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# Replace every element with the least greater element on its right

• Difficulty Level : Hard
• Last Updated : 20 Sep, 2021

Given an array of integers, replace every element with the least greater element on its right side in the array. If there are no greater elements on the right side, replace it with -1.

Examples:

```Input: [8, 58, 71, 18, 31, 32, 63, 92,
43, 3, 91, 93, 25, 80, 28]
Output: [18, 63, 80, 25, 32, 43, 80, 93,
80, 25, 93, -1, 28, -1, -1]```

A naive method is to run two loops. The outer loop will one by one pick array elements from left to right. The inner loop will find the smallest element greater than the picked element on its right side. Finally, the outer loop will replace the picked element with the element found by inner loop. The time complexity of this method will be O(n2).

A tricky solution would be to use Binary Search Trees. We start scanning the array from right to left and insert each element into the BST. For each inserted element, we replace it in the array by its inorder successor in BST. If the element inserted is the maximum so far (i.e. its inorder successor doesn’t exist), we replace it by -1.

Below is the implementation of the above idea –

## C++

 `// C++ program to replace every element with the``// least greater element on its right``#include ``using` `namespace` `std;` `// A binary Tree node``struct` `Node {``    ``int` `data;``    ``Node *left, *right;``};` `// A utility function to create a new BST node``Node* newNode(``int` `item)``{``    ``Node* temp = ``new` `Node;``    ``temp->data = item;``    ``temp->left = temp->right = NULL;` `    ``return` `temp;``}` `/* A utility function to insert a new node with``   ``given data in BST and find its successor */``Node* insert(Node* node, ``int` `data, Node*& succ)``{``    ` `    ``/* If the tree is empty, return a new node */``    ``if` `(node == NULL)``        ``return` `node = newNode(data);` `    ``// If key is smaller than root's key, go to left``    ``// subtree and set successor as current node``    ``if` `(data < node->data) {``        ``succ = node;``        ``node->left = insert(node->left, data, succ);``    ``}` `    ``// go to right subtree``    ``else` `if` `(data > node->data)``        ``node->right = insert(node->right, data, succ);``    ``return` `node;``}` `// Function to replace every element with the``// least greater element on its right``void` `replace(``int` `arr[], ``int` `n)``{``    ``Node* root = NULL;` `    ``// start from right to left``    ``for` `(``int` `i = n - 1; i >= 0; i--) {``        ``Node* succ = NULL;` `        ``// insert current element into BST and``        ``// find its inorder successor``        ``root = insert(root, arr[i], succ);` `        ``// replace element by its inorder``        ``// successor in BST``        ``if` `(succ)``            ``arr[i] = succ->data;``        ``else` `// No inorder successor``            ``arr[i] = -1;``    ``}``}` `// Driver Program to test above functions``int` `main()``{``    ``int` `arr[] = { 8,  58, 71, 18, 31, 32, 63, 92,``                  ``43, 3,  91, 93, 25, 80, 28 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``replace(arr, n);` `    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i] << ``" "``;` `    ``return` `0;``}`

## Java

 `// Java program to replace every element with``// the least greater element on its right``import` `java.io.*;` `class` `BinarySearchTree{``    ` `// A binary Tree node``class` `Node``{``    ``int` `data;``    ``Node left, right;` `    ``Node(``int` `d)``    ``{``        ``data = d;``        ``left = right = ``null``;``    ``}``}` `// Root of BST``static` `Node root;``static` `Node succ;` `// Constructor``BinarySearchTree()``{``    ``root = ``null``;``    ``succ = ``null``;``}` `// A utility function to insert a new node with``// given data in BST and find its successor``Node insert(Node node, ``int` `data)``{``    ` `    ``// If the tree is empty, return a new node``    ``if` `(node == ``null``)``    ``{``        ``node = ``new` `Node(data);``    ``}` `    ``// If key is smaller than root's key,``    ``// go to left subtree and set successor``    ``// as current node``    ``if` `(data < node.data)``    ``{``        ``succ = node;``        ``node.left = insert(node.left, data);``    ``}` `    ``// Go to right subtree``    ``else` `if` `(data > node.data)``        ``node.right = insert(node.right, data);``        ` `    ``return` `node;``}` `// Function to replace every element with the``// least greater element on its right``static` `void` `replace(``int` `arr[], ``int` `n)``{``    ``BinarySearchTree tree = ``new` `BinarySearchTree();` `    ``// start from right to left``    ``for``(``int` `i = n - ``1``; i >= ``0``; i--)``    ``{``        ``succ = ``null``;``        ` `        ``// Insert current element into BST and``        ``// find its inorder successor``        ``root = tree.insert(root, arr[i]);` `        ``// Replace element by its inorder``        ``// successor in BST``        ``if` `(succ != ``null``)``            ``arr[i] = succ.data;``            ` `        ``// No inorder successor``        ``else``            ``arr[i] = -``1``;``    ``}``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = ``new` `int``[] { ``8``, ``58``, ``71``, ``18``, ``31``,``                            ``32``, ``63``, ``92``, ``43``, ``3``,``                            ``91``, ``93``, ``25``, ``80``, ``28` `};``    ``int` `n = arr.length;` `    ``replace(arr, n);` `    ``for``(``int` `i = ``0``; i < n; i++)``        ``System.out.print(arr[i] + ``" "``);``}``}` `// The code is contributed by Tushar Bansal`

