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Find the Minimum length Unsorted Subarray, sorting which makes the complete array sorted

  • Difficulty Level : Medium
  • Last Updated : 22 Mar, 2021

Given an unsorted array arr[0..n-1] of size n, find the minimum length subarray arr[s..e] such that sorting this subarray makes the whole array sorted. 
Examples: 
1) If the input array is [10, 12, 20, 30, 25, 40, 32, 31, 35, 50, 60], your program should be able to find that the subarray lies between the indexes 3 and 8.
2) If the input array is [0, 1, 15, 25, 6, 7, 30, 40, 50], your program should be able to find that the subarray lies between the indexes 2 and 5.
 

Solution: 
1) Find the candidate unsorted subarray 
a) Scan from left to right and find the first element which is greater than the next element. Let s be the index of such an element. In the above example 1, s is 3 (index of 30). 
b) Scan from right to left and find the first element (first in right to left order) which is smaller than the next element (next in right to left order). Let e be the index of such an element. In the above example 1, e is 7 (index of 31).
2) Check whether sorting the candidate unsorted subarray makes the complete array sorted or not. If not, then include more elements in the subarray. 
a) Find the minimum and maximum values in arr[s..e]. Let minimum and maximum values be min and max. min and max for [30, 25, 40, 32, 31] are 25 and 40 respectively. 
b) Find the first element (if there is any) in arr[0..s-1] which is greater than min, change s to index of this element. There is no such element in above example 1. 
c) Find the last element (if there is any) in arr[e+1..n-1] which is smaller than max, change e to index of this element. In the above example 1, e is changed to 8 (index of 35)
3) Print s and e.
Implementation: 
 

C++




// C++ program to find the Minimum length Unsorted Subarray,
// sorting which makes the complete array sorted
#include<bits/stdc++.h>
using namespace std;
 
void printUnsorted(int arr[], int n)
{
int s = 0, e = n-1, i, max, min;
 
// step 1(a) of above algo
for (s = 0; s < n-1; s++)
{
    if (arr[s] > arr[s+1])
    break;
}
if (s == n-1)
{
    cout << "The complete array is sorted";
    return;
}
 
// step 1(b) of above algo
for(e = n - 1; e > 0; e--)
{
    if(arr[e] < arr[e-1])
    break;
}
 
// step 2(a) of above algo
max = arr[s]; min = arr[s];
for(i = s + 1; i <= e; i++)
{
    if(arr[i] > max)
    max = arr[i];
    if(arr[i] < min)
    min = arr[i];
}
 
// step 2(b) of above algo
for( i = 0; i < s; i++)
{
    if(arr[i] > min)
    {
    s = i;
    break;
    }    
}
 
// step 2(c) of above algo
for( i = n -1; i >= e+1; i--)
{
    if(arr[i] < max)
    {
    e = i;
    break;
    }
}
     
// step 3 of above algo
cout << "The unsorted subarray which"
     << " makes the given array" << endl
     << "sorted lies between the indees "
     << s << " and " << e;
return;
}
 
int main()
{
    int arr[] = {10, 12, 20, 30, 25,
                 40, 32, 31, 35, 50, 60};
    int arr_size = sizeof(arr)/sizeof(arr[0]);
    printUnsorted(arr, arr_size);
    getchar();
    return 0;
}
 
// This code is contributed
// by Akanksha Rai
C



// C program to find the Minimum length Unsorted Subarray,
// sorting which makes the complete array sorted
#include<stdio.h>
  
void printUnsorted(int arr[], int n)
{
  int s = 0, e = n-1, i, max, min;  
  
  // step 1(a) of above algo
  for (s = 0; s < n-1; s++)
  {
    if (arr[s] > arr[s+1])
      break;
  }
  if (s == n-1)
  {
    printf("The complete array is sorted");
    return;
  }
  
  // step 1(b) of above algo
  for(e = n - 1; e > 0; e--)
  {
    if(arr[e] < arr[e-1])
      break;
  }
  
  // step 2(a) of above algo
  max = arr[s]; min = arr[s];
  for(i = s + 1; i <= e; i++)
  {
    if(arr[i] > max)
      max = arr[i];
    if(arr[i] < min)
      min = arr[i];
  }
  
  // step 2(b) of above algo
  for( i = 0; i < s; i++)
  {
    if(arr[i] > min)
    { 
      s = i;
      break;
    }     
  }
  
