# Minimize Steps required to obtain Sorted Order of an Array

• Difficulty Level : Expert
• Last Updated : 10 May, 2021

Given an array arr[] consisting of a permutation of integers [1, N], derived by rearranging the sorted order [1, N], the task is to find the minimum number of steps after which the sorted order [1, N] is repeated, by repeating the same process by which arr[] is obtained from the sorted sequence at each step.

Examples:

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Input: arr[ ] = {3, 6, 5, 4, 1, 2}
Output:
Explanation:
Increasing Permutation: {1, 2, 3, 4, 5, 6}
Step 1 : arr[] = {3, 6, 5, 4, 1, 2} (Given array)
Step 2 : arr[] = {5, 2, 1, 4, 3, 6}
Step 3 : arr[] = {1, 6, 3, 4, 5, 2}
Step 4 : arr[] = {3, 2, 5, 4, 1, 6}
Step 5 : arr[] = {5, 6, 1, 4, 3, 2}
Step 6 : arr[] = {1, 2, 3, 4, 5, 6} (Increasing Permutation)
Therefore, the total number of steps required are 6.
Input: arr[ ] = [5, 1, 4, 3, 2]
Output:

Approach:
This problem can be solved simply by using the concept of Direct Addressing. Follow the steps given below to solve the problem:

• Initialize an array dat[] for direct addressing.
• Iterate over [1, N] and calculate the difference of the current index of every element from its index in the sorted sequence.
• Calculate the LCM of the array dat[].
• Now, print the obtained LCM as the minimum steps required to obtain the sorted order.

Below is the implementation of the above approach:

## C++14

 `// C++ Program to implement``// the above approach``#include ``using` `namespace` `std;` `// Function to find``// GCD of two numbers``int` `gcd(``int` `a, ``int` `b)``{``    ``if` `(b == 0)``        ``return` `a;` `    ``return` `gcd(b, a % b);``}` `// Function to calculate the``// LCM of array elements``int` `findlcm(``int` `arr[], ``int` `n)``{``    ``// Initialize result``    ``int` `ans = 1;` `    ``for` `(``int` `i = 1; i <= n; i++)``        ``ans = (((arr[i] * ans))``            ``/ (gcd(arr[i], ans)));` `    ``return` `ans;``}` `// Function to find minimum steps``// required to obtain sorted sequence``void` `minimumSteps(``int` `arr[], ``int` `n)``{` `    ``// Inititalize dat[] array for``    ``// Direct Address Table.``    ``int` `i, dat[n + 1];` `    ``for` `(i = 1; i <= n; i++)` `        ``dat[arr[i - 1]] = i;` `    ``int` `b[n + 1], j = 0, c;` `    ``// Calculating steps required``    ``// for each element to reach``    ``// its sorted position``    ``for` `(i = 1; i <= n; i++) {``        ``c = 1;``        ``j = dat[i];``        ``while` `(j != i) {``            ``c++;``            ``j = dat[j];``        ``}``        ``b[i] = c;``    ``}` `    ``// Calculate LCM of the array``    ``cout << findlcm(b, n);``}` `// Driver Code``int` `main()``{` `    ``int` `arr[] = { 5, 1, 4, 3, 2, 7, 6 };` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``minimumSteps(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program to implement``// the above approach``class` `GFG{``    ` `// Function to find``// GCD of two numbers``static` `int` `gcd(``int` `a, ``int` `b)``{``    ``if` `(b == ``0``)``        ``return` `a;` `    ``return` `gcd(b, a % b);``}` `// Function to calculate the``// LCM of array elements``static` `int` `findlcm(``int` `arr[], ``int` `n)``{``    ` `    ``// Initialize result``    ``int` `ans = ``1``;` `    ``for``(``int` `i = ``1``; i <= n; i++)``        ``ans = (((arr[i] * ans)) /``            ``(gcd(arr[i], ans)));` `    ``return` `ans;``}` `// Function to find minimum steps``// required to obtain sorted sequence``static` `void` `minimumSteps(``int` `arr[], ``int` `n)``{` `    ``// Inititalize dat[] array for``    ``// Direct Address Table.``    ``int` `i;``    ``int` `dat[] = ``new` `int``[n + ``1``];` `    ``for``(i = ``1``; i <= n; i++)``        ``dat[arr[i - ``1``]] = i;` `    ``int` `b[] = ``new` `int``[n + ``1``];``    ``int` `j = ``0``, c;` `    ``// Calculating steps required``    ``// for each element to reach``    ``// its sorted position``    ``for``(i = ``1``; i <= n; i++)``    ``{``        ``c = ``1``;``        ``j = dat[i];``        ` `        ``while` `(j != i)``        ``{``            ``c++;``            ``j = dat[j];``        ``}``        ``b[i] = c;``    ``}` `    ``// Calculate LCM of the array``    ``System.out.println(findlcm(b, n));``}` `// Driver code   ``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``5``, ``1``, ``4``, ``3``, ``2``, ``7``, ``6` `};` `    ``int` `N = arr.length;` `    ``minimumSteps(arr, N);``}``}` `// This code is contributed by rutvik_56`

