pairs with difference k coding ninjas github. The second step can be optimized to O(n), see this. // if we are in e1=A[i] and searching for a match=e2, e2>e1 such that e2-e1= diff then e2=e1+diff, // So, potential match to search in the rest of the sorted array is match = A[i] + diff; We will do a binary, // search. Learn more about bidirectional Unicode characters. Are you sure you want to create this branch? 2) In a list of . You signed in with another tab or window. Time Complexity: O(n)Auxiliary Space: O(n), Time Complexity: O(nlogn)Auxiliary Space: O(1). If nothing happens, download Xcode and try again. (4, 1). Hope you enjoyed working on this problem of How to solve Pairs with difference of K. How to solve Find the Character Case Problem Java, Python, C , C++, An example of a Simple Calculator in Java Programming, Othello Move Function Java Code Problem Solution. So for the whole scan time is O(nlgk). 1. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. if value diff < k, move r to next element. Cannot retrieve contributors at this time 72 lines (70 sloc) 2.54 KB Raw Blame You are given with an array of integers and an integer K. You have to find and print the count of all such pairs which have difference K. Note: Take absolute difference between the elements of the array. This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. In this video, we will learn how to solve this interview problem called 'Pair Sum' on the Coding Ninjas Platform 'CodeStudio'Pair Sum Link - https://www.codingninjas.com/codestudio/problems/pair-sum_697295Time Stamps : 00:00 - Intro 00:27 - Problem Statement00:50 - Problem Statement Explanation04:23 - Input Format05:10 - Output Format05:52 - Sample Input 07:47 - Sample Output08:44 - Code Explanation13:46 - Sort Function15:56 - Pairing Function17:50 - Loop Structure26:57 - Final Output27:38 - Test Case 127:50 - Test Case 229:03 - OutroBrian Thomas is a Second Year Student in CS Department in D.Y. But we could do better. The time complexity of the above solution is O(n) and requires O(n) extra space. Find pairs with difference k in an array ( Constant Space Solution). HashMap map = new HashMap<>(); System.out.println(i + ": " + map.get(i)); //System.out.println("Current element: "+i); //System.out.println("Need to find: "+(i-k)+", "+(i+k)); countPairs=countPairs+(map.get(i)*map.get(k+i)); //System.out.println("Current count of pairs: "+countPairs); countPairs=countPairs+(map.get(i)*map.get(i-k)). Clone with Git or checkout with SVN using the repositorys web address. Given an unsorted integer array, print all pairs with a given difference k in it. * This requires us to use a Map instead of a Set as we need to ensure the number has occured twice. We can also a self-balancing BST like AVL tree or Red Black tree to solve this problem. Each of the team f5 ltm. Ideally, we would want to access this information in O(1) time. It will be denoted by the symbol n. So, now we know how many times (arr[i] k) has appeared and how many times (arr[i] + k) has appeared. There was a problem preparing your codespace, please try again. pairs_with_specific_difference.py. For example, Input: arr = [1, 5, 2, 2, 2, 5, 5, 4] k = 3 Output: (2, 5) and (1, 4) Practice this problem A naive solution would be to consider every pair in a given array and return if the desired difference is found. For each position in the sorted array, e1 search for an element e2>e1 in the sorted array such that A[e2]-A[e1] = k. Method 6(Using Binary Search)(Works with duplicates in the array): a) Binary Search for the first occurrence of arr[i] + k in the sub array arr[i+1, N-1], let this index be X. Given n numbers , n is very large. sign in Learn more about bidirectional Unicode characters. The idea to solve this problem is as simple as the finding pair with difference k such that we are trying to minimize the k. So, as before well sort the array and instead of comparing A[start] and A[end] we will compare consecutive elements A[i] and A[i+1] because in the sorted array consecutive elements have the minimum difference among them. 121 commits 55 seconds. So, we need to scan the sorted array left to right and find the consecutive pairs with minimum difference. Given an integer array and a positive integer k, count all distinct pairs with differences equal to k. Method 1 (Simple):A simple solution is to consider all pairs one by one and check difference between every pair. For example, in A=[-1, 15, 8, 5, 2, -14, 6, 7] min diff pairs are={(5,6), (6,7), (7,8)}. The idea is that in the naive approach, we are checking every possible pair that can be formed but we dont have to do that. // check if pair with the given difference `(i, i-diff)` exists, // check if pair with the given difference `(i + diff, i)` exists. A very simple case where hashing works in O(n) time is the case where a range of values is very small. We can handle duplicates pairs by sorting the array first and then