  // step 2(c) of above algo
  for( i = n -1; i >= e+1; i--)
  {
    if(arr[i] < max)
    {
      e = i;
      break;
    }
  } 
      
  // step 3 of above algo
  printf(" The unsorted subarray which makes the given array "
         " sorted lies between the indees %d and %d", s, e);
  return;
}
  
int main()
{
  int arr[] = {10, 12, 20, 30, 25, 40, 32, 31, 35, 50, 60};
  int arr_size = sizeof(arr)/sizeof(arr[0]);
  printUnsorted(arr, arr_size);
  getchar();
  return 0;
}
Java



// Java program to find the Minimum length Unsorted Subarray,
// sorting which makes the complete array sorted
class Main
{
    static void printUnsorted(int arr[], int n)
    {
      int s = 0, e = n-1, i, max, min;  
       
      // step 1(a) of above algo
      for (s = 0; s < n-1; s++)
      {
        if (arr[s] > arr[s+1])
          break;
      }
      if (s == n-1)
      {
        System.out.println("The complete array is sorted");
        return;
      }
       
      // step 1(b) of above algo
      for(e = n - 1; e > 0; e--)
      {
        if(arr[e] < arr[e-1])
          break;
      }
       
      // step 2(a) of above algo
      max = arr[s]; min = arr[s];
      for(i = s + 1; i <= e; i++)
      {
        if(arr[i] > max)
          max = arr[i];
        if(arr[i] < min)
          min = arr[i];
      }
       
      // step 2(b) of above algo
      for( i = 0; i < s; i++)
      {
        if(arr[i] > min)
        { 
          s = i;
          break;
        }     
      }
       
      // step 2(c) of above algo
      for( i = n -1; i >= e+1; i--)
      {
        if(arr[i] < max)
        {
          e = i;
          break;
        }
      } 
           
      // step 3 of above algo
      System.out.println(" The unsorted subarray which"+
                         " makes the given array sorted lies"+
                       "  between the indices "+s+" and "+e);
      return;
    }
       
    public static void main(String args[])
    {
      int arr[] = {10, 12, 20, 30, 25, 40, 32, 31, 35, 50, 60};
      int arr_size = arr.length;
      printUnsorted(arr, arr_size);
    }
}
Python3



# Python3 program to find the Minimum length Unsorted Subarray,
# sorting which makes the complete array sorted
def printUnsorted(arr, n):
    e = n-1
    # step 1(a) of above algo
    for s in range(0,n-1):
        if arr[s] > arr[s+1]:
            break
         
    if s == n-1:
        print ("The complete array is sorted")
        exit()
 
    # step 1(b) of above algo
    e= n-1
    while e > 0:
        if arr[e] < arr[e-1]:
            break
        e -= 1
 
    # step 2(a) of above algo
    max = arr[s]
    min = arr[s]
    for i in range(s+1,e+1):
        if arr[i] > max:
            max = arr[i]
        if arr[i] < min:
            min = arr[i]
             
    # step 2(b) of above algo
    for i in range(s):
        if arr[i] > min:
            s = i
            break
 
    # step 2(c) of above algo
    i = n-1
    while i >= e+1:
        if arr[i] < max:
            e = i
            break
        i -= 1
     
    # step 3 of above algo
    print ("The unsorted subarray which makes the given array")
    print ("sorted lies between the indexes %d and %d"%( s, e))
 
arr = [10, 12, 20, 30, 25, 40, 32, 31, 35, 50, 60]
arr_size = len(arr)
printUnsorted(arr, arr_size)
 
# This code is contributed by Shreyanshi Arun
C#



// C# program to find the Minimum length Unsorted Subarray,
// sorting which makes the complete array sorted
 
using System;
 
class GFG
{
    static void printUnsorted(int []arr, int n)
    {
    int s = 0, e = n-1, i, max, min;
         
    // step 1(a) of above algo
    for (s = 0; s < n-1; s++)
    {
        if (arr[s] > arr[s+1])
        break;
    }
    if (s == n-1)
    {
        Console.Write("The complete " +
                            "array is sorted");
        return;
    }
         
    // step 1(b) of above algo
    for(e = n - 1; e > 0; e--)
    {
        if(arr[e] < arr[e-1])
        break;
    }
         
    // step 2(a) of above algo
    max = arr[s]; min = arr[s];
     
    for(i = s + 1; i <= e; i++)
    {
        if(arr[i] > max)
            max = arr[i];
         
        if(arr[i] < min)
            min = arr[i];
    }
         
    // step 2(b) of above algo
    for( i = 0; i < s; i++)
    {
        if(arr[i] > min)
        {
            s = i;
            break;
        }    
    }
         
