# Maximum Difference between Two Elements such that Larger Element Appears after the Smaller Element

Given an array arr[] of integers, find out the maximum difference between any two elements such that larger element appears after the smaller number.

Examples :

Input : arr = {2, 3, 10, 6, 4, 8, 1}
Output : 8
Explanation : The maximum difference is between 10 and 2.

Input : arr = {7, 9, 5, 6, 3, 2}
Output : 2
Explanation : The maximum difference is between 9 and 7.

Naive Approach:

We can solve this problem using two loops. In the outer loop, pick elements one by one and in the inner loop calculate the difference of the picked element with every other element in the array and compare the difference with the maximum difference calculated so far.

Below is the implementation of the above approach :

## C++

 `// C++ program to find Maximum difference ``// between two elements such that larger ``// element appears after the smaller number``#include ``using` `namespace` `std;` `/* The function assumes that there are ``   ``at least two elements in array. The ``   ``function returns a negative value if the``   ``array is sorted in decreasing order and  ``   ``returns 0 if elements are equal */``int` `maxDiff(``int` `arr[], ``int` `arr_size)``{     ``  ``int` `max_diff = arr[1] - arr[0];``  ``for` `(``int` `i = 0; i < arr_size; i++)``  ``{``    ``for` `(``int` `j = i+1; j < arr_size; j++)``    ``{     ``      ``if` `(arr[j] - arr[i] > max_diff) ``        ``max_diff = arr[j] - arr[i];``    ``} ``  ``}         ``  ``return` `max_diff;``} ` `/* Driver program to test above function */``int` `main()``{``  ``int` `arr[] = {1, 2, 90, 10, 110};``  ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``  ` `  ``// Function calling``  ``cout << ``"Maximum difference is "` `<< maxDiff(arr, n);` `  ``return` `0;``}`

## C

 `#include` `/* The function assumes that there are at least two``   ``elements in array.``   ``The function returns a negative value if the array is``   ``sorted in decreasing order. ``   ``Returns 0 if elements are equal */``int` `maxDiff(``int` `arr[], ``int` `arr_size)``{     ``  ``int` `max_diff = arr[1] - arr[0];``  ``int` `i, j;``  ``for` `(i = 0; i < arr_size; i++)``  ``{``    ``for` `(j = i+1; j < arr_size; j++)``    ``{        ``      ``if` `(arr[j] - arr[i] > max_diff)   ``         ``max_diff = arr[j] - arr[i];``    ``}    ``  ``}          ``  ``return` `max_diff;``}    ` `/* Driver program to test above function */``int` `main()``{``  ``int` `arr[] = {1, 2, 90, 10, 110};``  ``printf``(``"Maximum difference is %d"``,  maxDiff(arr, 5));``  ``getchar``();``  ``return` `0;``}`

## Java

 `// Java program to find Maximum difference ``// between two elements such that larger ``// element appears after the smaller number``import` `java.io.*;``public` `class` `MaximumDifference ``{``    ``/* The function assumes that there are at least two``       ``elements in array.``       ``The function returns a negative value if the array is``       ``sorted in decreasing order. ``       ``Returns 0 if elements are equal */``    ``int` `maxDiff(``int` `arr[], ``int` `arr_size) ``    ``{``        ``int` `max_diff = arr[``1``] - arr[``0``];``        ``int` `i, j;``        ``for` `(i = ``0``; i < arr_size; i++) ``        ``{``            ``for` `(j = i + ``1``; j < arr_size; j++) ``            ``{``                ``if` `(arr[j] - arr[i] > max_diff)``                    ``max_diff = arr[j] - arr[i];``            ``}``        ``}``        ``return` `max_diff;``    ``}` `    ``/* Driver program to test above functions */``    ``public` `static` `void` `main(String[] args) ``    ``{``        ``MaximumDifference maxdif = ``new` `MaximumDifference();``        ``int` `arr[] = {``1``, ``2``, ``90``, ``10``, ``110``};``        ``System.out.println(``"Maximum difference is "` `+ ``                                ``maxdif.maxDiff(arr, ``5``));``    ``}``}` `// This code has been contributed by Mayank Jaiswal`

