# Maximum distance between two occurrences of same element in array

Given an array with repeated elements, the task is to find the maximum distance between two occurrences of an element.

**Examples: **

Input : arr[] = {3, 2, 1, 2, 1, 4, 5, 8, 6, 7, 4, 2} Output: 10 // maximum distance for 2 is 11-1 = 10 // maximum distance for 1 is 4-2 = 2 // maximum distance for 4 is 10-5 = 5

A **simple solution** for this problem is to, one by one, pick each element from the array and find its **first** and **last** occurrence in the array and take the difference between the first and last occurrence for maximum distance. The **time complexity** for this approach is O(n^{2}).

An **efficient solution** to this problem is to use hashing. The idea is to traverse the input array and store the index of the first occurrence in a hash map. For every other occurrence, find the difference between the index and the first index stored in the hash map. If the difference is more than the result so far, then update the result.

Below are implementations of the idea. The implementation uses unordered_map in.

## C++

`// C++ program to find maximum distance between two` `// same occurrences of a number.` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to find maximum distance between equal elements` `int` `maxDistance(` `int` `arr[], ` `int` `n)` `{` ` ` `// Used to store element to first index mapping` ` ` `unordered_map<` `int` `, ` `int` `> mp;` ` ` `// Traverse elements and find maximum distance between` ` ` `// same occurrences with the help of map.` ` ` `int` `max_dist = 0;` ` ` `for` `(` `int` `i=0; i<n; i++)` ` ` `{` ` ` `// If this is first occurrence of element, insert its` ` ` `// index in map` ` ` `if` `(mp.find(arr[i]) == mp.end())` ` ` `mp[arr[i]] = i;` ` ` `// Else update max distance` ` ` `else` ` ` `max_dist = max(max_dist, i - mp[arr[i]]);` ` ` `}` ` ` `return` `max_dist;` `}` `// Driver program to run the case` `int` `main()` `{` ` ` `int` `arr[] = {3, 2, 1, 2, 1, 4, 5, 8, 6, 7, 4, 2};` ` ` `int` `n = ` `sizeof` `(arr)/` `sizeof` `(arr[0]);` ` ` `cout << maxDistance(arr, n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find maximum distance between two ` `// same occurrences of a number.` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG ` `{` ` ` `// Function to find maximum distance between equal elements ` ` ` `static` `int` `maxDistance(` `int` `[] arr, ` `int` `n)` ` ` `{` ` ` `// Used to store element to first index mapping` ` ` `HashMap<Integer, Integer> map = ` `new` `HashMap<>();` ` ` ` ` `// Traverse elements and find maximum distance between ` ` ` `// same occurrences with the help of map. ` ` ` `int` `max_dist = ` `0` `;` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++)` ` ` `{` ` ` `// If this is first occurrence of element, insert its ` ` ` `// index in map ` ` ` `if` `(!map.containsKey(arr[i]))` ` ` `map.put(arr[i], i);` ` ` `// Else update max distance ` ` ` `else` ` ` `max_dist = Math.max(max_dist, i - map.get(arr[i]));` ` ` `}` ` ` `return` `max_dist;` `}` `// Driver code` `public` `static` `void` `main(String args[])` `{` ` ` `int` `[] arr = {` `3` `, ` `2` `, ` `1` `, ` `2` `, ` `1` `, ` `4` `, ` `5` `, ` `8` `, ` `6` `, ` `7` `, ` `4` `, ` `2` `};` ` ` `int` `n = arr.length;` ` ` `System.out.println(maxDistance(arr, n));` `}` `} ` `// This code is contributed by rachana soma` |

## Python3

`# Python program to find maximum distance between two` `# same occurrences of a number.` `# Function to find maximum distance between equal elements` `def` `maxDistance(arr, n):` ` ` ` ` `# Used to store element to first index mapping` ` ` `mp ` `=` `{}` ` ` `# Traverse elements and find maximum distance between` ` ` `# same occurrences with the help of map.` ` ` `maxDict ` `=` `0` ` ` `for` `i ` `in` `range` `(n):` ` ` `# If this is first occurrence of element, insert its` ` ` `# index in map` ` ` `if` `arr[i] ` `not` `in` `mp.keys():` ` ` `mp[arr[i]] ` `=` `i` ` ` `# Else update max distance` ` ` `else` `:` ` ` `maxDict ` `=` `max` `(maxDict, i` `-` `mp[arr[i]])` ` ` `return` `maxDict` `# Driver Program` `if` `__name__` `=` `=` `'__main__'` `:` ` ` `arr ` `=` `[` `3` `, ` `2` `, ` `1` `, ` `2` `, ` `1` `, ` `4` `, ` `5` `, ` `8` `, ` `6` `, ` `7` `, ` `4` `, ` `2` `]` ` ` `n ` `=` `len` `(arr)` ` ` `print` `(maxDistance(arr, n))` ` ` `# Contributed By: Harshit Sidhwa` |

## C#

`// C# program to find maximum distance between two ` `// same occurrences of a number.` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG ` `{` ` ` `// Function to find maximum distance between equal elements ` ` ` `static` `int` `maxDistance(` `int` `[] arr, ` `int` `n)` ` ` `{` ` ` `// Used to store element to first index mapping` ` ` `Dictionary<` `int` `, ` `int` `> map = ` `new` `Dictionary<` `int` `, ` `int` `>();` ` ` ` ` `// Traverse elements and find maximum distance between ` ` ` `// same occurrences with the help of map. ` ` ` `int` `max_dist = 0;` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `{` ` ` `// If this is first occurrence of element, insert its ` ` ` `// index in map ` ` ` `if` `(!map.ContainsKey(arr[i]))` ` ` `map.Add(arr[i], i);` ` ` `// Else update max distance ` ` ` `else` ` ` `max_dist = Math.Max(max_dist, i - map[arr[i]]);` ` ` `}` ` ` `return` `max_dist;` `}` `// Driver code` `public` `static` `void` `Main(String []args)` `{` ` ` `int` `[] arr = {3, 2, 1, 2, 1, 4, 5, 8, 6, 7, 4, 2};` ` ` `int` `n = arr.Length;` ` ` `Console.WriteLine(maxDistance(arr, n));` `}` `}` `// This code is contributed by PrinciRaj1992` |

## Javascript

`<script>` `// Javascript program to find maximum distance between two ` `// same occurrences of a number.` ` ` `// Function to find maximum distance between equal elements ` ` ` `function` `maxDistance(arr, n)` ` ` `{` ` ` `// Used to store element to first index mapping` ` ` `let map = ` `new` `Map();` ` ` ` ` `// Traverse elements and find maximum distance between ` ` ` `// same occurrences with the help of map. ` ` ` `let max_dist = 0;` ` ` ` ` `for` `(let i = 0; i < n; i++)` ` ` `{` ` ` `// If this is first occurrence of element, insert its ` ` ` `// index in map ` ` ` `if` `(!map.has(arr[i]))` ` ` `map.set(arr[i], i);` ` ` ` ` `// Else update max distance ` ` ` `else` ` ` `max_dist = Math.max(max_dist, i - map.get(arr[i]));` ` ` `}` ` ` ` ` `return` `max_dist;` `}` `// Driver program ` ` ` `let arr = [3, 2, 1, 2, 1, 4, 5, 8, 6, 7, 4, 2];` ` ` `let n = arr.length;` ` ` `document.write(maxDistance(arr, n));` `</script>` |

**Output:**

10

**Time complexity :** O(n) under the assumption that unordered_map’s search and insert operations take O(1) time.

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