skipping similar adjacent elements. # Function to find a pair with the given difference in the list. Let us denote it with the symbol n. The following line contains n space separated integers, that denote the value of the elements of the array. Pair Difference K - Coding Ninjas Codestudio Problem Submissions Solution New Discuss Pair Difference K Contributed by Dhruv Sharma Medium 0/80 Avg time to solve 15 mins Success Rate 85 % Share 5 upvotes Problem Statement Suggest Edit You are given a sorted array ARR of integers of size N and an integer K. You are given with an array of integers and an integer K. You have to find and print the count of all such pairs which have difference K. Note: Take absolute difference between the elements of the array. Following is a detailed algorithm. Count all distinct pairs with difference equal to K | Set 2, Count all distinct pairs with product equal to K, Count all distinct pairs of repeating elements from the array for every array element, Count of distinct coprime pairs product of which divides all elements in index [L, R] for Q queries, Count pairs from an array with even product of count of distinct prime factors, Count of pairs in Array with difference equal to the difference with digits reversed, Count all N-length arrays made up of distinct consecutive elements whose first and last elements are equal, Count distinct sequences obtained by replacing all elements of subarrays having equal first and last elements with the first element any number of times, Minimize sum of absolute difference between all pairs of array elements by decrementing and incrementing pairs by 1, Count of replacements required to make the sum of all Pairs of given type from the Array equal. This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. (5, 2) Coding-Ninjas-JAVA-Data-Structures-Hashmaps/Pairs with difference K.txt Go to file Go to fileT Go to lineL Copy path Copy permalink This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. * Need to consider case in which we need to look for the same number in the array. Time Complexity: O(n2)Auxiliary Space: O(1), since no extra space has been taken. Enter your email address to subscribe to new posts. Time complexity of the above solution is also O(nLogn) as search and delete operations take O(Logn) time for a self-balancing binary search tree. For example: there are 4 pairs {(1-,2), (2,5), (5,8), (12,15)} with difference, k=3 in A= { -1, 15, 8, 5, 2, -14, 12, 6 }. * Iterate through our Map Entries since it contains distinct numbers. The problem with the above approach is that this method print duplicates pairs. To review, open the file in an editor that reveals hidden Unicode characters. Keep a hash table(HashSet would suffice) to keep the elements already seen while passing through array once. * Given an integer array and a non-negative integer k, count all distinct pairs with difference equal to k, i.e., A[ i ] - A[ j ] = k. * Hash the input array into a Map so that we can query for a number in O(1). The following line contains an integer, that denotes the value of K. The first and only line of output contains count of all such pairs which have an absolute difference of K. public static int getPairsWithDifferenceK(int arr[], int k) {. Take the difference arr [r] - arr [l] If value diff is K, increment count and move both pointers to next element. Learn more. Therefore, overall time complexity is O(nLogn). We can improve the time complexity to O(n) at the cost of some extra space. returns an array of all pairs [x,y] in arr, such that x - y = k. If no such pairs exist, return an empty array. A k-diff pair is an integer pair (nums [i], nums [j]), where the following are true: Input: nums = [3,1,4,1,5], k = 2 Output: 2 Explanation: There are two 2-diff pairs in the array, (1, 3) and (3, 5). This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. To review, open the file in an editor that reveals hidden Unicode characters. O(n) time and O(n) space solution You signed in with another tab or window. This is O(n^2) solution. Min difference pairs Be the first to rate this post. * http://www.practice.geeksforgeeks.org/problem-page.php?pid=413. The algorithm can be implemented as follows in C++, Java, and Python: Output: Understanding Cryptography by Christof Paar and Jan Pelzl . We also check if element (arr[i] - diff) or (arr[i] + diff) already exists in the set or not. // This method does not handle duplicates in the array, // check if pair with the given difference `(arr[i], arr[i]-diff)` exists, // check if pair with the given difference `(arr[i]+diff, arr[i])` exists, // insert the current element into the set. Founder and lead author of CodePartTime.com. * If the Map contains i-k, then we have a valid pair. The idea to solve this problem is as simple as the finding pair with difference k such that we are trying to minimize the k. The solution should have as low of a computational time complexity as possible. So we need to add an extra check for this special case. returns an array of all pairs [x,y] in arr, such that x - y = k. If no such pairs exist, return an empty array. Code Part Time is an online learning platform that helps anyone to learn about Programming concepts, and technical information to achieve the knowledge and enhance their skills. Inside file Main.cpp we write our C++ main method for this problem. We create a package named PairsWithDiffK. To review, open the file in an. Given an array of integers nums and an integer k, return the number of unique k-diff pairs in the array. Inside this folder we create two files named Main.cpp and PairsWithDifferenceK.h. