# 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 given array. If next greater element is not available in 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 '_'.
```

Asked in : Zoho

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

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

 `// Simple CPP 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; ` `} `

 `// 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 anuj_67. `

 `# Simple Python 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) `

 `// 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. `

 ` `

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 into set, we search elements. After we find iterator of the searched element, we move iterator to next (note that set stores elements in sorted order) to find element which is just greater.

 `// Efficient CPP 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; ` `} `

Output :
```7 6 10 9 15 3 2 _ 8
```

Time Complexity : O(n Log n). Note that 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 in same time and same auxiliary space.

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Improved By : jit_t, vt_m, manishshaw1

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