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k-th missing element in sorted array
• Difficulty Level : Medium
• Last Updated : 04 Jun, 2021

Given an increasing sequence a[], we need to find the K-th missing contiguous element in the increasing sequence which is not present in the sequence. If no k-th missing element is there output -1.

Examples :

```Input : a[] = {2, 3, 5, 9, 10};
k = 1;
Output : 4
Explanation: Missing Element in the increasing
sequence are {4, 6, 7, 8}. So k-th missing element
is 4

Input : a[] = {2, 3, 5, 9, 10, 11, 12};
k = 4;
Output : 8
Explanation: missing element in the increasing
sequence are {4, 6, 7, 8}  so k-th missing
element is 8```

Approach 1: Start iterating over the array elements, and for every element check if next element is consecutive or not, if not, then take difference between these two, and check if difference is greater than or equal to given k, then calculate ans = a[i] + count, else iterate for next element.

## C++

 `#include ``using` `namespace` `std;` `// Function to find k-th``// missing element``int` `missingK(``int` `a[], ``int` `k,``             ``int` `n)``{``    ``int` `difference = 0,``        ``ans = 0, count = k;``    ``bool` `flag = 0;``    ` `    ``// interating over the array``    ``for``(``int` `i = 0 ; i < n - 1; i++)``    ``{  ``        ``difference = 0;``        ` `        ``// check if i-th and``        ``// (i + 1)-th element``        ``// are not consecutive``        ``if` `((a[i] + 1) != a[i + 1])``        ``{``            ` `            ``// save their difference``            ``difference +=``                ``(a[i + 1] - a[i]) - 1;``            ` `            ``// check for difference``            ``// and given k``            ``if` `(difference >= count)``                ``{``                    ``ans = a[i] + count;``                    ``flag = 1;``                    ``break``;``                ``}``            ``else``                ``count -= difference;``        ``}``    ``}``    ` `    ``// if found``    ``if``(flag)``        ``return` `ans;``    ``else``        ``return`  `-1;``}` `// Driver code``int` `main()``{``    ``// Input array``    ``int` `a[] = {1, 5, 11, 19};``    ` `    ``// k-th missing element``    ``// to be found in the array``    ``int` `k = 11;``    ``int` `n = ``sizeof``(a) / ``sizeof``(a);``    ` `    ``// calling function to``    ``// find missing element``    ``int` `missing = missingK(a, k, n);``    ` `    ``cout << missing << endl;``    ` `    ``return` `0;``}`

## Java

 `// Java program to check for``// even or odd``import` `java.io.*;``import` `java.util.*;`` ` `public` `class` `GFG {``     ` `    ``// Function to find k-th``    ``// missing element``    ``static` `int` `missingK(``int` `[]a, ``int` `k,``                                 ``int` `n)``    ``{``        ``int` `difference = ``0``,``            ``ans = ``0``, count = k;``        ``boolean` `flag = ``false``;``         ` `        ``// interating over the array``        ``for``(``int` `i = ``0` `; i < n - ``1``; i++)``        ``{``            ``difference = ``0``;``             ` `            ``// check if i-th and``            ``// (i + 1)-th element``            ``// are not consecutive``            ``if` `((a[i] + ``1``) != a[i + ``1``])``            ``{``                 ` `                ``// save their difference``                ``difference +=``                    ``(a[i + ``1``] - a[i]) - ``1``;``                 ` `                ``// check for difference``                ``// and given k``                ``if` `(difference >= count)``                    ``{``                        ``ans = a[i] + count;``                        ``flag = ``true``;``                        ``break``;``                    ``}``                ``else``                    ``count -= difference;``            ``}``        ``}``         ` `        ``// if found``        ``if``(flag)``            ``return` `ans;``        ``else``            ``return` `-``1``;``    ``}``     ` `    ``// Driver code``    ``public` `static` `void` `main(String args[])``    ``{``         ` `        ``// Input array``        ``int` `[]a = {``1``, ``5``, ``11``, ``19``};``         ` `        ``// k-th missing element``        ``// to be found in the array``        ``int` `k = ``11``;``        ``int` `n = a.length;``         ` `        ``// calling function to``        ``// find missing element``        ``int` `missing = missingK(a, k, n);``         ` `        ``System.out.print(missing);``    ``}`` ` `}`` ` `// This code is contributed by``// Manish Shaw (manishshaw1)`