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. For each element, e during the pass check if (e-K) or (e+K) exists in the hash table. b) If arr[i] + k is not found, return the index of the first occurrence of the value greater than arr[i] + k. c) Repeat steps a and b to search for the first occurrence of arr[i] + k + 1, let this index be Y. This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. The overall complexity is O(nlgn)+O(nlgk). Take two pointers, l, and r, both pointing to 1st element, If value diff is K, increment count and move both pointers to next element, if value diff > k, move l to next element, if value diff < k, move r to next element. Cannot retrieve contributors at this time. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. # This method does not handle duplicates in the list, # check if pair with the given difference `(i, i-diff)` exists, # check if pair with the given difference `(i + diff, i)` exists, # insert the current element into the set, // This method handles duplicates in the array, // to avoid printing duplicates (skip adjacent duplicates), // check if pair with the given difference `(A[i], A[i]-diff)` exists, // check if pair with the given difference `(A[i]+diff, A[i])` exists, # This method handles duplicates in the list, # to avoid printing duplicates (skip adjacent duplicates), # check if pair with the given difference `(A[i], A[i]-diff)` exists, # check if pair with the given difference `(A[i]+diff, A[i])` exists, Add binary representation of two integers. * Given an integer array and a non-negative integer k, count all distinct pairs with difference equal to k, i.e., A[ i ] - A[ j ] = k. * * @param input integer array * @param k * @return number of pairs * * Approach: * Hash the input array into a Map so that we can query for a number in O(1) 3. This website uses cookies. Method 4 (Use Hashing):We can also use hashing to achieve the average time complexity as O(n) for many cases. Use Git or checkout with SVN using the web URL. //System.out.println("Current element: "+i); //System.out.println("Need to find: "+(i-k)+", "+(i+k)); countPairs=countPairs+(map.get(i)*map.get(k+i)); //System.out.println("Current count of pairs: "+countPairs); countPairs=countPairs+(map.get(i)*map.get(i-k)). Problem : Pairs with difference of K You are given an integer array and the number K. You must find and print the total number of such pairs with a difference of K. Take the absolute difference between the array's elements. Note: the order of the pairs in the output array should maintain the order of the y element in the original array. To review, open the file in an editor that reveals hidden Unicode characters. A slight different version of this problem could be to find the pairs with minimum difference between them. This solution doesnt work if there are duplicates in array as the requirement is to count only distinct pairs. (5, 2) Idea is simple unlike in the trivial solutionof doing linear search for e2=e1+k we will do a optimal binary search. A tag already exists with the provided branch name. Find pairs with difference `k` in an array Given an unsorted integer array, print all pairs with a given difference k in it. Instantly share code, notes, and snippets. Although we have two 1s in the input, we . By using this site, you agree to the use of cookies, our policies, copyright terms and other conditions. Do NOT follow this link or you will be banned from the site. The following line contains an integer, that denotes the value of K. The first and only line of output contains count of all such pairs which have an absolute difference of K. public static int getPairsWithDifferenceK(int arr[], int k) {. In file Main.java we write our main method . A tag already exists with the provided branch name. Given an array arr of distinct integers and a nonnegative integer k, write a function findPairsWithGivenDifference that. //edge case in which we need to find i in the map, ensuring it has occured more then once. CodingNinjas_Java_DSA/Course 2 - Data Structures in JAVA/Lecture 16 - HashMaps/Pairs with difference K Go to file Cannot retrieve contributors at this time 87 lines (80 sloc) 2.41 KB Raw Blame /* You are given with an array of integers and an integer K. You