# Minimize cost to sort given array by sorting unsorted subarrays

• Last Updated : 19 Jan, 2022

Given an array arr[] of size N, the task is to minimize the  cost to sort the array by sorting any unsorted subarray where the cost of the operation is the difference between the maximum and minimum element of that subarray. This operation can be performed infinite times including 0.

Examples:

Input: arr[] = {1, 7, 5, 2, 1, 8}
Output: 6
Explanation: The subarray from index [1,4] can be chosen and can be sorted with cost = 7 – 1 = 6

Input: arr[] = { 1, 4, 3, 5, 6 ,13, 10}
Output: 4
Explanation: The subarray from index index [1,2] and [5,6] can be sorted with cost of  4 – 3 and 13 – 10 = 1 + 3 = 4

Approach: This can be solved using the greedy approach, the elements already sorted don’t require any cost so only the subarrays that have unsorted elements must be considered to sort. Multiset can be used to store the elements that are not in sorted order and the difference between the last and first element of multiset gives the cost.

Follow these steps to solve the above problem:

• Initialize a vector v and copy the arr into it and assign the size of the vector to the variable n.
• Now sort the vector v.
• Initialize 2 multisets m1 and m2 to store the unsorted and sorted subarray respectively and cost = 0  to store the result.
• Now iterate through the range [0,N) and check
• If v[i] is not equal to arr[i]
• Insert arr[i] into m1 and v[i] into m2
• When both the multisets are the same add the difference between the last and first element of the set to the cost.
• Clear both the multisets to make them used by the next unsorted subarray.
• Print the cost.

Below is the implementation of the above approach.

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the minimum cost``// to sort the array in ascending order``int` `minimum_cost(vector<``int``> arr)``{``    ``// Copy the arr into vector and sort it``    ``vector<``int``> sorted = arr;``    ``int` `n = arr.size();``    ``sort(sorted.begin(), sorted.end());` `    ``// Initialize the two multisets to store``    ``// sorted and the unordered elements``    ``multiset<``int``> m1, m2;` `    ``// Initialize cost to store final answer``    ``int` `cost = 0;` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``if` `(sorted[i] != arr[i]) {``            ``m1.insert(arr[i]);``            ``m2.insert(sorted[i]);` `            ``// If both the multisets are equal,``            ``// the unordered subarray is sorted``            ``if` `(m1 == m2) {``                ``// The cost is difference``                ``// between mini and max``                ``cost += (*m1.rbegin() -``                         ``*m2.begin());` `                ``// Clear the multisets to make``                ``// use of it again``                ``m1.clear();``                ``m2.clear();``            ``}``        ``}``    ``}``    ``return` `cost;``}` `// Driver code``int` `main()``{``    ``// Initialize the queries``    ``vector<``int``> arr = { 1, 7, 5, 2, 1, 8 };``    ``cout << minimum_cost(arr);` `    ``return` `0;``}`

## Java

 `// Java code to implement the above approach``import` `java.util.*;` `class` `GFG {` `  ``// Function to find the minimum cost``  ``// to sort the array in ascending order``  ``public` `static` `int` `minimum_cost(``int``[] arr)``  ``{` `    ``// Copy the arr into vector and sort it``    ``int` `n = arr.length;``    ``int``[] sorted = ``new` `int``[n];``    ``sorted = arr.clone();``    ``Arrays.sort(sorted);` `    ``// Initialize the two multisets to store``    ``// sorted and the unordered elements``    ``SortedSet m1 = ``new` `TreeSet();``    ``SortedSet m2 = ``new` `TreeSet();` `    ``// Initialize cost to store final answer``    ``int` `cost = ``0``;` `    ``for` `(``int` `i = ``0``; i < n; i++) {``      ``if` `(sorted[i] != arr[i]) {``        ``m1.add(arr[i]);``        ``m2.add(sorted[i]);` `        ``// If both the multisets are equal,``        ``// the unordered subarray is sorted``        ``if` `(m1.equals(m2))``        ``{` `          ``// The cost is difference``          ``// between mini and max``          ``cost += (Collections.max(m1) - Collections.min(m2));` `          ``// Clear the multisets to make``          ``// use of it again``          ``m1.clear();``          ``m2.clear();``        ``}``      ``}``    ``}``    ``return` `cost;``  ``}` `  ``// Driver code``  ``public` `static` `void` `main (String[] args)``  ``{``    ` `    ``// Initialize the queries``    ``int``[] arr = { ``1``, ``7``, ``5``, ``2``, ``1``, ``8` `};``    ``System.out.println(minimum_cost(arr));` `  ``}``}` `// This code is contributed by Shubham Singh`