## Python3

 `# Function to find k-th``# missing element``def` `missingK(a, k, n) :` `    ``difference ``=` `0``    ``ans ``=` `0``    ``count ``=` `k``    ``flag ``=` `0``    ` `    ``# interating over the array``    ``for` `i ``in` `range` `(``0``, n``-``1``) :``        ``difference ``=` `0``        ` `        ``# check if i-th and``        ``# (i + 1)-th element``        ``# are not consecutive``        ``if` `((a[i] ``+` `1``) !``=` `a[i ``+` `1``]) :``        ` `            ` `            ``# save their difference``            ``difference ``+``=` `(a[i ``+` `1``] ``-` `a[i]) ``-` `1``            ` `            ``# check for difference``            ``# and given k``            ``if` `(difference >``=` `count) :``                    ``ans ``=` `a[i] ``+` `count``                    ``flag ``=` `1``                    ``break``            ``else` `:``                ``count ``-``=` `difference    ``    ` `    ``# if found``    ``if``(flag) :``        ``return` `ans``    ``else` `:``        ``return` `-``1` `# Driver code``# Input array``a ``=` `[``1``, ``5``, ``11``, ``19``]` `# k-th missing element``# to be found in the array``k ``=` `11``n ``=` `len``(a)` `# calling function to``# find missing element``missing ``=` `missingK(a, k, n)` `print``(missing)` `# This code is contributed by``# Manish Shaw (manishshaw1)`

## C#

 `// C# program to check for``// even or odd``using` `System;``using` `System.Collections.Generic;` `class` `GFG {``    ` `    ``// Function to find k-th``    ``// missing element``    ``static` `int` `missingK(``int` `[]a, ``int` `k,``                                 ``int` `n)``    ``{``        ``int` `difference = 0,``            ``ans = 0, count = k;``        ``bool` `flag = ``false``;``        ` `        ``// interating over the array``        ``for``(``int` `i = 0 ; i < n - 1; i++)``        ``{``            ``difference = 0;``            ` `            ``// check if i-th and``            ``// (i + 1)-th element``            ``// are not consecutive``            ``if` `((a[i] + 1) != a[i + 1])``            ``{``                ` `                ``// save their difference``                ``difference +=``                    ``(a[i + 1] - a[i]) - 1;``                ` `                ``// check for difference``                ``// and given k``                ``if` `(difference >= count)``                    ``{``                        ``ans = a[i] + count;``                        ``flag = ``true``;``                        ``break``;``                    ``}``                ``else``                    ``count -= difference;``            ``}``        ``}``        ` `        ``// if found``        ``if``(flag)``            ``return` `ans;``        ``else``            ``return` `-1;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ` `        ``// Input array``        ``int` `[]a = {1, 5, 11, 19};``        ` `        ``// k-th missing element``        ``// to be found in the array``        ``int` `k = 11;``        ``int` `n = a.Length;``        ` `        ``// calling function to``        ``// find missing element``        ``int` `missing = missingK(a, k, n);``        ` `        ``Console.Write(missing);``    ``}` `}` `// This code is contributed by``// Manish Shaw (manishshaw1)`

## PHP

 `= ``\$count``)``                ``{``                    ``\$ans` `= ``\$a``[``\$i``] + ``\$count``;``                    ``\$flag` `= 1;``                    ``break``;``                ``}``            ``else``                ``\$count` `-= ``\$difference``;``        ``}``    ``}``    ` `    ``// if found``    ``if``(``\$flag``)``        ``return` `\$ans``;``    ``else``        ``return` `-1;``}` `// Driver Code` `// Input array``\$a` `= ``array``(1, 5, 11, 19);` `// k-th missing element``// to be found in the array``\$k` `= 11;``\$n` `= ``count``(``\$a``);` `// calling function to``// find missing element``\$missing` `= missingK(``\$a``, ``\$k``, ``\$n``);` `echo` `\$missing``;` `// This code is contributed by Manish Shaw``// (manishshaw1)``?>`

## Javascript

 ``
Output
```14
```

Time Complexity :O(n), where n is the number of elements in the array.

