# Check whether an array can be made strictly increasing by removing at most one element

Given an array arr[] consisting of N integers, the task is to check whether it is possible to make the given array strictly increasing by removing at most one element. If it is possible to make the array strictly increasing, then print “Yes”. Otherwise, print “No”.

Examples:

Input: arr[] = {1, 1, 2}
Output: Yes
Explanation: Removing an occurrence of 1 modifies the array to {1, 2}, which is strictly increasing array.

Input: arr[] = {2, 2, 3, 4, 5, 5}
Output: No

Approach: The given problem can be solved by traversing the array arr[] and count the indices satisfying the condition arr[i-1] >= arr[i]. Follow the steps below to solve the problem:

• Initialize two variables, say count as 0 and index as -1, to store the count of elements needed to be removed and the index of the removed element respectively.
• Traverse the given array over the range [1, N – 1] and if the value of arr[i – 1] is at least arr[i] increment the value of count by 1 and update the value of the index as i.
• If the value of count is greater than 1, then print “No” and return.
• Otherwise, check for the following conditions:
• If the value of count is equal to 0, then print “Yes” and return.
• If the index is either equal to (N – 1) or equal to 0, then print “Yes” and return.
• Check if removing the element at index makes the arr[index – 1] < arr[index + 1], then print “Yes” and return.
• Check if removing the element at index – 1 makes the arr[index – 2] < arr[index], where index – 2 >= 0, then print “Yes” and return.
• Check if index < 0, then print “Yes” and return.
• After completing the above steps, if none of the above cases are satisfied, then print “No”.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach`   `#include ` `using` `namespace` `std;`   `// Function to find if is it possible` `// to make the array strictly increasing` `// by removing at most one element` `bool` `check(``int` `arr[], ``int` `n)` `{` `    ``// Stores the count of numbers that` `    ``// are needed to be removed` `    ``int` `count = 0;`   `    ``// Store the index of the element` `    ``// that needs to be removed` `    ``int` `index = -1;`   `    ``// Traverse the range [1, N - 1]` `    ``for` `(``int` `i = 1; i < n; i++) {`   `        ``// If arr[i-1] is greater than` `        ``// or equal to arr[i]` `        ``if` `(arr[i - 1] >= arr[i]) {`   `            ``// Increment the count by 1` `            ``count++;`   `            ``// Update index` `            ``index = i;` `        ``}` `    ``}`   `    ``// If count is greater than one` `    ``if` `(count > 1)` `        ``return` `false``;`   `    ``// If no element is removed` `    ``if` `(count == 0)` `        ``return` `true``;`   `    ``// If only the last or the` `    ``// first element is removed` `    ``if` `(index == n - 1 || index == 1)` `        ``return` `true``;`   `    ``// If a[index] is removed` `    ``if` `(arr[index - 1] < arr[index + 1])` `        ``return` `true``;`   `    ``// If a[index - 1] is removed` `    ``if` `(index - 2 >= 0 && arr[index - 2] < arr[index])` `        ``return` `true``;` `      `  `      ``// if there is no element to compare` `      ``if``(index < 0)` `          ``return` `true``;`   `    ``return` `false``;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { 1, 2, 5, 3, 5 };` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``if` `(check(arr, N))` `        ``cout << ``"Yes"``;` `    ``else` `        ``cout << ``"No"``;`   `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `class` `GFG{`   `// Function to find if is it possible` `// to make the array strictly increasing` `// by removing at most one element` `public` `static` `boolean` `check(``int` `arr[], ``int` `n)` `{` `    `  `    ``// Stores the count of numbers that` `    ``// are needed to be removed` `    ``int` `count = ``0``;`   `    ``// Store the index of the element` `    ``// that needs to be removed` `    ``int` `index = -``1``;`   `    ``// Traverse the range [1, N - 1]` `    ``for``(``int` `i = ``1``; i < n; i++) ` `    ``{` `        `  `        ``// If arr[i-1] is greater than` `        ``// or equal to arr[i]` `        ``if` `(arr[i - ``1``] >= arr[i])` `        ``{` `            `  `            ``// Increment the count by 1` `            ``count++;`   `            ``// Update index` `            ``index = i;` `        ``}` `    ``}`   `    ``// If count is greater than one` `    ``if` `(count > ``1``)` `        ``return` `false``;`   `    ``// If no element is removed` `    ``if` `(count == ``0``)` `        ``return` `true``;`   `    ``// If only the last or the` `    ``// first element is removed` `    ``if` `(index == n - ``1` `|| index == ``1``)` `        ``return` `true``;`   `    ``// If a[index] is removed` `    ``if` `(arr[index - ``1``] < arr[index + ``1``])` `        ``return` `true``;`   `    ``// If a[index - 1] is removed` `    ``if` `(index - ``2` `>= ``0` `&& arr[index - ``2``] < arr[index])` `        ``return` `true``;` `      `  `      ``// if there is no element to compare` `      ``if``(index < ``0``)` `          ``return` `true``;`   `    ``return` `false``;` `}`   `// Driver Code` `public` `static` `void` `main(String args[])` `{` `    ``int` `[]arr = { ``1``, ``2``, ``5``, ``3``, ``5` `};` `    ``int` `N = arr.length;` `    `  `    ``if` `(check(arr, N))` `        ``System.out.println(``"Yes"``);` `    ``else` `        ``System.out.println(``"No"``);` `}` `}`   `// This code is contributed by SoumikMondal`

