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Smallest greater elements in whole array

An array is given of n length, and we need to calculate the next greater element for each element in the given array. If the next greater element is not available in the given array then we need to fill ‘_’ at that index place.

Examples :

```Input :  6 3 9 8 10 2 1 15 7
Output : 7 6 10 9 15 3 2 _ 8
Here every element of array has next greater
element but at index 7,
15 is the greatest element of given array
and no other element is greater from 15
so at the index of 15 we fill with '_' .

Input  : 13 6 7 12
Output : _ 7 12 13
Here, at index 0, 13 is the greatest
value in given array and no other
array element is greater from 13 so
at index 0 we fill '_'.```

A simple solution is to use two loops nested. The outer loop picks all elements one by one and the inner loop finds the next greater element by linearly searching from beginning to end.

C++

 `// Simple C++ program to find smallest greater element in` `// whole array for every element.` `#include ` `using` `namespace` `std;`   `void` `smallestGreater(``int` `arr[], ``int` `n)` `{` `    ``for` `(``int` `i = 0; i < n; i++) {`   `        ``// Find the closest greater element for arr[j] in` `        ``// the entire array.` `        ``int` `diff = INT_MAX, closest = -1;` `        ``for` `(``int` `j = 0; j < n; j++) {` `            ``if` `(arr[i] < arr[j] && arr[j] - arr[i] < diff) {` `                ``diff = arr[j] - arr[i];` `                ``closest = j;` `            ``}` `        ``}`   `        ``// Check if arr[i] is largest` `        ``(closest == -1) ? cout << ``"_ "` `                        ``: cout << arr[closest] << ``" "``;` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `ar[] = { 6, 3, 9, 8, 10, 2, 1, 15, 7 };` `    ``int` `n = ``sizeof``(ar) / ``sizeof``(ar[0]);` `    ``smallestGreater(ar, n);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

C

 `// Simple C program to find smallest greater element in` `// whole array for every element.` `#include ` `#include `   `void` `smallestGreater(``int` `arr[], ``int` `n)` `{` `    ``for` `(``int` `i = 0; i < n; i++) {`   `        ``// Find the closest greater element for arr[j] in` `        ``// the entire array.` `        ``int` `diff = INT_MAX, closest = -1;` `        ``for` `(``int` `j = 0; j < n; j++) {` `            ``if` `(arr[i] < arr[j] && arr[j] - arr[i] < diff) {` `                ``diff = arr[j] - arr[i];` `                ``closest = j;` `            ``}` `        ``}`   `        ``// Check if arr[i] is largest` `        ``(closest == -1) ? ``printf``(``"_ "``)` `                        ``: ``printf``(``"%d "``,arr[closest]);` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `ar[] = { 6, 3, 9, 8, 10, 2, 1, 15, 7 };` `    ``int` `n = ``sizeof``(ar) / ``sizeof``(ar[0]);` `    ``smallestGreater(ar, n);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

Java

 `// Simple Java program to find smallest greater element in` `// whole array for every element.` `import` `java.io.*;`   `class` `GFG {` `    ``static` `void` `smallestGreater(``int` `arr[], ``int` `n)` `    ``{` `        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``// Find the closest greater element for arr[j]` `            ``// in  the entire array.` `            ``int` `diff = Integer.MAX_VALUE;` `            ``int` `closest = -``1``;` `            ``for` `(``int` `j = ``0``; j < n; j++) {` `                ``if` `(arr[i] < arr[j] && arr[j] - arr[i] < diff) {` `                    ``diff = arr[j] - arr[i];` `                    ``closest = j;` `                ``}` `            ``}`   `            ``// Check if arr[i] is largest` `            ``if` `(closest == -``1``)` `                ``System.out.print(``"_ "``);` `            ``else` `                ``System.out.print(arr[closest] + ``" "``);` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `ar[] = { ``6``, ``3``, ``9``, ``8``, ``10``, ``2``, ``1``, ``15``, ``7` `};` `        ``int` `n = ar.length;` `        ``smallestGreater(ar, n);` `    ``}` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

Python3

