# Maximum difference between first and last indexes of an element in array

Given an array of n integers. The task is to find the difference of first and last index of each distinct element so as to maximize the difference.

Examples:

```Input : {2, 1, 3, 4, 2, 1, 5, 1, 7}
Output : 6
Element 1 has its first index = 1
and last index = 7
Difference = 7 - 1 = 6
Other elements have a smaller first and last
index difference

Input : {2, 2, 1, 1, 8, 8, 3, 5, 3}
Output : 2
Maximum difference is for indexes of element 3.
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

A simple approach is to run two loops and find the difference for each element and accordingly update the max_diff. It has a time complexity of O(n2) and the approach also needs to keep track of the elements that have been visited so that difference for them is not calculated unnecessarily.

An efficient approach uses hashing. It has the following steps.

1. Traverse the input array from left to right.
2. For each distinct element map its first and last index in the hash table.
3. Traverse the hash table and calculate the first and last index difference for each element.
4. Accordingly update the max_diff.

In the following implementation unordered_map has been used for hashing as the range of integers is not known.

## C++

 `// C++ implementation to find the maximum difference  ` `// of first and last index of array elements ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// function to find the ` `// maximum difference ` `int` `maxDifference(``int` `arr[], ``int` `n) ` `{ ` `    ``// structure to store first and last ` `    ``// index of each distinct element ` `    ``struct` `index ` `    ``{ ` `        ``int` `f, l; ` `    ``}; ` `     `  `    ``// maps each element to its ` `    ``// 'index' structure ` `    ``unordered_map<``int``, index> um; ` `     `  `    ``for` `(``int` `i=0; i::iterator itr; ` ` `  `    ``// traversing 'um' ` `    ``for` `(itr=um.begin(); itr != um.end(); itr++) ` `    ``{    ` `        ``// difference of last and first index ` `        ``// of each element ` `        ``diff = (itr->second).l - (itr->second).f; ` `         `  `        ``// update 'max_dff' ` `        ``if` `(max_diff < diff) ` `            ``max_diff = diff; ` `    ``} ` `     `  `    ``// required maximum difference ` `    ``return` `max_diff; ` `} ` ` `  ` `  `// Driver program to test above ` `int` `main() ` `{ ` `    ``int` `arr[] = {2, 1, 3, 4, 2, 1, 5, 1, 7}; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``cout << ``"Maximum Difference = "`  `         ``<

## Java

 `// Java implementation to find the maximum difference  ` `// of first and last index of array elements ` `import` `java.util.HashMap; ` `import` `java.util.Map; ` ` `  `public` `class` `MaxDiffIndexHashing { ` ` `  `    ``static` `class` `Element { ` `        ``int` `first; ` `        ``int` `second; ` ` `  `        ``public` `Element() { ` `            ``super``(); ` `        ``} ` ` `  `        ``public` `Element(``int` `first, ``int` `second) { ` `            ``super``(); ` `            ``this``.first = first; ` `            ``this``.second = second; ` `        ``} ` `    ``} ` ` `  `    ``public` `static` `void` `main(String[] args) { ` ` `  `        ``int` `arr[]={``2``, ``1``, ``3``, ``4``, ``2``, ``1``, ``5``, ``1``, ``7``}; ` `        ``System.out.println(``"Maximum Difference= "``+ maxDiffIndices(arr)); ` `    ``} ` ` `  `    ``private` `static` `int` `maxDiffIndices(``int``[] arr) { ` `        ``int` `n = arr.length; ` `        ``int` `maxDiffIndex = ``0``; ` `        ``Map map = ``new` `HashMap(); ` ` `  `        ``for` `(``int` `i = ``0``; i < n; i++) { ` `            ``if` `(map.containsKey(arr[i])) { ` `                ``Element e = map.get(arr[i]); ` `                ``e.second = i; ` `            ``} ``else` `{ ` `                ``Element e = ``new` `Element(); ` `                ``e.first = i; ` `                ``map.put(arr[i], e); ` `            ``} ` ` `  `        ``} ` ` `  `        ``for` `(Map.Entry entry : map.entrySet()) { ` `            ``Element e = entry.getValue(); ` `            ``if` `((e.second - e.first) > maxDiffIndex) ` `                ``maxDiffIndex = e.second - e.first; ` `        ``} ` ` `  `        ``return` `maxDiffIndex; ` `    ``} ` ` `  `}         `

Output:

```Maximum Difference = 6
```

Time Complexity: O(n)

This article is contributed by Ayush Jauhari. 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.

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Improved By : Vardhan Vishnu

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