/6
• Iterate through a loop from i=1….N
• S -= A[i]
• Sum_Sq -= (A[i]*A[i])
• It will give two equations
x-y = S – (1)
x^2 – y^2 = Sum_sq
x+ y = (Sum_sq/S) – (2)

## C++

 `#include ` `using` `namespace` `std;` `vector<``int``>repeatedNumber(``const` `vector<``int``> &A) {``    ``long` `long` `int` `len = A.size();``    ``long` `long` `int` `Sum_N = (len * (len+1) ) /2, Sum_NSq = (len * (len +1) *(2*len +1) )/6;``    ``long` `long` `int` `missingNumber=0, repeating=0;``    ` `    ``for``(``int` `i=0;i ans;``    ``ans.push_back(repeating);``    ``ans.push_back(missingNumber);``    ``return` `ans;``    ` `}`  `int` `main(``void``){``        ``std::vector<``int``> v = {4, 3, 6, 2, 1, 6,7};``    ``vector<``int``> res = repeatedNumber(v);``    ``for``(``int` `x: res){``        ``cout<< x<<``"  "``;``    ``}``    ``cout<

## Java

 `import` `java.util.*;``import` `java.math.BigInteger;``class` `GFG ``{``    ``static` `Vector repeatedNumber(``int``[] a) ``    ``{``       ` `        ``BigInteger n=BigInteger.valueOf(a.length);``  ` `        ``BigInteger s=BigInteger.valueOf(``0``);``        ``BigInteger ss=BigInteger.valueOf(``0``);` `        ``for``(``int` `x : a)``        ``{``            ``s=  s.add(BigInteger.valueOf(x));``            ``ss= ss.add(BigInteger.valueOf(x).multiply(BigInteger.valueOf(x))); ``        ``}` `        ``BigInteger as= n.multiply(n.add(BigInteger.valueOf(``1``))).divide(BigInteger.valueOf(``2``));``        ``BigInteger ass= as.multiply(BigInteger.valueOf(``2``).multiply(n).add(BigInteger.valueOf(``1``))).divide(BigInteger.valueOf(``3``));` `        ``BigInteger sub=as.subtract(s);``        ``BigInteger add=(ass.subtract(ss)).divide(sub);``        ``//(ass-ss)/sub;` `        ``int` `b = sub.add(add).divide(BigInteger.valueOf(``2``)).intValue();``        ``//(sub+add)/2;``        ``int` `A = BigInteger.valueOf(b).subtract(sub).intValue();``        ``Vector ans = ``new` `Vector<>();``        ``ans.add(A);``        ``ans.add(b);``        ``return` `ans;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args) ``    ``{``        ``int``[] v = { ``4``, ``3``, ``6``, ``2``, ``1``, ``6``, ``7` `};``        ``Vector res = repeatedNumber(v);``        ``for` `(``int` `x : res) ``        ``{``            ``System.out.print(x + ``" "``);``        ``}``    ``}``}` `// This code is contributed by Rajput-Ji`

## Python3

 `def` `repeatedNumber(A):``    ` `    ``length ``=` `len``(A)``    ``Sum_N ``=` `(length ``*` `(length ``+` `1``)) ``/``/` `2``    ``Sum_NSq ``=` `((length ``*` `(length ``+` `1``) ``*``                     ``(``2` `*` `length ``+` `1``)) ``/``/` `6``)``    ` `    ``missingNumber, repeating ``=` `0``, ``0``    ` `    ``for` `i ``in` `range``(``len``(A)):``        ``Sum_N ``-``=` `A[i]``        ``Sum_NSq ``-``=` `A[i] ``*` `A[i]``        ` `    ``missingNumber ``=` `(Sum_N ``+` `Sum_NSq ``/``/``                             ``Sum_N) ``/``/` `2``    ``repeating ``=` `missingNumber ``-` `Sum_N``    ` `    ``ans ``=` `[]``    ``ans.append(repeating)``    ``ans.append(missingNumber)``    ` `    ``return` `ans` `# Driver code``v ``=` `[ ``4``, ``3``, ``6``, ``2``, ``1``, ``6``, ``7` `]``res ``=` `repeatedNumber(v)` `for` `i ``in` `res:``    ``print``(i, end ``=` `" "``)` `# This code is contributed by stutipathak31jan `

## C#

 `using` `System;``using` `System.Collections.Generic;` `class` `GFG ``{``    ``static` `List<``int``> repeatedNumber(``int``[] A) ``    ``{``        ``int` `len = A.Length;``        ``int` `Sum_N = (len * (len + 1)) / 2;``        ``int` `Sum_NSq = (len * (len + 1) * ``                        ``(2 * len + 1)) / 6;``        ``int` `missingNumber = 0, repeating = 0;` `        ``for` `(``int` `i = 0; i < A.Length; i++) ``        ``{``            ``Sum_N -= A[i];``            ``Sum_NSq -= A[i] * A[i];``        ``}` `        ``missingNumber = (Sum_N + Sum_NSq / ``                                 ``Sum_N) / 2;``        ``repeating = missingNumber - Sum_N;``        ``List<``int``> ans = ``new` `List<``int``>();``        ``ans.Add(repeating);``        ``ans.Add(missingNumber);``        ``return` `ans;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main(String[] args) ``    ``{``        ``int``[] v = { 4, 3, 6, 2, 1, 6, 7 };``        ``List<``int``> res = repeatedNumber(v);``        ``foreach` `(``int` `x ``in` `res) ``        ``{``            ``Console.Write(x + ``" "``);``        ``}``    ``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output
```6  5

```

Time Complexity: O(n)
Auxiliary Space: O(1)

Previous
Next