## Python3

 `# Python3 program to implement``# the above approach` `# Function to find``# GCD of two numbers``def` `gcd(a, b):` `    ``if``(b ``=``=` `0``):``        ``return` `a` `    ``return` `gcd(b, a ``%` `b)` `# Function to calculate the``# LCM of array elements``def` `findlcm(arr, n):` `    ``# Initialize result``    ``ans ``=` `1` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ``ans ``=` `((arr[i] ``*` `ans) ``/``/``            ``(gcd(arr[i], ans)))` `    ``return` `ans` `# Function to find minimum steps``# required to obtain sorted sequence``def` `minimumSteps(arr, n):` `    ``# Inititalize dat[] array for``    ``# Direct Address Table.``    ``dat ``=` `[``0``] ``*` `(n ``+` `1``)` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ``dat[arr[i ``-` `1``]] ``=` `i` `    ``b ``=` `[``0``] ``*` `(n ``+` `1``)``    ``j ``=` `0` `    ``# Calculating steps required``    ``# for each element to reach``    ``# its sorted position``    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ``c ``=` `1``        ``j ``=` `dat[i]``        ``while``(j !``=` `i):``            ``c ``+``=` `1``            ``j ``=` `dat[j]` `        ``b[i] ``=` `c` `    ``# Calculate LCM of the array``    ``print``(findlcm(b, n))` `# Driver Code``arr ``=` `[ ``5``, ``1``, ``4``, ``3``, ``2``, ``7``, ``6` `]` `N ``=` `len``(arr)` `minimumSteps(arr, N)` `# This code is contributed by Shivam Singh`

## C#

 `// C# program to implement``// the above approach``using` `System;` `class` `GFG{``    ` `// Function to find``// GCD of two numbers``static` `int` `gcd(``int` `a, ``int` `b)``{``    ``if` `(b == 0)``        ``return` `a;` `    ``return` `gcd(b, a % b);``}` `// Function to calculate the``// LCM of array elements``static` `int` `findlcm(``int` `[]arr, ``int` `n)``{``    ` `    ``// Initialize result``    ``int` `ans = 1;` `    ``for``(``int` `i = 1; i <= n; i++)``        ``ans = (((arr[i] * ans)) /``            ``(gcd(arr[i], ans)));` `    ``return` `ans;``}` `// Function to find minimum steps``// required to obtain sorted sequence``static` `void` `minimumSteps(``int` `[]arr, ``int` `n)``{` `    ``// Inititalize dat[] array for``    ``// Direct Address Table.``    ``int` `i;``    ``int` `[]dat = ``new` `int``[n + 1];` `    ``for``(i = 1; i <= n; i++)``        ``dat[arr[i - 1]] = i;` `    ``int` `[]b = ``new` `int``[n + 1];``    ``int` `j = 0, c;` `    ``// Calculating steps required``    ``// for each element to reach``    ``// its sorted position``    ``for``(i = 1; i <= n; i++)``    ``{``        ``c = 1;``        ``j = dat[i];``        ` `        ``while` `(j != i)``        ``{``            ``c++;``            ``j = dat[j];``        ``}``        ``b[i] = c;``    ``}` `    ``// Calculate LCM of the array``    ``Console.WriteLine(findlcm(b, n));``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 5, 1, 4, 3, 2, 7, 6 };` `    ``int` `N = arr.Length;` `    ``minimumSteps(arr, N);``}``}` `// This code is contributed by gauravrajput1`

## Javascript

 ``
Output:
`6`

Time Complexity: O(NlogN)
Auxiliary Space: O(N)

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