Approach 2:

Apply a binary search. Since the array is sorted we can find at any given index how many numbers are missing as arr[index] – (index+1). We would leverage this knowledge and apply binary search to narrow down our hunt to find that index from which getting the missing number is easier.

Below is the implementation of the above approach:

## C++

 `// CPP program for above approach``#include ``#include ``using` `namespace` `std;` `// Function to find``// kth missing number``int` `missingK(vector<``int``>& arr, ``int` `k)``{``  ``int` `n = arr.size();``  ``int` `l = 0, u = n - 1, mid;``  ` `  ``while``(l <= u)``  ``{``    ``mid = (l + u)/2;``    ` `    ``int` `numbers_less_than_mid = arr[mid] -``                                    ``(mid + 1);``    ` `    ``// If the total missing number``    ``// count is equal to k we can iterate``    ``// backwards for the first missing number``    ``// and that will be the answer.``    ``if``(numbers_less_than_mid == k)``    ``{``      ` `      ``// To further optimize we check``      ``// if the previous element's``      ``// missing number count is equal``      ``// to k. Eg: arr = [4,5,6,7,8]``      ``// If you observe in the example array,``      ``// the total count of missing numbers for all``      ``// the indices are same, and we are``      ``// aiming to narrow down the``      ``// search window and achieve O(logn)``      ``// time complexity which``      ``// otherwise would've been O(n).``      ``if``(mid > 0 && (arr[mid - 1] - (mid)) == k)``      ``{``        ``u = mid - 1;``        ``continue``;``      ``}``      ``// Else we return arr[mid] - 1.``      ``return` `arr[mid]-1;``    ``}``    ` `    ``// Here we appropriately``    ``// narrow down the search window.``    ``if``(numbers_less_than_mid < k)``    ``{``      ``l = mid + 1;``    ``}``    ``else` `if``(k < numbers_less_than_mid)``    ``{``      ``u = mid - 1;``    ``}``  ``}``  ` `  ``// In case the upper limit is -ve``  ``// it means the missing number set``  ``// is 1,2,..,k and hence we directly return k.``  ``if``(u < 0)``    ``return` `k;``  ` `  ``// Else we find the residual count``  ``// of numbers which we'd then add to``  ``// arr[u] and get the missing kth number.``  ``int` `less = arr[u] - (u + 1);``  ``k -= less;``  ` `  ``// Return arr[u] + k``  ``return` `arr[u] + k;``}` `// Driver Code``int` `main()``{``    ``vector<``int``> arr = {2,3,4,7,11};``    ``int` `k = 5;``  ` `    ``// Function Call``    ``cout <<``"Missing kth number = "``<<``                        ``missingK(arr, k)<

## Java

 `// Java program for above approach``public` `class` `GFG``{` `  ``// Function to find``  ``// kth missing number``  ``static` `int` `missingK(``int``[] arr, ``int` `k)``  ``{``    ``int` `n = arr.length;``    ``int` `l = ``0``, u = n - ``1``, mid;   ``    ``while``(l <= u)``    ``{``      ``mid = (l + u)/``2``;       ``      ``int` `numbers_less_than_mid = arr[mid] -``        ``(mid + ``1``);` `      ``// If the total missing number``      ``// count is equal to k we can iterate``      ``// backwards for the first missing number``      ``// and that will be the answer.``      ``if``(numbers_less_than_mid == k)``      ``{` `        ``// To further optimize we check``        ``// if the previous element's``        ``// missing number count is equal``        ``// to k. Eg: arr = [4,5,6,7,8]``        ``// If you observe in the example array,``        ``// the total count of missing numbers for all``        ``// the indices are same, and we are``        ``// aiming to narrow down the``        ``// search window and achieve O(logn)``        ``// time complexity which``        ``// otherwise would've been O(n).