## Python3

 `# Python3 program for the above approach`   `# Function to find if is it possible` `# to make the array strictly increasing` `# by removing at most one element` `def` `check(arr, n):` `  `  `    ``# Stores the count of numbers that` `    ``# are needed to be removed` `    ``count ``=` `0`   `    ``# Store the index of the element` `    ``# that needs to be removed` `    ``index ``=` `-``1`   `    ``# Traverse the range [1, N - 1]` `    ``for` `i ``in` `range``(``1``, n):`   `        ``# If arr[i-1] is greater than` `        ``# or equal to arr[i]` `        ``if` `(arr[i ``-` `1``] >``=` `arr[i]):` `            ``# Increment the count by 1` `            ``count ``+``=` `1`   `            ``# Update index` `            ``index ``=` `i`   `    ``# If count is greater than one` `    ``if` `(count > ``1``):` `        ``return` `False`   `    ``# If no element is removed` `    ``if` `(count ``=``=` `0``):` `        ``return` `True`   `    ``# If only the last or the` `    ``# first element is removed` `    ``if` `(index ``=``=` `n ``-` `1` `or` `index ``=``=` `1``):` `        ``return` `True`   `    ``# If a[index] is removed` `    ``if` `(arr[index ``-` `1``] < arr[index ``+` `1``]):` `        ``return` `True`   `    ``# If a[index - 1] is removed` `    ``if` `(arr[index ``-` `2``] < arr[index]):` `        ``return` `True`   `    ``return` `False`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``1``, ``2``, ``5``, ``3``, ``5``]` `    ``N ``=` `len``(arr)` `    ``if` `(check(arr, N)):` `        ``print``(``"Yes"``)` `    ``else``:` `        ``print``(``"No"``)`   `# This code is contributed by mohitkumar 29.`

## C#

 `// C# program for the above approach` `using` `System;`   `class` `GFG{`   `// Function to find if is it possible` `// to make the array strictly increasing` `// by removing at most one element` `public` `static` `bool` `check(``int``[] arr, ``int` `n)` `{` `    `  `    ``// Stores the count of numbers that` `    ``// are needed to be removed` `    ``int` `count = 0;`   `    ``// Store the index of the element` `    ``// that needs to be removed` `    ``int` `index = -1;`   `    ``// Traverse the range [1, N - 1]` `    ``for``(``int` `i = 1; i < n; i++)` `    ``{` `        `  `        ``// If arr[i-1] is greater than` `        ``// or equal to arr[i]` `        ``if` `(arr[i - 1] >= arr[i])` `        ``{` `            `  `            ``// Increment the count by 1` `            ``count++;`   `            ``// Update index` `            ``index = i;` `        ``}` `    ``}`   `    ``// If count is greater than one` `    ``if` `(count > 1)` `        ``return` `false``;`   `    ``// If no element is removed` `    ``if` `(count == 0)` `        ``return` `true``;`   `    ``// If only the last or the` `    ``// first element is removed` `    ``if` `(index == n - 1 || index == 1)` `        ``return` `true``;`   `    ``// If a[index] is removed` `    ``if` `(arr[index - 1] < arr[index + 1])` `        ``return` `true``;`   `    ``// If a[index - 1] is removed` `    ``if` `(arr[index - 2] < arr[index])` `        ``return` `true``;`   `    ``return` `false``;` `}`   `// Driver Code` `public` `static` `void` `Main(``string``[] args)` `{` `    ``int``[] arr = { 1, 2, 5, 3, 5 };` `    ``int` `N = arr.Length;`   `    ``if` `(check(arr, N))` `        ``Console.WriteLine(``"Yes"``);` `    ``else` `        ``Console.WriteLine(``"No"``);` `}` `}`   `// This code is contributed by ukasp`

## Javascript

 ``

Output

```Yes

```

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

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