## Python3

 `# Python3 program to replace every element``# with the least greater element on its right` `# A binary Tree node``class` `Node:``    ` `    ``def` `__init__(``self``, d):``        ` `        ``self``.data ``=` `d``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `# A utility function to insert a new node with``# given data in BST and find its successor``def` `insert(node, data):``    ` `    ``global` `succ``    ` `    ``# If the tree is empty, return a new node``    ``root ``=` `node` `    ``if` `(node ``=``=` `None``):``        ``return` `Node(data)` `    ``# If key is smaller than root's key, go to left``    ``# subtree and set successor as current node``    ``if` `(data < node.data):``        ` `        ``#print("1")``        ``succ ``=` `node``        ``root.left ``=` `insert(node.left, data)` `    ``# Go to right subtree``    ``elif` `(data > node.data):``        ``root.right ``=` `insert(node.right, data)``        ` `    ``return` `root` `# Function to replace every element with the``# least greater element on its right``def` `replace(arr, n):``    ` `    ``global` `succ``    ``root ``=` `None` `    ``# Start from right to left``    ``for` `i ``in` `range``(n ``-` `1``, ``-``1``, ``-``1``):``        ``succ ``=` `None` `        ``# Insert current element into BST and``        ``# find its inorder successor``        ``root ``=` `insert(root, arr[i])` `        ``# Replace element by its inorder``        ``# successor in BST``        ``if` `(succ):``            ``arr[i] ``=` `succ.data``        ` `        ``# No inorder successor``        ``else``:  ``            ``arr[i] ``=` `-``1``            ` `    ``return` `arr` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``arr ``=` `[ ``8``, ``58``, ``71``, ``18``, ``31``, ``32``, ``63``,``            ``92``, ``43``, ``3``, ``91``, ``93``, ``25``, ``80``, ``28` `]``    ``n ``=` `len``(arr)``    ``succ ``=` `None` `    ``arr ``=` `replace(arr, n)` `    ``print``(``*``arr)` `# This code is contributed by mohit kumar 29`

## C#

 `// C# program to replace every element with``// the least greater element on its right``using` `System;` `class` `BinarySearchTree{``    ` `// A binary Tree node``public` `class` `Node``{``    ``public` `int` `data;``    ``public` `Node left, right;``    ` `    ``public` `Node(``int` `d)``    ``{``        ``data = d;``        ``left = right = ``null``;``    ``}``}` `// Root of BST``public` `static` `Node root;``public` `static` `Node succ;` `// Constructor``public` `BinarySearchTree()``{``    ``root = ``null``;``    ``succ = ``null``;``}` `// A utility function to insert a new node with``// given data in BST and find its successor``public` `static` `Node insert(Node node, ``int` `data)``{``    ` `    ``// If the tree is empty, return a new node``    ``if` `(node == ``null``)``    ``{``        ``node = ``new` `Node(data);``    ``}``    ` `    ``// If key is smaller than root's key,``    ``// go to left subtree and set successor``    ``// as current node``    ``if` `(data < node.data)``    ``{``        ``succ = node;``        ``node.left = insert(node.left, data);``    ``}``    ` `    ``// Go to right subtree``    ``else` `if` `(data > node.data)``    ``{``        ``node.right = insert(node.right, data);``    ``}``    ``return` `node;``}` `// Function to replace every element with the``// least greater element on its right``public` `static` `void` `replace(``int``[] arr, ``int` `n)``{``    ``//BinarySearchTree tree = new BinarySearchTree();``    ``// Start from right to left``    ``for``(``int` `i = n - 1; i >= 0; i--)``    ``{``        ``succ = ``null``;``        ` `        ``// Insert current element into BST and``        ``// find its inorder successor``        ``root = BinarySearchTree.insert(root, arr[i]);``        ` `        ``// Replace element by its inorder``        ``// successor in BST``        ``if` `(succ != ``null``)``        ``{``            ``arr[i] = succ.data;``        ``}``        ` `        ``// No inorder successor``        ``else``        ``{``            ``arr[i] = -1;``        ``}``    ``}``}` `// Driver code``static` `public` `void` `Main()``{``    ``int``[] arr = { 8, 58, 71, 18, 31,``                  ``32, 63, 92, 43, 3,``                  ``91, 93, 25, 80, 28 };``    ``int` `n = arr.Length;``    ` `    ``replace(arr, n);``    ` `    ``for``(``int` `i = 0; i < n; i++)``    ``{``        ``Console.Write(arr[i]+``" "``);``    ``}``}``}` `// This code is contributed by rag2127`

## Javascript

 ``
Output
`18 63 80 25 32 43 80 93 80 25 93 -1 28 -1 -1 `

The worst-case time complexity of the above solution is also O(n2) as it uses BST. The worst-case will happen when array is sorted in ascending or descending order. The complexity can easily be reduced to O(nlogn) by using balanced trees like red-black trees.

