# Search insert position of K in a sorted array

Given a sorted array arr[] consisting of N distinct integers and an integer K, the task is to find the index of K, if it’s present in the array arr[]. Otherwise, find the index where K must be inserted to keep the array sorted.

Examples:

Input: arr[] = {1, 3, 5, 6}, K = 5
Output: 2
Explanation: Since 5 is found at index 2 as arr = 5, the output is 2.

Input: arr[] = {1, 3, 5, 6}, K = 2
Output: 1
Explanation: Since 2 is not present in the array but can be inserted at index 1 to make the array sorted.

Naive Approach: Follow the steps below to solve the problem:

• Iterate over every element of the array arr[] and search for integer K.
• If any array element is found to be equal to K, then print index of K.
• Otherwise, if any array element is found to be greater than K, print that index as the insert position of K. If no element is found to be exceeding K, K must be inserted after the last array element.

Below is the implementation of above approach :

## C++

 `// C++ program for the above approach`   `#include ` `using` `namespace` `std;`   `// Function to find insert position of K` `int` `find_index(``int` `arr[], ``int` `n, ``int` `K)` `{` `    ``// Traverse the array` `    ``for` `(``int` `i = 0; i < n; i++)`   `        ``// If K is found` `        ``if` `(arr[i] == K)` `            ``return` `i;`   `        ``// If current array element` `        ``// exceeds K` `        ``else` `if` `(arr[i] > K)` `            ``return` `i;`   `    ``// If all elements are smaller` `    ``// than K` `    ``return` `n;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { 1, 3, 5, 6 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``int` `K = 2;` `    ``cout << find_index(arr, n, K) << endl;` `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `import` `java.io.*;`   `class` `GFG{`   `// Function to find insert position of K` `static` `int` `find_index(``int``[] arr, ``int` `n, ``int` `K)` `{` `    `  `    ``// Traverse the array` `    ``for``(``int` `i = ``0``; i < n; i++)` `    `  `        ``// If K is found` `        ``if` `(arr[i] == K)` `            ``return` `i;`   `        ``// If current array element` `        ``// exceeds K` `        ``else` `if` `(arr[i] > K)` `            ``return` `i;`   `    ``// If all elements are smaller` `    ``// than K` `    ``return` `n;` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int``[] arr = { ``1``, ``3``, ``5``, ``6` `};` `    ``int` `n = arr.length;` `    ``int` `K = ``2``;` `    `  `    ``System.out.println(find_index(arr, n, K));` `}` `}`   `// This code is contributed by akhilsaini`

## Python3

 `# Python program for the above approach`   `# Function to find insert position of K` `def` `find_index(arr, n, K):` `    `  `    ``# Traverse the array` `    ``for` `i ``in` `range``(n):` `        `  `        ``# If K is found` `        ``if` `arr[i] ``=``=` `K:` `            ``return` `i` `            `  `        ``# If arr[i] exceeds K` `        ``elif` `arr[i] > K:` `            ``return` `i` `            `  `    ``# If all array elements are smaller` `    ``return` `n`   `# Driver Code` `arr ``=` `[``1``, ``3``, ``5``, ``6``]` `n ``=` `len``(arr)` `K ``=` `2` `print``(find_index(arr, n, K))`

## C#

 `// C# program for the above approach` `using` `System;`   `class` `GFG{`   `// Function to find insert position of K` `static` `int` `find_index(``int``[] arr, ``int` `n, ``int` `K)` `{` `    `  `    ``// Traverse the array` `    ``for``(``int` `i = 0; i < n; i++)` `    `  `        ``// If K is found` `        ``if` `(arr[i] == K)` `            ``return` `i;`   `        ``// If current array element` `        ``// exceeds K` `        ``else` `if` `(arr[i] > K)` `            ``return` `i;`   `    ``// If all elements are smaller` `    ``// than K` `    ``return` `n;` `}`   `// Driver Code` `public` `static` `void` `Main()` `{` `    ``int``[] arr = { 1, 3, 5, 6 };` `    ``int` `n = arr.Length;` `    ``int` `K = 2;` `    `  `    ``Console.WriteLine(find_index(arr, n, K));` `}` `}`   `// This code is contributed by akhilsaini`

Output:

```1

```

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

Efficient Approach: To optimize the above approach, the idea is to use Binary Search. Follow the steps below to solve the problem:

• Set start and end as 0 and N – 1, where the start and end variables denote the lower and upper bound of the search space respectively.
• Calculate mid = (start + end) / 2.
• If arr[mid] is found to be equal to K, print mid as the required answer.
• If arr[mid] exceeds K, set low = mid + 1. Otherwise, set high = mid – 1.