## Python3

 `# Python 3 code to find Maximum difference``# between two elements such that larger ``# element appears after the smaller number` `# The function assumes that there are at ``# least two elements in array. The function ``# returns a negative value if the array is``# sorted in decreasing order. Returns 0 ``# if elements are equal``def` `maxDiff(arr, arr_size):``    ``max_diff ``=` `arr[``1``] ``-` `arr[``0``]``    ` `    ``for` `i ``in` `range``( arr_size ):``        ``for` `j ``in` `range``( i``+``1``, arr_size ):``            ``if``(arr[j] ``-` `arr[i] > max_diff): ``                ``max_diff ``=` `arr[j] ``-` `arr[i]``    ` `    ``return` `max_diff``    ` `# Driver program to test above function ``arr ``=` `[``1``, ``2``, ``90``, ``10``, ``110``]``size ``=` `len``(arr)``print` `(``"Maximum difference is"``, maxDiff(arr, size))` `# This code is contributed by Swetank Modi`

## C#

 `// C# code to find Maximum difference``using` `System;` `class` `GFG {` `    ``// The function assumes that there ``    ``// are at least two elements in array.``    ``// The function returns a negative ``    ``// value if the array is sorted in ``    ``// decreasing order. Returns 0 if``    ``// elements are equal ``    ``static` `int` `maxDiff(``int``[] arr, ``int` `arr_size)``    ``{``        ``int` `max_diff = arr[1] - arr[0];``        ``int` `i, j;``        ``for` `(i = 0; i < arr_size; i++) {``            ``for` `(j = i + 1; j < arr_size; j++) {``                ``if` `(arr[j] - arr[i] > max_diff)``                    ``max_diff = arr[j] - arr[i];``            ``}``        ``}``        ``return` `max_diff;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{` `        ``int``[] arr = { 1, 2, 90, 10, 110 };``        ``Console.Write(``"Maximum difference is "` `+ ``                                ``maxDiff(arr, 5));``    ``}``}` `// This code is contributed by Sam007`

## Javascript

 ``

## PHP

 ` ``\$max_diff``) ``        ``\$max_diff` `= ``\$arr``[``\$j``] - ``\$arr``[``\$i``];``    ``} ``}     ``return` `\$max_diff``;``} ` `// Driver Code``\$arr` `= ``array``(1, 2, 90, 10, 110);``\$n` `= sizeof(``\$arr``);` `// Function calling``echo` `"Maximum difference is "` `. ``             ``maxDiff(``\$arr``, ``\$n``);` `// This code is contributed ``// by Akanksha Rai(Abby_akku)`

Output
`Maximum difference is 109`

Time Complexity : O(n^2)
Auxiliary Space : O(1)

Efficient Approach:

In this method, instead of taking difference of the picked element with every other element, we take the difference with the minimum element found so far. So we need to keep track of 2 things:
1) Maximum difference found so far (max_diff).
2) Minimum number visited so far (min_element).

Below is the implementation of the above idea:

## C++

 `// C++ program to find Maximum difference ``// between two elements such that larger ``// element appears after the smaller number``#include ``using` `namespace` `std;` `/* The function assumes that there are ``   ``at least two elements in array. The ``   ``function returns a negative value if the``   ``array is sorted in decreasing order and  ``   ``returns 0 if elements are equal */``int` `maxDiff(``int` `arr[], ``int` `arr_size)``{``     ``// Maximum difference found so far``     ``int` `max_diff = arr[1] - arr[0];``     ` `     ``// Minimum number visited so far ``     ``int` `min_element = arr[0];``     ``for``(``int` `i = 1; i < arr_size; i++)``     ``{     ``       ``if` `(arr[i] - min_element > max_diff)                             ``       ``max_diff = arr[i] - min_element;``       ` `       ``if` `(arr[i] < min_element)``       ``min_element = arr[i];                     ``     ``}``     ` `     ``return` `max_diff;``} ` `/* Driver program to test above function */``int` `main()``{``  ``int` `arr[] = {1, 2, 90, 10, 110};``  ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``  ` `  ``// Function calling``  ``cout << ``"Maximum difference is "` `<< maxDiff(arr, n);` `  ``return` `0;``}`

