# Check if maximum difference between indices of Non-Zero Elements is greater than X

Given an array arr[] and an integer X, the task is to check that maximum difference between indices of the non-zero elements is greater than or equal to X
Examples:

Input: arr[] = {1, 0, 1}, X = 3
Output: No
Explanation:
Maximum Difference between the indices of non-zero elements is 2.

Input: arr[] = {1, 0, 0, 0, 0, 0, 1}, X = 6
Output: Yes
Explanation:
Maximum Difference between the indices of non-zero elemente is 6.

Approach: The idea is to maintain the occurrence of last non-zero element in the array and As soon as there is a new element which is non-zero then compare the distance between the last occurrence index to the current index. If the difference between them is greater than or equal to X. Then, update the last occurrence of the non-zero element and continue checking. Otherwise, return False.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to check that ` `// maximum difference of indices between ` `// non-zero elements if greater than X ` `#include ` `using` `namespace` `std; ` ` `  `// Function to check that maximum  ` `// difference of indices between ` `// non-zero elements if greater than X ` `void` `findRuleFollowed(``int` `arr[], ``int` `n, ``int` `x) ` `{ ` `    ``int` `last_occur = -1; ` `    ``bool` `flag = ``true``; ` `     `  `    ``// Loop to iterate over the elements  ` `    ``// of the array  ` `    ``for``(``int` `i = 0; i < n; i++) ` `    ``{ ` `         `  `        ``// Condition if there is a last occured ` `        ``// non-zero element in the array ` `        ``if` `(arr[i] != 0 && last_occur != -1) ` `        ``{ ` `            ``int` `diff = i - last_occur; ` `            ``if` `(diff >= x) ` `            ``{ ` `                ``continue``; ` `            ``} ` `            ``else` `            ``{ ` `                ``flag = ``false``; ` `                ``break``; ` `            ``} ` `        ``} ` `        ``else` `if` `(arr[i] != 0 && last_occur == -1) ` `        ``{ ` `            ``last_occur = i; ` `        ``} ` `    ``} ` `     `  `    ``// Condition to check if the  ` `    ``// maximum difference is maintained ` `    ``if` `(flag) ` `        ``cout << ``"YES"``; ` `    ``else` `        ``cout << ``"NO"``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 0, 1, 0, 0, 1 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(0); ` `    ``int` `x = 3; ` `     `  `    ``// Function call ` `    ``findRuleFollowed(arr, n, x); ` `} ` ` `  `// This code is contributed by ankitkumar34 `

## Java

 `// Java implementation to check that ` `// maximum difference of indices between ` `// non-zero elements if greater than X ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `     `  `// Function to check that maximum ` `// difference of indices between ` `// non-zero elements if greater than X ` `static` `void` `findRuleFollowed(``int` `arr[], ``int` `n, ``int` `x) ` `{ ` `    ``int` `last_occur = -``1``; ` `    ``boolean` `flag = ``true``; ` `     `  `    ``// Loop to iterate over the elements  ` `    ``// of the array  ` `    ``for``(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `         `  `        ``// Condition if there is a last occured ` `        ``// non-zero element in the array ` `        ``if` `(arr[i] != ``0` `&& last_occur != -``1``) ` `        ``{ ` `            ``int` `diff = i - last_occur; ` `            ``if` `(diff >= x) ` `            ``{ ` `                ``continue``; ` `            ``} ` `            ``else` `            ``{ ` `                ``flag = ``false``; ` `                ``break``; ` `            ``} ` `        ``} ` `        ``else` `if` `(arr[i] != ``0` `&& last_occur == -``1``) ` `        ``{ ` `            ``last_occur = i; ` `        ``} ` `    ``} ` `     `  `    ``// Condition to check if the  ` `    ``// maximum difference is maintained ` `    ``if` `(flag) ` `        ``System.out.println(``"YES"``); ` `    ``else` `        ``System.out.println(``"NO"``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `arr[] = { ``0``, ``1``, ``0``, ``0``, ``1` `}; ` `    ``int` `n = arr.length; ` `    ``int` `x = ``3``; ` `     `  `    ``// Function call ` `    ``findRuleFollowed(arr, n, x); ` `} ` `} ` ` `  `// This code is contributed by ankitkumar34 `

## Python3

 `# Python3 implementation to check that ` `# maximum difference of indices between ` `# non-zero elements if greater than X ` ` `  `# Function to check that ` `# maximum difference of indices between ` `# non-zero elements if greater than X ` `def` `findRuleFollowed(arr, x): ` `    ``last_occur ``=` `-``1` `    ``flag ``=` `True` `     `  `    ``# Loop to iterate over the elements  ` `    ``# of the array  ` `    ``for` `i ``in` `range``(``len``(arr)): ` `         `  `        ``# Condition if there is a last occured ` `        ``# non-zero element in the array ` `        ``if` `arr[i] !``=` `0` `and` `last_occur !``=` `-``1``: ` `            ``diff ``=` `i ``-` `last_occur ` `            ``if` `diff >``=` `x: ` `                ``continue` `            ``else``: ` `                ``flag ``=` `False` `                ``break` `        ``elif` `arr[i] !``=` `0` `and` `last_occur ``=``=` `-``1``: ` `            ``last_occur ``=` `i ` `     `  `    ``# Condition to check if the  ` `    ``# maximum difference is maintained ` `    ``if` `flag: ` `        ``print``(``"YES"``) ` `    ``else``: ` `        ``print``(``"NO"``) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``arr ``=` `[``0``, ``1``, ``0``, ``0``, ``1``] ` `    ``x ``=` `3` `     `  `    ``# Function Call ` `    ``findRuleFollowed(arr, x) `

## C#

 `// C# implementation to check that ` `// maximum difference of indices between ` `// non-zero elements if greater than X ` `using` `System; ` ` `  `class` `GFG{ ` `     `  `// Function to check that maximum ` `// difference of indices between ` `// non-zero elements if greater than X ` `static` `void` `findRuleFollowed(``int` `[]arr,  ` `                             ``int` `n, ``int` `x) ` `{ ` `    ``int` `last_occur = -1; ` `    ``bool` `flag = ``true``; ` `     `  `    ``// Loop to iterate over the elements  ` `    ``// of the array  ` `    ``for``(``int` `i = 0; i < n; i++) ` `    ``{ ` `         `  `        ``// Condition if there is a last occured ` `        ``// non-zero element in the array ` `        ``if` `(arr[i] != 0 && last_occur != -1) ` `        ``{ ` `            ``int` `diff = i - last_occur; ` `             `  `            ``if` `(diff >= x) ` `            ``{ ` `                ``continue``; ` `            ``} ` `            ``else` `            ``{ ` `                ``flag = ``false``; ` `                ``break``; ` `            ``} ` `        ``} ` `        ``else` `if` `(arr[i] != 0 && last_occur == -1) ` `        ``{ ` `            ``last_occur = i; ` `        ``} ` `    ``} ` `     `  `    ``// Condition to check if the  ` `    ``// maximum difference is maintained ` `    ``if` `(flag) ` `        ``Console.WriteLine(``"YES"``); ` `    ``else` `        ``Console.WriteLine(``"NO"``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``int` `[]arr = { 0, 1, 0, 0, 1 }; ` `    ``int` `n = arr.Length; ` `    ``int` `x = 3; ` `     `  `    ``// Function call ` `    ``findRuleFollowed(arr, n, x); ` `} ` `} ` ` `  `// This code is contributed by Amit Katiyar`

Output:

```YES
```

Time Complexity: O(N)

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