    // step 2(c) of above algo
    for( i = n -1; i >= e+1; i--)
    {
        if(arr[i] < max)
        {
            e = i;
            break;
        }
    }
             
    // step 3 of above algo
    Console.Write(" The unsorted subarray which"+
            " makes the given array sorted lies \n"+
              " between the indices "+s+" and "+e);
    return;
    }
         
    public static void Main()
    {
        int []arr = {10, 12, 20, 30, 25, 40,
                                32, 31, 35, 50, 60};
        int arr_size = arr.Length;
         
        printUnsorted(arr, arr_size);
    }
}
 
// This code contributed by Sam007
PHP



<?php
// PHP program to find the Minimum length Unsorted Subarray,
// sorting which makes the complete array sorted
function printUnsorted(&$arr, $n)
{
    $s = 0;
    $e = $n - 1;
     
    // step 1(a) of above algo
    for ($s = 0; $s < $n - 1; $s++)
    {
        if ($arr[$s] > $arr[$s + 1])
        break;
    }
    if ($s == $n - 1)
    {
        echo "The complete array is sorted";
        return;
    }
     
    // step 1(b) of above algo
    for($e = $n - 1; $e > 0; $e--)
    {
        if($arr[$e] < $arr[$e - 1])
        break;
    }
     
    // step 2(a) of above algo
    $max = $arr[$s];
    $min = $arr[$s];
    for($i = $s + 1; $i <= $e; $i++)
    {
        if($arr[$i] > $max)
            $max = $arr[$i];
        if($arr[$i] < $min)
            $min = $arr[$i];
    }
     
    // step 2(b) of above algo
    for( $i = 0; $i < $s; $i++)
    {
        if($arr[$i] > $min)
        {
            $s = $i;
            break;
        }    
    }
     
    // step 2(c) of above algo
    for( $i = $n - 1; $i >= $e + 1; $i--)
    {
        if($arr[$i] < $max)
        {
            $e = $i;
            break;
        }
    }
         
    // step 3 of above algo
    echo " The unsorted subarray which makes " .
                     "the given array " . "\n" .
            " sorted lies between the indees " .
                              $s . " and " . $e;
    return;
}
 
// Driver code
$arr = array(10, 12, 20, 30, 25, 40,
             32, 31, 35, 50, 60);
$arr_size = sizeof($arr);
printUnsorted($arr, $arr_size);
 
// This code is contributed
// by ChitraNayal
?>
Javascript



<script>
 
// Javascript program to find the Minimum length Unsorted Subarray, 
// sorting which makes the complete array sorted
     
    function printUnsorted(arr,n)
    {
        let s = 0, e = n-1, i, max, min;
        // step 1(a) of above algo
        for (s = 0; s < n-1; s++)
        {
            if (arr[s] > arr[s+1])
                break;
        }
        if (s == n-1)
        {
            document.write("The complete array is sorted");
            return;
        }
        // step 1(b) of above algo
        for(e = n - 1; e > 0; e--)
        {
            if(arr[e] < arr[e-1])
                break;
        }
        // step 2(a) of above algo
        max = arr[s]; min = arr[s];
        for(i = s + 1; i <= e; i++)
        {
            if(arr[i] > max)
                max = arr[i];
            if(arr[i] < min)
                min = arr[i];
        }
        // step 2(b) of above algo
        for( i = 0; i < s; i++)
        {
            if(arr[i] > min)
            {
                s = i;
                break;
            }
        }
        // step 2(c) of above algo
        for( i = n -1; i >= e+1; i--)
        {
            if(arr[i] < max)
            {
                e = i;
                break;
            }
        }
        // step 3 of above algo
        document.write(" The unsorted subarray which"+
                         " makes the given array sorted lies"+
                       "  between the indees "+s+" and "+e);
        return;
    }
    let arr=[10, 12, 20, 30, 25, 40, 32, 31, 35, 50, 60];
    let arr_size = arr.length;
    printUnsorted(arr, arr_size);
     
    // This code is contributed by avanitrachhadiya2155
     
</script>
Output : 
 
 The unsorted subarray which makes the given array 
sorted lies between the indees 3 and 8
Time Complexity: O(n)
 


Please write comments if you find the above code/algorithm incorrect, or find better ways to solve the same problem.
 
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.
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