## C

 `#include` `/* The function assumes that there are at least two``elements in array.``The function returns a negative value if the array is``sorted in decreasing order.``Returns 0 if elements are equal */``int` `maxDiff(``int` `arr[], ``int` `arr_size)``{``int` `max_diff = arr[1] - arr[0];``int` `min_element = arr[0];``int` `i;``for``(i = 1; i < arr_size; i++)``{     ``    ``if` `(arr[i] - min_element > max_diff)                             ``    ``max_diff = arr[i] - min_element;``    ``if` `(arr[i] < min_element)``        ``min_element = arr[i];                     ``}``return` `max_diff;``} ` `/* Driver program to test above function */``int` `main()``{``int` `arr[] = {1, 2, 6, 80, 100};``int` `size = ``sizeof``(arr)/``sizeof``(arr[0]);``printf``(``"Maximum difference is %d"``, maxDiff(arr, size));``getchar``();``return` `0;``}`

## Java

 `// Java program to find Maximum difference ``// between two elements such that larger ``// element appears after the smaller number``import` `java.io.*;``public` `class` `MaximumDifference ``{``    ``/* The function assumes that there are at least two``       ``elements in array.``       ``The function returns a negative value if the array is``       ``sorted in decreasing order.``       ``Returns 0 if elements are equal  */``    ``int` `maxDiff(``int` `arr[], ``int` `arr_size) ``    ``{``        ``int` `max_diff = arr[``1``] - arr[``0``];``        ``int` `min_element = arr[``0``];``        ``int` `i;``        ``for` `(i = ``1``; i < arr_size; i++) ``        ``{``            ``if` `(arr[i] - min_element > max_diff)``                ``max_diff = arr[i] - min_element;``            ``if` `(arr[i] < min_element)``                ``min_element = arr[i];``        ``}``        ``return` `max_diff;``    ``}` `    ``/* Driver program to test above functions */``    ``public` `static` `void` `main(String[] args) ``    ``{``        ``MaximumDifference maxdif = ``new` `MaximumDifference();``        ``int` `arr[] = {``1``, ``2``, ``90``, ``10``, ``110``};``        ``int` `size = arr.length;``        ``System.out.println(``"MaximumDifference is "` `+ ``                                ``maxdif.maxDiff(arr, size));``    ``}``}` `// This code has been contributed by Mayank Jaiswal`

## Python3

 `# Python 3 code to find Maximum difference``# between two elements such that larger ``# element appears after the smaller number` `# The function assumes that there are ``# at least two elements in array.``# The function returns a negative ``# value if the array is sorted in ``# decreasing order. Returns 0 if ``# elements are equal``def` `maxDiff(arr, arr_size):``    ``max_diff ``=` `arr[``1``] ``-` `arr[``0``]``    ``min_element ``=` `arr[``0``]``    ` `    ``for` `i ``in` `range``( ``1``, arr_size ):``        ``if` `(arr[i] ``-` `min_element > max_diff):``            ``max_diff ``=` `arr[i] ``-` `min_element``    ` `        ``if` `(arr[i] < min_element):``            ``min_element ``=` `arr[i]``    ``return` `max_diff``    ` `# Driver program to test above function ``arr ``=` `[``1``, ``2``, ``6``, ``80``, ``100``]``size ``=` `len``(arr)``print` `(``"Maximum difference is"``, ``        ``maxDiff(arr, size))` `# This code is contributed by Swetank Modi`