``        ``if``(mid > ``0` `&& (arr[mid - ``1``] - (mid)) == k)``        ``{``          ``u = mid - ``1``;``          ``continue``;``        ``}` `        ``// Else we return arr[mid] - 1.``        ``return` `arr[mid] - ``1``;``      ``}` `      ``// Here we appropriately``      ``// narrow down the search window.``      ``if``(numbers_less_than_mid < k)``      ``{``        ``l = mid + ``1``;``      ``}``      ``else` `if``(k < numbers_less_than_mid)``      ``{``        ``u = mid - ``1``;``      ``}``    ``}` `    ``// In case the upper limit is -ve``    ``// it means the missing number set``    ``// is 1,2,..,k and hence we directly return k.``    ``if``(u < ``0``)``      ``return` `k;` `    ``// Else we find the residual count``    ``// of numbers which we'd then add to``    ``// arr[u] and get the missing kth number.``    ``int` `less = arr[u] - (u + ``1``);``    ``k -= less;` `    ``// Return arr[u] + k``    ``return` `arr[u] + k;``  ``}` `  ``// Driver code``  ``public` `static` `void` `main(String[] args)``  ``{``    ``int``[] arr = {``2``,``3``,``4``,``7``,``11``};``    ``int` `k = ``5``;` `    ``// Function Call``    ``System.out.println(``"Missing kth number = "``+ missingK(arr, k));``  ``}``}` `// This code is contributed by divyesh072019.`

## Python3

 `# Python3 program for above approach` `# Function to find``# kth missing number``def` `missingK(arr, k):``  ``n ``=` `len``(arr)``  ``l ``=` `0``  ``u ``=` `n ``-` `1``  ``mid ``=` `0``  ``while``(l <``=` `u):``    ``mid ``=` `(l ``+` `u)``/``/``2``;``    ``numbers_less_than_mid ``=` `arr[mid] ``-` `(mid ``+` `1``);``    ` `    ``# If the total missing number``    ``# count is equal to k we can iterate``    ``# backwards for the first missing number``    ``# and that will be the answer.``    ``if``(numbers_less_than_mid ``=``=` `k):``      ` `      ``# To further optimize we check``      ``# if the previous element's``      ``# missing number count is equal``      ``# to k. Eg: arr = [4,5,6,7,8]``      ``# If you observe in the example array,``      ``# the total count of missing numbers for all``      ``# the indices are same, and we are``      ``# aiming to narrow down the``      ``# search window and achieve O(logn)``      ``# time complexity which``      ``# otherwise would've been O(n).``      ``if``(mid > ``0` `and` `(arr[mid ``-` `1``] ``-` `(mid)) ``=``=` `k):   ``        ``u ``=` `mid ``-` `1``;``        ``continue``;``      ` `      ``# Else we return arr[mid] - 1.``      ``return` `arr[mid]``-``1``;``      ` `    ``# Here we appropriately``    ``# narrow down the search window.``    ``if``(numbers_less_than_mid < k):   ``      ``l ``=` `mid ``+` `1``;``    ``elif``(k < numbers_less_than_mid):``      ``u ``=` `mid ``-` `1``;` `  ``# In case the upper limit is -ve``  ``# it means the missing number set``  ``# is 1,2,..,k and hence we directly return k.``  ``if``(u < ``0``):``    ``return` `k;``  ` `  ``# Else we find the residual count``  ``# of numbers which we'd then add to``  ``# arr[u] and get the missing kth number.``  ``less ``=` `arr[u] ``-` `(u ``+` `1``);``  ``k ``-``=` `less;``  ` `  ``# Return arr[u] + k``  ``return` `arr[u] ``+` `k;` `# Driver Code``if` `__name__``=``=``'__main__'``:` `    ``arr ``=` `[``2``,``3``,``4``,``7``,``11``];``    ``k ``=` `5``;``  ` `    ``# Function Call``    ``print``(``"Missing kth number = "``+` `str``(missingK(arr, k)))``    ` `# This code is contributed by rutvik_56.`