 `# Simple Python3 program to find smallest` `# greater element in whole array for ` `# every element.` `def` `smallestGreater(arr, n) :` `    ``for` `i ``in` `range``(``0``, n) :`   `        ``# Find the closest greater element ` `        ``# for arr[j] in the entire array.` `        ``diff ``=` `1000``; ` `        ``closest ``=` `-``1``;` `        ``for` `j ``in` `range``(``0``, n) :` `            ``if` `( arr[i] < arr[j] ``and` `                  ``arr[j] ``-` `arr[i] < diff) :` `                ``diff ``=` `arr[j] ``-` `arr[i];` `                ``closest ``=` `j;     ` `        `  `        ``# Check if arr[i] is largest` `        ``if` `(closest ``=``=` `-``1``) :` `            ``print` `(``"_ "``, end ``=` `"");` `        ``else` `:` `            ``print` `(``"{} "``.``format``(arr[closest]),` `                                    ``end ``=` `"");`   `# Driver code` `ar ``=` `[``6``, ``3``, ``9``, ``8``, ``10``, ``2``, ``1``, ``15``, ``7``];` `n ``=` `len``(ar) ;` `smallestGreater(ar, n);`   `# This code is contributed by Manish Shaw` `# (manishshaw1)`

C#

 `// Simple C# program to find` `// smallest greater element in ` `// whole array for every element.` `using` `System;`   `class` `GFG ` `{` `static` `void` `smallestGreater(``int` `[]arr, ` `                            ``int` `n)` `{` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{`   `        ``// Find the closest greater` `        ``// element for arr[j] in ` `        ``// the entire array.` `        ``int` `diff = ``int``.MaxValue;` `        ``int` `closest = -1;` `        ``for` `(``int` `j = 0; j < n; j++) ` `        ``{` `            ``if` `(arr[i] < arr[j] && ` `                ``arr[j] - arr[i] < diff)` `            ``{` `                ``diff = arr[j] - arr[i];` `                ``closest = j;         ` `            ``}` `        ``}` `        `  `        ``// Check if arr[i] is largest` `        ``if``(closest == -1)` `        ``Console.Write( ``"_ "` `);` `        ``else` `        ``Console.Write(arr[closest] + ``" "``);` `    ``}` `}`   `// Driver code` `public` `static` `void` `Main() ` `{` `    ``int` `[]ar = {6, 3, 9, 8, 10, ` `                ``2, 1, 15, 7};` `    ``int` `n = ar.Length;` `    ``smallestGreater(ar, n);` `}` `}`   `// This code is contributed by anuj_67.`

PHP

 ``

Javascript

 ``

Output:

`7 6 10 9 15 3 2 _ 8`

Time Complexity: O(n*n)
Auxiliary Space: O(1)

An efficient solution is to one by one insert elements in a set (A self-balancing binary search tree). After inserting it into the set, we search elements. After we find the iterator of the searched element, we move the iterator to next (note that set stores elements in sorted order) to find an element that is just greater.

C++

 `// Efficient C++ program to find smallest` `// greater element in whole array for ` `// every element.` `#include ` `using` `namespace` `std;`   `void` `smallestGreater(``int` `arr[], ``int` `n)` `{` `    ``set<``int``> s;` `    ``for` `(``int` `i = 0; i < n; i++) ` `       ``s.insert(arr[i]);`   `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{` `       ``auto` `it = s.find(arr[i]);` `       ``it++;` `       ``if` `(it != s.end())           ` `          ``cout << *it << ``" "``;       ` `       ``else` `          ``cout << ``"_ "``;` `     ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `ar[] = { 6, 3, 9, 8, 10, 2, 1, 15, 7 };` `    ``int` `n = ``sizeof``(ar) / ``sizeof``(ar[0]);` `    ``smallestGreater(ar, n);` `    ``return` `0;` `}`

Java

 `// Efficient Java program to ` `// find smallest greater element ` `// in whole array for every element.` `import` `java.util.*;` `class` `GFG{`   `static` `void` `smallestGreater(``int` `arr[], ` `                            ``int` `n) ` `{` `  ``HashSet s = ``new` `HashSet<>();` `  ``for` `(``int` `i = ``0``; i < n; i++)` `    ``s.add(arr[i]);` `  ``Vector newAr = ``new` `Vector<>();` `  ``for` `(``int` `p : s) ` `  ``{` `    ``newAr.add(p);` `  ``}`   `  ``for` `(``int` `i = ``0``; i < n; i++) ` `  ``{` `    ``int` `temp = lowerBound(newAr, ``0``, ` `                          ``newAr.size(), ` `                          ``arr[i]);` `    ``if` `(temp  < n)` `      ``System.out.print(newAr.get(temp) + ``" "``);` `    ``else` `      ``System.out.print(``"_ "``);` `  ``}` `}`   `static` `int` `lowerBound(Vector vec, ` `                      ``int` `low, ``int` `high, ` `                      ``int` `element) ` `{` `  ``int``[] array = ``new` `int``[vec.size()];` `  ``int` `k = ``0``;` `  ``for` `(Integer val : vec) ` `  ``{` `    ``array[k] = val;` `    ``k++;` `  ``}` `  `  `  ``// vec.clear();` `  ``while` `(low < high)` `  ``{` `    ``int` `middle = low + ` `                 ``(high - low) / ``2``;` `    ``if` `(element > array[middle]) ` `    ``{` `      ``low = middle + ``1``;` `    ``} ``else` `    ``{` `      ``high = middle;` `    ``}` `  ``}`   `  ``return` `low+``1``;` `}`   `// Driver code` `public` `static` `void` `main(String[] args) ` `{` `  ``int` `ar[] = {``6``, ``3``, ``9``, ``8``, ` `              ``10``, ``2``, ``1``, ``15``, ``7``};` `  ``int` `n = ar.length;` `  ``smallestGreater(ar, n);` `}` `}`   `// This code is contributed by gauravrajput1`

Python3

 `# Efficient Python3 program to` `# find smallest greater element` `# in whole array for every element` `def` `smallestGreater(arr, n):` `    `  `    ``s ``=` `set``()` `    `  `    ``for` `i ``in` `range``(n):` `        ``s.add(arr[i])` `        `  `    ``newAr ``=` `[]` `    `  `    ``for` `p ``in` `s:` `        ``newAr.append(p)`   `    ``for` `i ``in` `range``(n):` `        ``temp ``=` `lowerBound(newAr, ``0``, ``len``(newAr),` `                          ``arr[i])` `                          `  `        ``if` `(temp < n):` `            ``print``(newAr[temp], end ``=` `" "``)` `        ``else``:` `            ``print``(``"_ "``, end ``=` `"")`   `def` `lowerBound(vec, low, high, element):` `    `  `    ``array ``=` `[``0``] ``*` `(``len``(vec))` `    `  `    ``k ``=` `0` `    `  `    ``for` `val ``in` `vec:` `        ``array[k] ``=` `val` `        ``k ``+``=` `1` `        `  `    ``# vec.clear();` `    ``while` `(low < high):` `        ``middle ``=` `low ``+` `int``((high ``-` `low) ``/` `2``)` `        `  `        ``if` `(element > array[middle]):` `            ``low ``=` `middle ``+` `1` `        ``else``:` `            ``high ``=` `middle`   `    ``return` `low ``+` `1`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    `  `    ``ar ``=` `[ ``6``, ``3``, ``9``, ``8``, ``10``, ``2``, ``1``, ``15``, ``7` `]` `    ``n ``=` `len``(ar)` `    `  `    ``smallestGreater(ar, n)`   `# This code is contributed by shikhasingrajput`

C#

 `// Efficient C# program to` `// find smallest greater element` `// in whole array for every element.` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG{`   `static` `void` `smallestGreater(``int``[] arr, ` `                                ``int` `n)` `{` `  ``HashSet<``int``> s = ``new` `HashSet<``int``>();` `  ``for` `(``int` `i = 0; i < n; i++)` `  ``{` `    ``s.Add(arr[i]);` `  ``}` `  `  `  ``int``[] newAr = ``new` `int``[s.Count];` `  ``int` `j = 0;` `  ``foreach``(``int` `p ``in` `s)` `  ``{` `    ``newAr[j] = p;` `    ``j++;` `  ``}` `  `  `  ``Array.Sort(newAr);` `  `  `  ``for` `(``int` `i = 0; i < n; i++) ` `  ``{` `    ``int` `temp = lowerBound(newAr, 0, ` `                          ``newAr.GetLength(0), ` `                          ``arr[i]);` `    ``if` `(temp < n)` `      ``Console.Write(newAr[temp] + ``" "``);` `    ``else` `      ``Console.Write(``"_ "``);` `  ``}` `}`   `static` `int` `lowerBound(``int``[] array, ``int` `low, ` `                      ``int` `high, ``int` `element)` `{` `  ``while` `(low < high) ` `  ``{` `    ``int` `middle = low + (high - ` `                 ``low) / 2;` `    `  `    ``if` `(element > array[middle]) ` `    ``{` `      ``low = middle + 1;` `    ``}` `    ``else` `    ``{` `      ``high = middle;` `    ``}` `  ``}` `  ``return` `low + 1;` `}`   `// Driver code` `public` `static` `void` `Main(String[] args)` `{` `  ``int``[] ar = {6, 3, 9, 8, ` `              ``10, 2, 1, 15, 7};` `  ``int` `n = ar.Length;` `  ``smallestGreater(ar, n);` `}` `}`   `// This code is contributed by 29AjayKumar`

Javascript

 ``

Output :

`7 6 10 9 15 3 2 _ 8`

Time Complexity: O(n Log n). Note that the self-balancing search tree (implemented by set in C++) insert operations take O(Log n) time to insert and find.
Auxiliary Space: O(n)

We can also use sorting followed by binary searches to solve the above problem at the same time and the same auxiliary space.

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