## C#

 `// C# code to find Maximum difference``using` `System;` `class` `GFG {``    ` `    ``// The function assumes that there ``    ``// are at least two elements in array.``    ``// The function returns a negative ``    ``// value if the array is sorted in``    ``// decreasing order.Returns 0 if ``    ``// elements are equal ``    ``static` `int` `maxDiff(``int``[] arr, ``int` `arr_size)``    ``{``        ``int` `max_diff = arr[1] - arr[0];``        ``int` `min_element = arr[0];``        ``int` `i;``        ``for` `(i = 1; i < arr_size; i++) {``            ``if` `(arr[i] - min_element > max_diff)``                ``max_diff = arr[i] - min_element;``            ``if` `(arr[i] < min_element)``                ``min_element = arr[i];``        ``}``        ``return` `max_diff;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int``[] arr = { 1, 2, 90, 10, 110 };``        ``int` `size = arr.Length;``        ``Console.Write(``"MaximumDifference is "` `+``                               ``maxDiff(arr, size));``    ``}``}` `// This code is contributed by Sam007`

## Javascript

 ``

## PHP

 ` ``\$max_diff``)                             ``    ``\$max_diff` `= ``\$arr``[``\$i``] - ``\$min_element``;``        ` `    ``if` `(``\$arr``[``\$i``] < ``\$min_element``)``    ``\$min_element` `= ``\$arr``[``\$i``];                     ``    ``}``    ` `    ``return` `\$max_diff``;``}` `// Driver Code``\$arr` `= ``array``(1, 2, 90, 10, 110);``\$n` `= ``count``(``\$arr``);` `// Function calling``echo` `"Maximum difference is "` `.``             ``maxDiff(``\$arr``, ``\$n``);` `// This code is contributed by Sam007``?>`

Output
`Maximum difference is 109`

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

First find the difference between the adjacent elements of the array and store all differences in an auxiliary array diff[] of size n-1. Now this problems turns into finding the maximum sum subarray of this difference array. Thanks to Shubham Mittal for suggesting this solution.

Below is the implementation :

## C++

 `// C++ program to find Maximum difference ``// between two elements such that larger ``// element appears after the smaller number``#include ``using` `namespace` `std;` `/* The function assumes that there are ``   ``at least two elements in array. The ``   ``function returns a negative value if the``   ``array is sorted in decreasing order and  ``   ``returns 0 if elements are equal */``int` `maxDiff (``int` `arr[], ``int` `n)``{``    ``// Initialize diff, current sum and max sum``    ``int` `diff = arr[1]-arr[0];``    ``int` `curr_sum = diff;``    ``int` `max_sum = curr_sum;` `    ``for``(``int` `i=1; i 0)``        ``curr_sum += diff;``        ``else``        ``curr_sum = diff;` `        ``// Update max sum, if needed``        ``if` `(curr_sum > max_sum)``        ``max_sum = curr_sum;``    ``}` `    ``return` `max_sum;``}` `/* Driver program to test above function */``int` `main()``{``  ``int` `arr[] = {80, 2, 6, 3, 100};``  ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``  ` `  ``// Function calling``  ``cout << ``"Maximum difference is "` `<< maxDiff(arr, n);` `  ``return` `0;``}`

## Java

 `// Java program to find Maximum ``// difference between two elements ``// such that larger element appears ``// after the smaller number ``import` `java.io.*;``public` `class` `GFG``{``    ` `/* The function assumes that there``are at least two elements in array. ``The function returns a negative ``value if the array is sorted in ``decreasing order and returns 0 if``elements are equal */``static` `int` `maxDiff (``int` `arr[], ``int` `n) ``{ ``    ``// Initialize diff, current ``    ``// sum and max sum ``    ``int` `diff = arr[``1``] - arr[``0``]; ``    ``int` `curr_sum = diff; ``    ``int` `max_sum = curr_sum; ` `    ``for``(``int` `i = ``1``; i < n - ``1``; i++) ``    ``{ ``        ``// Calculate current diff ``        ``diff = arr[i + ``1``] - arr[i]; ` `        ``// Calculate current sum ``        ``if` `(curr_sum > ``0``) ``        ``curr_sum += diff; ``        ``else``        ``curr_sum = diff; ` `        ``// Update max sum, if needed ``        ``if` `(curr_sum > max_sum) ``        ``max_sum = curr_sum; ``    ``} ` `    ``return` `max_sum; ``} ` `// Driver Code``public` `static` `void` `main(String[] args) ``{ ``int` `arr[] = {``80``, ``2``, ``6``, ``3``, ``100``}; ``int` `n = arr.length; ``    ` `// Function calling ``System.out.print(``"Maximum difference is "` `+ ``                          ``maxDiff(arr, n)); ``}``} ` `// This code is contributed by Smitha`