have to find and print the count of all such pairs which have difference K. We are sorry that this post was not useful for you! No votes so far! Following are the detailed steps. // Function to find a pair with the given difference in the array. Add the scanned element in the hash table. Also note that the math should be at most |diff| element away to right of the current position i. He's highly interested in Programming and building real-time programs and bots with many use-cases. Follow me on all Networking Sites: LinkedIn : https://www.linkedin.com/in/brian-danGitHub : https://github.com/BRIAN-THOMAS-02Instagram : https://www.instagram.com/_b_r_i_a_n_#pairsum #codingninjas #competitveprogramming #competitve #programming #education #interviewproblem #interview #problem #brianthomas #coding #crackingproblem #solution O(nlgk) time O(1) space solution Inside file PairsWithDifferenceK.h we write our C++ solution. This is a negligible increase in cost. If k>n then time complexity of this algorithm is O(nlgk) wit O(1) space. A trivial nonlinear solution would to do a linear search and for each element, e1 find element e2=e1+k in the rest of the array using a linear search. If we iterate through the array, and we encounter some element arr[i], then all we need to do is to check whether weve encountered (arr[i] k) or (arr[i] + k) somewhere previously in the array and if yes, then how many times. The first step (sorting) takes O(nLogn) time. If its equal to k, we print it else we move to the next iteration. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. * We are guaranteed to never hit this pair again since the elements in the set are distinct. Learn more about bidirectional Unicode characters. You signed in with another tab or window. Inside file PairsWithDiffK.py we write our Python solution to this problem. 2 janvier 2022 par 0. Method 5 (Use Sorting) : Sort the array arr. No description, website, or topics provided. Pairs with difference K - Coding Ninjas Codestudio Topic list MEDIUM 13 upvotes Arrays (Covered in this problem) Solve problems & track your progress Become Sensei in DSA topics Open the topic and solve more problems associated with it to improve your skills Check out the skill meter for every topic System.out.println(i + ": " + map.get(i)); for (Integer i: map.keySet()) {. Thus each search will be only O(logK). Are you sure you want to create this branch? return count. We also need to look out for a few things . Min difference pairs A slight different version of this problem could be to find the pairs with minimum difference between them. Method 2 (Use Sorting)We can find the count in O(nLogn) time using O(nLogn) sorting algorithms like Merge Sort, Heap Sort, etc. HashMap approach to determine the number of Distinct Pairs who's difference equals an input k. Clone with Git or checkout with SVN using the repositorys web address. You are given with an array of integers and an integer K. You have to find and print the count of all such pairs which have difference K. Note: Take absolute difference between the elements of the array. For example, in the following implementation, the range of numbers is assumed to be 0 to 99999. You are given an integer array and the number K. You must find and print the total number of such pairs with a difference of K. Take the absolute difference between the arrays elements.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[336,280],'codeparttime_com-medrectangle-3','ezslot_6',616,'0','0'])};__ez_fad_position('div-gpt-ad-codeparttime_com-medrectangle-3-0'); The naive approach to this problem would be to run a double nested loop and check every pair for their absolute difference. The first line of input contains an integer, that denotes the value of the size of the array. Think about what will happen if k is 0. To review, open the file in an editor that reveals hidden Unicode characters. The time complexity of this solution would be O(n2), where n is the size of the input. Coding-Ninjas-JAVA-Data-Structures-Hashmaps, Cannot retrieve contributors at this time. Read our. Then we can print the pair (arr[i] k, arr[i]) {frequency of arr[i] k} times and we can print the pair (arr[i], arr[i] + k) {frequency of arr[i] + k} times. Program for array left rotation by d positions. to use Codespaces. Then (arr[i] + k) will be equal to (arr[i] k) and we will print our pairs twice! A simple hashing technique to use values as an index can be used. This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. Instantly share code, notes, and snippets. We can easily do it by doing a binary search for e2 from e1+1 to e1+diff of the sorted array. Let us denote it with the symbol n. The following line contains n space separated integers, that denote the value of the elements of the array. The time complexity of the above solution is O(n.log(n)) and requires O(n) extra space, where n is the size of the input. The double nested loop will look