Given an array of n integers where each value represents number of chocolates in a packet. Each packet can have variable number of chocolates. There are m students, the task is to distribute chocolate packets such that:

- Each student gets one packet.
- The difference between the number of chocolates in packet with maximum chocolates and packet with minimum chocolates given to the students is minimum.

**Examples:**

Input :arr[] = {7, 3, 2, 4, 9, 12, 56}

m = 3

Output:Minimum Difference is 2

We have seven packets of chocolates and

we need to pick three packets for 3 students

If we pick 2, 3 and 4, we get the minimum

difference between maximum and minimum packet

sizes.

Input :arr[] = {3, 4, 1, 9, 56, 7, 9, 12}

m = 5

Output:Minimum Difference is 6

The set goes like 3,4,7,9,9 and the output

is 9-3 = 6

Input :arr[] = {12, 4, 7, 9, 2, 23, 25, 41,

30, 40, 28, 42, 30, 44, 48,

43, 50}

m = 7

Output:Minimum Difference is 10

We need to pick 7 packets. We pick 40, 41,

42, 44, 48, 43 and 50 to minimize difference

between maximum and minimum.

Source: Flipkart Interview Experience

A **simple solution** is to generate all subsets of size m of arr[0..n-1]. For every subset, find the difference between the maximum and minimum elements in it. Finally, return the minimum difference.

An **efficient solution** is based on the observation that to minimize the difference, we must choose consecutive elements from a sorted packet. We first sort the array arr[0..n-1], then find the subarray of size m with the minimum difference between last and first elements.

Below image is a dry run of the above approach:

Below is the implementation of the above approach:

## C++

`// C++ program to solve chocolate distribution ` `// problem ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// arr[0..n-1] represents sizes of packets ` `// m is number of students. ` `// Returns minimum difference between maximum ` `// and minimum values of distribution. ` `int` `findMinDiff(` `int` `arr[], ` `int` `n, ` `int` `m) ` `{ ` ` ` `// if there are no chocolates or number ` ` ` `// of students is 0 ` ` ` `if` `(m==0 || n==0) ` ` ` `return` `0; ` ` ` ` ` `// Sort the given packets ` ` ` `sort(arr, arr+n); ` ` ` ` ` `// Number of students cannot be more than ` ` ` `// number of packets ` ` ` `if` `(n < m) ` ` ` `return` `-1; ` ` ` ` ` `// Largest number of chocolates ` ` ` `int` `min_diff = INT_MAX; ` ` ` ` ` `// Find the subarray of size m such that ` ` ` `// difference between last (maximum in case ` ` ` `// of sorted) and first (minimum in case of ` ` ` `// sorted) elements of subarray is minimum. ` ` ` ` ` `for` `(` `int` `i=0; i+m-1<n; i++) ` ` ` `{ ` ` ` `int` `diff = arr[i+m-1] - arr[i]; ` ` ` `if` `(diff < min_diff) ` ` ` `min_diff = diff; ` ` ` `} ` ` ` `return` `min_diff; ` `} ` ` ` `int` `main() ` `{ ` ` ` `int` `arr[] = {12, 4, 7, 9, 2, 23, 25, 41, ` ` ` `30, 40, 28, 42, 30, 44, 48, ` ` ` `43, 50}; ` ` ` `int` `m = 7; ` `// Number of students ` ` ` `int` `n = ` `sizeof` `(arr)/` `sizeof` `(arr[0]); ` ` ` `cout << ` `"Minimum difference is "` ` ` `<< findMinDiff(arr, n, m); ` ` ` `return` `0; ` `} ` |

