Maximum distance between two occurrences of same element in array

Given an array with repeated elements, the task is to find the maximum distance 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

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

A simple solution for this problem is to one by one pick each element from array and find its first and last occurrence in array and take difference of first and last occurrence for maximum distance. Time complexity for this approach is O(n²).

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

Python

# 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 

Output:

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

This article is contributed by Shashank Mishra ( Gullu ). 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 write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes

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

C++

Java

Python

C#

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