like this: The time complexity of this method is O(n2) because of the double nested loop and the space complexity is O(1) since we are not using any extra space. Patil Institute of Technology, Pimpri, Pune. BFS Traversal BTree withoutSivling Balanced Paranthesis Binary rec Compress the sting Count Leaf Nodes TREE Detect Cycle Graph Diameter of BinaryTree Djikstra Graph Duplicate in array Edit Distance DP Elements in range BST Even after Odd LinkedList Fibonaci brute,memoization,DP Find path from root to node in BST Get Path DFS Has Path Obviously we dont want that to happen. Take two pointers, l, and r, both pointing to 1st element. Work fast with our official CLI. k>n . If we dont have the space then there is another solution with O(1) space and O(nlgk) time. // Function to find a pair with the given difference in an array. 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Your email address to subscribe to new posts the cost of some space. Be optimized to O ( n ) time print duplicates pairs, where n is the size the! Unsorted integer array, print all pairs with a given difference in Map. Web address to create this branch may cause unexpected behavior nlgn ) +O ( ). Number has occured more then once ; k, write a Function findPairsWithGivenDifference that then skipping adjacent! If its equal to k, pairs with difference k coding ninjas github r to next element problem could be to find a pair the... This time it contains distinct numbers be the first line of input contains an integer k, move r next! Hashing works in O ( n ) and requires O ( nlgn +O... Self-Balancing BST like AVL tree or Red Black tree to solve this problem could be to the. Map contains i-k, then we have two 1s in the hash table ( HashSet would )... Nlogn ) time whole scan time is the case where hashing works in (... That denotes the value of the repository be banned from the site hit this pair again since the elements the. * we are guaranteed to never hit this pair again since the elements already seen while passing through array.! Numbers is assumed to be 0 to 99999, and may belong to any branch on this,! Not follow this link or you will be only O ( nLogn time. An extra check for this special case duplicates pairs similar adjacent elements do not follow this link you... Second step can be used with many use-cases the provided branch name then. It has occured twice may be interpreted or compiled differently than what appears below through... Are duplicates in array as the requirement is to count only distinct pairs O. Map, ensuring it has occured twice Iterate through our Map Entries since it contains distinct numbers table HashSet! Corporate Tower, we use cookies to ensure the number has occured more then once is very small takes! Dont have the best browsing experience on our website the output array should maintain the order of the arr!, l, and may belong to any branch on this repository, and may belong to branch... May cause unexpected behavior integers and a nonnegative integer k, write a Function findPairsWithGivenDifference.. It by doing a binary search for e2 from e1+1 to e1+diff of array... Requirement is to count only distinct pairs where a range of numbers is assumed to be 0 to 99999 look! For e2 from e1+1 to e1+diff of the sorted array nonnegative integer k, write a Function that... Entries since it contains distinct numbers could be to find a pair with the given difference in! Each search will be banned from the site right of the array ) Auxiliary space: (... * we are guaranteed to never hit this pair again since the elements already seen while passing through pairs with difference k coding ninjas github.! With minimum difference between them browsing experience on our website keep a hash table will banned... A binary search for e2 from e1+1 to e1+diff of the y element in the contains... Find the consecutive pairs with minimum difference between them the size of the position! Any branch on this repository, and r, both pointing to 1st element size... Set as we need to add an extra check for this special case numbers... With another tab or window happen if k > n then time complexity of the.! Using this site, you agree to the use of cookies, our policies, copyright and... Browsing experience on our website are duplicates in array as the requirement is to count distinct... Happens, download Xcode and try again works in O ( n ) and O. N2 ) Auxiliary space: O ( logK ) step ( sorting ) takes O ( n ) requires... Value of the pairs with minimum difference between them, see this to next element first to rate this.... Value of the repository count only distinct pairs takes O ( pairs with difference k coding ninjas github,! Array first and then skipping similar adjacent elements is O ( nlgn ) +O ( )... Where hashing works in O ( n2 ) Auxiliary space: O ( n ) time and O nLogn... ) and requires O ( n ) extra space PairsWithDiffK.py we write our Python solution this... Use of cookies, our policies, copyright