## C#

 `// C# program for above approach``using` `System;``class` `GFG {``    ` `    ``// Function to find``    ``// kth missing number``    ``static` `int` `missingK(``int``[] arr, ``int` `k)``    ``{``      ``int` `n = arr.Length;``      ``int` `l = 0, u = n - 1, mid;``       ` `      ``while``(l <= u)``      ``{``        ``mid = (l + u)/2;``         ` `        ``int` `numbers_less_than_mid = arr[mid] -``                                        ``(mid + 1);``         ` `        ``// If the total missing number``        ``// count is equal to k we can iterate``        ``// backwards for the first missing number``        ``// and that will be the answer.``        ``if``(numbers_less_than_mid == k)``        ``{``           ` `          ``// To further optimize we check``          ``// if the previous element's``          ``// missing number count is equal``          ``// to k. Eg: arr = [4,5,6,7,8]``          ``// If you observe in the example array,``          ``// the total count of missing numbers for all``          ``// the indices are same, and we are``          ``// aiming to narrow down the``          ``// search window and achieve O(logn)``          ``// time complexity which``          ``// otherwise would've been O(n).``          ``if``(mid > 0 && (arr[mid - 1] - (mid)) == k)``          ``{``            ``u = mid - 1;``            ``continue``;``          ``}``          ` `          ``// Else we return arr[mid] - 1.``          ``return` `arr[mid] - 1;``        ``}``         ` `        ``// Here we appropriately``        ``// narrow down the search window.``        ``if``(numbers_less_than_mid < k)``        ``{``          ``l = mid + 1;``        ``}``        ``else` `if``(k < numbers_less_than_mid)``        ``{``          ``u = mid - 1;``        ``}``      ``}``       ` `      ``// In case the upper limit is -ve``      ``// it means the missing number set``      ``// is 1,2,..,k and hence we directly return k.``      ``if``(u < 0)``        ``return` `k;``       ` `      ``// Else we find the residual count``      ``// of numbers which we'd then add to``      ``// arr[u] and get the missing kth number.``      ``int` `less = arr[u] - (u + 1);``      ``k -= less;``       ` `      ``// Return arr[u] + k``      ``return` `arr[u] + k;``    ``}` `  ``// Driver code``  ``static` `void` `Main()``  ``{``    ``int``[] arr = {2,3,4,7,11};``    ``int` `k = 5;``   ` `    ``// Function Call``    ``Console.WriteLine(``"Missing kth number = "``+ missingK(arr, k));``  ``}``}` `// This code is contributed by divyeshrabadiya07.`
Output
```Missing kth number = 9
```

Time Complexity: O(logn), where n is the number of elements in the array.

Approach 3 ( Using Map) : We will traverse the array and mark each of the element as visited in mapand we will also keep track of the min and max element present so that we know the lower and upper bound for  the given particular input. Then we start a loop from lower to upper bound and maintain a count variable . As soon we found a element which is not present in map we increment the count and until count becomes equal to k.

## C++14

 `#include ``#include ``using` `namespace` `std;` `int` `solve(``int` `arr[] , ``int` `k , ``int` `n)``{``      ``unordered_map<``int`  `,``int``> umap;``      ``int` `mins = 99999;``      ``int` `maxs = -99999;``      ``for``(``int` `i=0 ; i arr[i])``          ``mins = arr[i];  ``//keeping track of minimum element``        ``if``(maxs < arr[i])``          ``maxs = arr[i]; ``//keeping track of maximum element i.e. upper bound``    ``}``      ``int` `counts = 0;``      ``//iterate from lower to upper bound``      ``for``(``int` `i=mins ; i<=maxs ; i++)``    ``{``          ``if``(umap[i] == 0)``          ``counts++;``          ``if``(counts == k)``          ``return` `i;``    ``}``      ``return` `-1;``}``int` `main() {` `    ``int` `arr[] = {2, 3, 5, 9, 10, 11, 12} ;``      ``int` `k = 4;``      ``cout << solve(arr , k , 7) ; ``//(array , k , size of array)``    ``return` `0;``}`
Output
`8`

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