## Python3

 `# python3 program for the above approach` `# Function to find the minimum cost``# to sort the array in ascending order``def` `minimum_cost(arr):` `    ``# Copy the arr into vector and sort it``    ``sorted` `=` `arr.copy()``    ``n ``=` `len``(arr)``    ``sorted``.sort()` `    ``# Initialize the two multisets to store``    ``# sorted and the unordered elements``    ``m1 ``=` `set``()``    ``m2 ``=` `set``()` `    ``# Initialize cost to store final answer``    ``cost ``=` `0` `    ``for` `i ``in` `range``(``0``, n):``        ``if` `(``sorted``[i] !``=` `arr[i]):``            ``m1.add(arr[i])``            ``m2.add(``sorted``[i])` `            ``# If both the multisets are equal,``            ``# the unordered subarray is sorted``            ``if` `(m1 ``=``=` `m2):``                ``# The cost is difference``                ``# between mini and max``                ``cost ``+``=` `(``list``(m1)[``len``(``list``(m1)) ``-` `1``] ``-``                         ``list``(m2)[``0``])` `                ``# Clear the multisets to make``                ``# use of it again``                ``m1.clear()``                ``m2.clear()` `    ``return` `cost` `# Driver code``if` `__name__ ``=``=` `"__main__"``:` `    ``# Initialize the queries``    ``arr ``=` `[``1``, ``7``, ``5``, ``2``, ``1``, ``8``]``    ``print``(minimum_cost(arr))` `    ``# This code is contributed by rakeshsahni`

## C#

 `// C# code to implement the above approach``using` `System;``using` `System.Collections.Generic;` `public` `class` `GFG{` `  ``// Function to find the minimum cost``  ``// to sort the array in ascending order``  ``public` `static` `int` `minimum_cost(``int``[] arr)``  ``{` `    ``// Copy the arr into vector and sort it``    ``int` `n = arr.Length;``    ``int``[] sorted = ``new` `int``[n];``    ``Array.Copy(arr, 0, sorted, 0, n);``    ``Array.Sort(sorted);` `    ``// Initialize the two multisets to store``    ``// sorted and the unordered elements``    ``SortedSet<``int``> m1 = ``new` `SortedSet<``int``>();``    ``SortedSet<``int``> m2 = ``new` `SortedSet<``int``>();` `    ``// Initialize cost to store final answer``    ``int` `cost = 0;` `    ``for` `(``int` `i = 0; i < n; i++) {``      ``if` `(sorted[i] != arr[i]) {``        ``m1.Add(arr[i]);``        ``m2.Add(sorted[i]);` `        ``// If both the multisets are equal,``        ``// the unordered subarray is sorted``        ``if` `(m1.SetEquals(m2))``        ``{` `          ``// The cost is difference``          ``// between mini and max``          ``cost += (m1.Max - m2.Min);` `          ``// Clear the multisets to make``          ``// use of it again``          ``m1.Clear();``          ``m2.Clear();``        ``}``      ``}``    ``}``    ``return` `cost;``  ``}` `  ``// Driver code``  ``public` `static` `void` `Main()``  ``{``    ``// Initialize the queries``    ``int``[] arr = { 1, 7, 5, 2, 1, 8 };``    ``Console.Write(minimum_cost(arr));` `  ``}``}` `// This code is contributed by Shubham Singh`

## Javascript

 ``

Output
`6`

Time Complexity: O(N * logN )
Auxiliary Space: O(N)

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