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## Java

`// JAVA Code For Chocolate Distribution ` `// Problem ` `import` `java.util.*; ` ` ` `class` `GFG { ` ` ` ` ` `// arr[0..n-1] represents sizes of ` ` ` `// packets. m is number of students. ` ` ` `// Returns minimum difference between ` ` ` `// maximum and minimum values of ` ` ` `// distribution. ` ` ` `static` `int` `findMinDiff(` `int` `arr[], ` `int` `n, ` ` ` `int` `m) ` ` ` `{ ` ` ` `// if there are no chocolates or ` ` ` `// number of students is 0 ` ` ` `if` `(m == ` `0` `|| n == ` `0` `) ` ` ` `return` `0` `; ` ` ` ` ` `// Sort the given packets ` ` ` `Arrays.sort(arr); ` ` ` ` ` `// Number of students cannot be ` ` ` `// more than number of packets ` ` ` `if` `(n < m) ` ` ` `return` `-` `1` `; ` ` ` ` ` `// Largest number of chocolates ` ` ` `int` `min_diff = Integer.MAX_VALUE; ` ` ` ` ` `// Find the subarray of size m ` ` ` `// such that difference between ` ` ` `// last (maximum in case of ` ` ` `// sorted) and first (minimum in ` ` ` `// case of sorted) elements of ` ` ` `// subarray is minimum. ` ` ` ` ` `for` `(` `int` `i = ` `0` `; i + m - ` `1` `< n; i++) ` ` ` `{ ` ` ` `int` `diff = arr[i+m-` `1` `] - arr[i]; ` ` ` `if` `(diff < min_diff) ` ` ` `min_diff = diff; ` ` ` `} ` ` ` `return` `min_diff; ` ` ` `} ` ` ` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `int` `arr[] = {` `12` `, ` `4` `, ` `7` `, ` `9` `, ` `2` `, ` `23` `, ` ` ` `25` `, ` `41` `, ` `30` `, ` `40` `, ` `28` `, ` ` ` `42` `, ` `30` `, ` `44` `, ` `48` `, ` `43` `, ` ` ` `50` `}; ` ` ` ` ` `int` `m = ` `7` `; ` `// Number of students ` ` ` ` ` `int` `n = arr.length; ` ` ` `System.out.println(` `"Minimum difference is "` ` ` `+ findMinDiff(arr, n, m)); ` ` ` ` ` `} ` `} ` `// This code is contributed by Arnav Kr. Mandal. ` |

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## Python3

`# Python3 program to solve ` `# chocolate distribution ` `# problem ` ` ` `import` `sys; ` ` ` `# arr[0..n-1] represents sizes of packets ` `# m is number of students. ` `# Returns minimum difference between maximum ` `# and minimum values of distribution. ` `def` `findMinDiff(arr, n, m): ` ` ` ` ` `# if there are no chocolates or number ` ` ` `# of students is 0 ` ` ` `if` `(m` `=` `=` `0` `or` `n` `=` `=` `0` `): ` ` ` `return` `0` ` ` ` ` `# Sort the given packets ` ` ` `arr.sort() ` ` ` ` ` `# Number of students cannot be more than ` ` ` `# number of packets ` ` ` `if` `(n < m): ` ` ` `return` `-` `1` ` ` ` ` `# Largest number of chocolates ` ` ` `min_diff ` `=` `sys.maxsize ` ` ` ` ` `# Find the subarray of size m such that ` ` ` `# difference between last (maximum in case ` ` ` `# of sorted) and first (minimum in case of ` ` ` `# sorted) elements of subarray is minimum. ` ` ` `i` `=` `0` ` ` `while` `(i` `+` `m` `-` `1` `<n ): ` ` ` ` ` `diff ` `=` `arr[i` `+` `m` `-` `1` `] ` `-` `arr[i] ` ` ` `if` `(diff < min_diff): ` ` ` `min_diff ` `=` `diff ` ` ` ` ` `i` `+` `=` `1` ` ` ` ` `return` `min_diff ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` `arr ` `=` `[` `12` `, ` `4` `, ` `7` `, ` `9` `, ` `2` `, ` `23` `, ` `25` `, ` `41` `, ` ` ` `30` `, ` `40` `, ` `28` `, ` `42` `, ` `30` `, ` `44` `, ` `48` `, ` ` ` `43` `, ` `50` `] ` ` ` `m ` `=` `7` `# Number of students ` ` ` `n ` `=` `len` `(arr) ` ` ` `print` `(` `"Minimum difference is"` `, findMinDiff(arr, n, m)) ` ` ` `#This code is contributed by Smitha ` |