Below is the implementation of above approach :

## C++

 `// C++ program for the above approach`   `#include ` `using` `namespace` `std;`   `// Function to find insert position of K` `int` `find_index(``int` `arr[], ``int` `n, ``int` `K)` `{` `    ``// Lower and upper bounds` `    ``int` `start = 0;` `    ``int` `end = n - 1;`   `    ``// Traverse the search space` `    ``while` `(start <= end) {` `        ``int` `mid = (start + end) / 2;`   `        ``// If K is found` `        ``if` `(arr[mid] == K)` `            ``return` `mid;`   `        ``else` `if` `(arr[mid] < K)` `            ``start = mid + 1;`   `        ``else` `            ``end = mid - 1;` `    ``}`   `    ``// Return insert position` `    ``return` `end + 1;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { 1, 3, 5, 6 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``int` `K = 2;` `    ``cout << find_index(arr, n, K) << endl;` `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `import` `java.io.*;`   `class` `GFG{`   `// Function to find insert position of K` `static` `int` `find_index(``int``[] arr, ``int` `n, ``int` `K)` `{` `    `  `    ``// Lower and upper bounds` `    ``int` `start = ``0``;` `    ``int` `end = n - ``1``;`   `    ``// Traverse the search space` `    ``while` `(start <= end) ` `    ``{` `        ``int` `mid = (start + end) / ``2``;`   `        ``// If K is found` `        ``if` `(arr[mid] == K)` `            ``return` `mid;`   `        ``else` `if` `(arr[mid] < K)` `            ``start = mid + ``1``;`   `        ``else` `            ``end = mid - ``1``;` `    ``}`   `    ``// Return insert position` `    ``return` `end + ``1``;` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int``[] arr = { ``1``, ``3``, ``5``, ``6` `};` `    ``int` `n = arr.length;` `    ``int` `K = ``2``;` `    `  `    ``System.out.println(find_index(arr, n, K));` `}` `}`   `// This code is contributed by akhilsaini`

## Python3

 `# Python program to implement` `# the above approach`   `# Function to find insert position of K` `def` `find_index(arr, n, B):`   `    ``# Lower and upper bounds` `    ``start ``=` `0` `    ``end ``=` `n ``-` `1`   `    ``# Traverse the search space` `    ``while` `start<``=` `end:`   `        ``mid ``=``(start ``+` `end)``/``/``2`   `        ``if` `arr[mid] ``=``=` `K:` `            ``return` `mid`   `        ``elif` `arr[mid] < K:` `            ``start ``=` `mid ``+` `1` `        ``else``:` `            ``end ``=` `mid``-``1`   `    ``# Return the insert position` `    ``return` `end ``+` `1`   `# Driver Code` `arr ``=` `[``1``, ``3``, ``5``, ``6``]` `n ``=` `len``(arr)` `K ``=` `2` `print``(find_index(arr, n, K))`

## C#

 `// C# program for the above approach` `using` `System;`   `class` `GFG{`   `// Function to find insert position of K` `static` `int` `find_index(``int``[] arr, ``int` `n, ``int` `K)` `{` `    `  `    ``// Lower and upper bounds` `    ``int` `start = 0;` `    ``int` `end = n - 1;`   `    ``// Traverse the search space` `    ``while` `(start <= end) ` `    ``{` `        ``int` `mid = (start + end) / 2;`   `        ``// If K is found` `        ``if` `(arr[mid] == K)` `            ``return` `mid;`   `        ``else` `if` `(arr[mid] < K)` `            ``start = mid + 1;`   `        ``else` `            ``end = mid - 1;` `    ``}`   `    ``// Return insert position` `    ``return` `end + 1;` `}`   `// Driver Code` `public` `static` `void` `Main()` `{` `    ``int``[] arr = { 1, 3, 5, 6 };` `    ``int` `n = arr.Length;` `    ``int` `K = 2;` `    `  `    ``Console.WriteLine(find_index(arr, n, K));` `}` `}`   `// This code is contributed by akhilsaini`

Output:

```1

```

Time Complexity: O(log N)
Auxiliary Space: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : akhilsaini

Article Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.