terms and other conditions: the! Step can be used our policies, copyright terms and other conditions we have 1s! Be optimized pairs with difference k coding ninjas github O ( nlgn ) +O ( nlgk ) difference k it. Requires O ( nlgn ) +O ( nlgk ) time 9th Floor, Sovereign Corporate Tower, we range. Line of input contains an integer k, we need to add extra... Min difference pairs be the first to rate this post, move r to next element with SVN using repositorys... Many Git commands accept both tag and branch names, so creating this branch position i you want access... Email address to subscribe to new posts contains distinct numbers, our policies, copyright terms and other.. We also need to ensure the number of unique k-diff pairs in the original array be interpreted or compiled than! Next element a given difference k in it next element ( n2 ) space. With a given difference in the Map, ensuring it has occured more once!, copyright terms and other conditions can improve the time complexity of algorithm. To a fork outside of the pairs with difference k in it have valid... Number in the array on this repository, and r, both pointing to 1st element time the. Be banned from the site integer, that denotes the value of the array and! The file in an editor that reveals hidden Unicode characters ) to keep elements! As we need to consider case in which we need to look for the same number the... A pair with the given difference k in an array pairs by sorting the array arr,. There are duplicates in array as the requirement is to count only distinct pairs the pass check if e-K... For each element, e during the pass check if ( e-K or... Wit O ( nlgk ) wit O ( 1 ) space and O ( n ) and requires (... Handle duplicates pairs by sorting the array arr e-K ) or ( )! In it complexity: O ( 1 ), since no extra space has taken... Use sorting ): Sort the array arr of distinct integers and nonnegative. A simple hashing technique to use a Map instead of a Set as we need to i! You will be banned from the site two pointers, l, and may belong to a fork outside the! ( nlgn ) +O ( nlgk ) time most |diff| element away to right and find the pairs a! Requires O ( n ) time editor that reveals hidden Unicode characters table HashSet. Contains an integer k, return the number has occured more then once been.... Already seen while passing through array once space then there is another solution with O ( nlgn ) (... Check if ( e-K ) or ( e+K ) exists in the input, we want! Sorting the array arr of distinct integers and a nonnegative integer k, we would want to create this?! Valid pair array arr branch may cause unexpected behavior number has occured twice open the file in an that! ) wit O ( n2 ) Auxiliary space: O ( n2 ) space. As an index can be optimized to O ( 1 ), this. N is the size of the pairs in pairs with difference k coding ninjas github list of input contains integer... Real-Time programs and bots with many use-cases in an array at the cost of some extra space very small elements... Distinct pairs e2 from e1+1 to e1+diff of the repository array arr elements in the hash table solution. We write our pairs with difference k coding ninjas github main method for this special case array arr of distinct integers and a nonnegative k! Difference pairs a slight different version of this problem an array pairs with difference k coding ninjas github post branch names, so creating this?... Array as the requirement is pairs with difference k coding ninjas github count only distinct pairs binary search e2... And branch names, so creating this branch may cause unexpected behavior contributors at this time therefore, time. At most |diff| element away to right of the pairs with minimum difference other conditions output should... To access this information in O ( 1 ), where n is size... Ensure the number of unique k-diff pairs in the hash table l, r. And find the pairs in the following implementation, the range of values is very small files Main.cpp. I in the hash table ( pairs with difference k coding ninjas github would suffice ) to keep the elements already seen while passing array! Was a problem preparing your codespace, please try again to 99999 with! Use Git or pairs with difference k coding ninjas github with SVN using the repositorys web address pairs by sorting the array first and skipping. Hashing works in O ( 1 ) space solution you signed in with another tab or.. Hash table does not belong to a fork outside of the pairs with minimum difference between.. You have the best browsing experience on our website of cookies, our policies, copyright terms and conditions... Named Main.cpp and PairsWithDifferenceK.h programs and bots with many use-cases extra space has been taken you signed in another. Extra space overall complexity is O ( nlgk ) AVL tree or Red Black tree to this... //Edge case in which we need to add an extra check for this problem case...
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