## Python3

 `# Python3 program to find Maximum difference ``# between two elements such that larger ``# element appears after the smaller number` `# The function assumes that there are ``# at least two elements in array. The ``# function returns a negative value if ``# the array is sorted in decreasing ``# order and returns 0 if elements are equal``def` `maxDiff (arr, n):``    ` `    ``# Initialize diff, current ``    ``# sum and max sum``    ``diff ``=` `arr[``1``] ``-` `arr[``0``]``    ``curr_sum ``=` `diff``    ``max_sum ``=` `curr_sum` `    ``for` `i ``in` `range``(``1``, n ``-` `1``):``        ` `        ``# Calculate current diff``        ``diff ``=` `arr[i ``+` `1``] ``-` `arr[i]` `        ``# Calculate current sum``        ``if` `(curr_sum > ``0``):``            ``curr_sum ``+``=` `diff``        ``else``:``            ``curr_sum ``=` `diff` `        ``# Update max sum, if needed``        ``if` `(curr_sum > max_sum):``            ``max_sum ``=` `curr_sum``    ``return` `max_sum` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=` `[``80``, ``2``, ``6``, ``3``, ``100``]``    ``n ``=` `len``(arr)``        ` `    ``# Function calling``    ``print``(``"Maximum difference is"``,``                  ``maxDiff(arr, n))` `# This code is contributed ``# by 29AjayKumar`

## C#

 `// C# program to find Maximum ``// difference between two elements ``// such that larger element appears ``// after the smaller number ``using` `System;``class` `GFG``{``    ` `/* The function assumes that there``are at least two elements in array. ``The function returns a negative ``value if the array is sorted in ``decreasing order and returns 0 if``elements are equal */``static` `int` `maxDiff (``int``[] arr, ``int` `n) ``{ ``    ``// Initialize diff, current ``    ``// sum and max sum ``    ``int` `diff = arr[1] - arr[0]; ``    ``int` `curr_sum = diff; ``    ``int` `max_sum = curr_sum; ` `    ``for``(``int` `i = 1; i < n - 1; i++) ``    ``{ ``        ``// Calculate current diff ``        ``diff = arr[i + 1] - arr[i]; ` `        ``// Calculate current sum ``        ``if` `(curr_sum > 0) ``        ``curr_sum += diff; ``        ``else``        ``curr_sum = diff; ` `        ``// Update max sum, if needed ``        ``if` `(curr_sum > max_sum) ``        ``max_sum = curr_sum; ``    ``} ` `    ``return` `max_sum; ``} ` `// Driver Code``public` `static` `void` `Main() ``{ ``int``[] arr = {80, 2, 6, 3, 100}; ``int` `n = arr.Length; ``    ` `// Function calling ``Console.WriteLine(``"Maximum difference is "` `+ ``                        ``maxDiff(arr, n)); ``}``} ` `// This code is contributed ``// by Akanksha Rai(Abby_akku)`

## Javascript

 ``

## PHP

 ` 0)``            ``\$curr_sum` `+= ``\$diff``;``        ``else``            ``\$curr_sum` `= ``\$diff``;` `        ``// Update max sum, if needed``        ``if` `(``\$curr_sum` `> ``\$max_sum``)``        ``\$max_sum` `= ``\$curr_sum``;``    ``}` `    ``return` `\$max_sum``;``}` `// Driver Code``\$arr` `= ``array``(80, 2, 6, 3, 100);``\$n` `= sizeof(``\$arr``);` `// Function calling``echo` `"Maximum difference is "``,``            ``maxDiff(``\$arr``, ``\$n``);` `// This code is contributed ``// by Sach_code``?>`

Output
`Maximum difference is 98`

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

Below is a variation of this problem:
Maximum difference of sum of elements in two rows in a matrix
Please write comments if you find any bug in above codes/algorithms, or find other ways to solve the same problem

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