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## C#

`// C# Code For Chocolate Distribution ` `// Problem ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `// arr[0..n-1] represents sizes of ` ` ` `// packets. m is number of students. ` ` ` `// Returns minimum difference between ` ` ` `// maximum and minimum values of ` ` ` `// distribution. ` ` ` `static` `int` `findMinDiff(` `int` `[]arr, ` `int` `n, ` ` ` `int` `m) ` ` ` `{ ` ` ` ` ` `// if there are no chocolates or ` ` ` `// number of students is 0 ` ` ` `if` `(m == 0 || n == 0) ` ` ` `return` `0; ` ` ` ` ` `// Sort the given packets ` ` ` `Array.Sort(arr); ` ` ` ` ` `// Number of students cannot be ` ` ` `// more than number of packets ` ` ` `if` `(n < m) ` ` ` `return` `-1; ` ` ` ` ` `// Largest number of chocolates ` ` ` `int` `min_diff = ` `int` `.MaxValue; ` ` ` ` ` `// Find the subarray of size m ` ` ` `// such that difference between ` ` ` `// last (maximum in case of ` ` ` `// sorted) and first (minimum in ` ` ` `// case of sorted) elements of ` ` ` `// subarray is minimum. ` ` ` ` ` `for` `(` `int` `i = 0; i + m - 1 < n; i++) ` ` ` `{ ` ` ` `int` `diff = arr[i+m-1] - arr[i]; ` ` ` ` ` `if` `(diff < min_diff) ` ` ` `min_diff = diff; ` ` ` `} ` ` ` ` ` `return` `min_diff; ` ` ` `} ` ` ` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `[]arr = {12, 4, 7, 9, 2, 23, ` ` ` `25, 41, 30, 40, 28, ` ` ` `42, 30, 44, 48, 43, ` ` ` `50}; ` ` ` ` ` `int` `m = 7; ` `// Number of students ` ` ` ` ` `int` `n = arr.Length; ` ` ` ` ` `Console.WriteLine(` `"Minimum difference is "` ` ` `+ findMinDiff(arr, n, m)); ` ` ` ` ` `} ` `} ` ` ` `// This code is contributed by vt_m. ` |

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## PHP

`<?php ` `// PHP program to solve ` `// chocolate distribution ` `// problem ` ` ` `// arr[0..n-1] represents ` `// sizes of packets m is ` `// number of students. ` `// Returns minimum difference ` `// between maximum and minimum ` `// values of distribution. ` `function` `findMinDiff(` `$arr` `, ` `$n` `, ` `$m` `) ` `{ ` ` ` `// if there are no ` ` ` `// chocolates or number ` ` ` `// of students is 0 ` ` ` `if` `(` `$m` `== 0 || ` `$n` `== 0) ` ` ` `return` `0; ` ` ` ` ` `// Sort the given packets ` ` ` `sort(` `$arr` `); ` ` ` ` ` `// Number of students ` ` ` `// cannot be more than ` ` ` `// number of packets ` ` ` `if` `(` `$n` `< ` `$m` `) ` ` ` `return` `-1; ` ` ` ` ` `// Largest number ` ` ` `// of chocolates ` ` ` `$min_diff` `= PHP_INT_MAX; ` ` ` ` ` `// Find the subarray of size ` ` ` `// m such that difference ` ` ` `// between last (maximum in ` ` ` `// case of sorted) and first ` ` ` `// (minimum in case of sorted) ` ` ` `// elements of subarray is minimum. ` ` ` ` ` `for` `(` `$i` `= 0; ` ` ` `$i` `+ ` `$m` `- 1 < ` `$n` `; ` `$i` `++) ` ` ` `{ ` ` ` `$diff` `= ` `$arr` `[` `$i` `+ ` `$m` `- 1] - ` ` ` `$arr` `[` `$i` `]; ` ` ` `if` `(` `$diff` `< ` `$min_diff` `) ` ` ` `$min_diff` `= ` `$diff` `; ` ` ` `} ` ` ` `return` `$min_diff` `; ` `} ` ` ` `// Driver Code ` `$arr` `= ` `array` `(12, 4, 7, 9, 2, 23, ` ` ` `25, 41, 30, 40, 28, ` ` ` `42, 30, 44, 48, 43, 50); ` ` ` `$m` `= 7; ` `// Number of students ` `$n` `= sizeof(` `$arr` `); ` `echo` `"Minimum difference is "` `, ` ` ` `findMinDiff(` `$arr` `, ` `$n` `, ` `$m` `); ` ` ` `// This code is contributed by ajit ` `?> ` |

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**Output:**

Minimum difference is 10

**Time Complexity :** O(n Log n) as we apply sorting before subarray search.

This article is contributed by **Roshni Agarwal**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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