Another Approach:

We can use the Next Greater Element using stack algorithm to solve this problem in O(Nlog(N)) time and O(N) space.

Algorithm:

1. First, we take an array of pairs namely temp, and store each element and its index in this array,i.e. temp[i] will be storing {arr[i],i}.
2. Sort the array according to the array elements.
3. Now get the next greater index for each and every index of the temp array in an array namely index by using Next Greater Element using stack.
4. Now index[i] stores the index of the next least greater element of the element temp[i].first and if index[i] is -1, then it means that there is no least greater element of the element temp[i].second at its right side.
5. Now take a result array where result[i] will be equal to a[indexes[temp[i].second]] if index[i] is not -1 otherwise result[i] will be equal to -1.

Below is the implementation of the above approach

## C++

 `#include ``using` `namespace` `std;``// function to get the next least greater index for each and``// every temp.second of the temp array using stack this``// function is similar to the Next Greter element for each``// and every element of an array using stack difference is``// we are finding the next greater index not value and the``// indexes are stored in the temp[i].second for all i``vector<``int``> nextGreaterIndex(vector >& temp)``{``    ``int` `n = temp.size();``    ``// initially result[i] for all i is -1``    ``vector<``int``> res(n, -1);``    ``stack<``int``> stack;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``// if the stack is empty or this index is smaller``        ``// than the index stored at top of the stack then we``        ``// push this index to the stack``        ``if` `(stack.empty() || temp[i].second < stack.top())``            ``stack.push(``                ``temp[i].second); ``// notice temp[i].second is``                                 ``// the index``        ``// else this index (i.e. temp[i].second) is greater``        ``// than the index stored at top of the stack we pop``        ``// all the indexes stored at stack's top and for all``        ``// these indexes we make this index i.e.``        ``// temp[i].second as their next greater index``        ``else` `{``            ``while` `(!stack.empty()``                   ``&& temp[i].second > stack.top()) {``                ``res[stack.top()] = temp[i].second;``                ``stack.pop();``            ``}``            ``// after that push the current index to the stack``            ``stack.push(temp[i].second);``        ``}``    ``}``    ``// now res will store the next least greater indexes for``    ``// each and every indexes stored at temp[i].second for``    ``// all i``    ``return` `res;``}``// now we will be using above function for finding the next``// greater index for each and every indexes stored at``// temp[i].second``vector<``int``> replaceByLeastGreaterUsingStack(``int` `arr[],``                                            ``int` `n)``{``    ``// first of all in temp we store the pairs of {arr[i].i}``    ``vector > temp;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``temp.push_back({ arr[i], i });``    ``}``    ``// we sort the temp according to the first of the pair``    ``// i.e value``    ``sort(temp.begin(), temp.end());``    ``// now indexes vector will store the next greater index``    ``// for each temp[i].second index``    ``vector<``int``> indexes = nextGreaterIndex(temp);``    ``// we initialize a result vector with all -1``    ``vector<``int``> res(n, -1);``    ``for` `(``int` `i = 0; i < n; i++) {``        ``// now if there is no next greater index after the``        ``// index temp[i].second the result will be -1``        ``// otherwise the result will be the element of the``        ``// array arr at index indexes[temp[i].second]``        ``if` `(indexes[temp[i].second] != -1)``            ``res[temp[i].second]``                ``= arr[indexes[temp[i].second]];``    ``}``    ``// return the res which will store the least greater``    ``// element of each and every element in the array at its``    ``// right side``    ``return` `res;``}``// driver code``int` `main()``{``    ``int` `arr[] = { 8,  58, 71, 18, 31, 32, 63, 92,``                  ``43, 3,  91, 93, 25, 80, 28 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);``    ``auto` `res = replaceByLeastGreaterUsingStack(arr, n);``    ``cout << ``"Least Greater elements on the right side are "``         ``<< endl;``    ``for` `(``int` `i : res)``        ``cout << i << ``' '``;``    ``cout << endl;``    ``return` `0;``} ``// this code is contributed by Dipti Prakash Sinha`
Output
```Least Greater elements on the right side are
18 63 80 25 32 43 80 93 80 25 93 -1 28 -1 -1 ```