Length of the largest subarray with contiguous elements | Set 1

Given an array of distinct integers, find length of the longest subarray which contains numbers that can be arranged in a continuous sequence. 

Examples:

Input:  arr[] = {10, 12, 11};
Output: Length of the longest contiguous subarray is 3

Input:  arr[] = {14, 12, 11, 20};
Output: Length of the longest contiguous subarray is 2

Input:  arr[] = {1, 56, 58, 57, 90, 92, 94, 93, 91, 45};
Output: Length of the longest contiguous subarray is 5

We strongly recommend to minimize the browser and try this yourself first.

The important thing to note in question is, it is given that all elements are distinct. If all elements are distinct, then a subarray has contiguous elements if and only if the difference between maximum and minimum elements in subarray is equal to the difference between last and first indexes of subarray. So the idea is to keep track of minimum and maximum element in every subarray. 

The following is the implementation of above idea. 

C++

#include<iostream>
using namespace std;

// Utility functions to find minimum and maximum of
// two elements
int min(int x, int y) { return (x < y)? x : y; }
int max(int x, int y) { return (x > y)? x : y; }

// Returns length of the longest contiguous subarray
int findLength(int arr[], int n)
{
    int max_len = 1;  // Initialize result
    for (int i=0; i<n-1; i++)
    {
        // Initialize min and max for all subarrays starting with i
        int mn = arr[i], mx = arr[i];

        // Consider all subarrays starting with i and ending with j
        for (int j=i+1; j<n; j++)
        {
            // Update min and max in this subarray if needed
            mn = min(mn, arr[j]);
            mx = max(mx, arr[j]);

            // If current subarray has all contiguous elements
            if ((mx - mn) == j-i)
                max_len = max(max_len, mx-mn+1);
        }
    }
    return max_len;  // Return result
}

// Driver program to test above function
int main()
{
    int arr[] = {1, 56, 58, 57, 90, 92, 94, 93, 91, 45};
    int n = sizeof(arr)/sizeof(arr[0]);
    cout << "Length of the longest contiguous subarray is "
         << findLength(arr, n);
    return 0;
}

Java

class LargestSubArray2
{
    // Utility functions to find minimum and maximum of
    // two elements

    int min(int x, int y)
    {
        return (x < y) ? x : y;
    }

    int max(int x, int y)
    {
        return (x > y) ? x : y;
    }

    // Returns length of the longest contiguous subarray
    int findLength(int arr[], int n)
    {
        int max_len = 1;  // Initialize result
        for (int i = 0; i < n - 1; i++)
        {
            // Initialize min and max for all subarrays starting with i
            int mn = arr[i], mx = arr[i];

            // Consider all subarrays starting with i and ending with j
            for (int j = i + 1; j < n; j++)
            {
                // Update min and max in this subarray if needed
                mn = min(mn, arr[j]);
                mx = max(mx, arr[j]);

                // If current subarray has all contiguous elements
                if ((mx - mn) == j - i)
                    max_len = max(max_len, mx - mn + 1);
            }
        }
        return max_len;  // Return result
    }

    public static void main(String[] args)
    {
        LargestSubArray2 large = new LargestSubArray2();
        int arr[] = {1, 56, 58, 57, 90, 92, 94, 93, 91, 45};
        int n = arr.length;
        System.out.println("Length of the longest contiguous subarray is "
                + large.findLength(arr, n));
    }
}

// This code has been contributed by Mayank Jaiswal

Python3

# Python3 program to find length
# of the longest subarray

# Utility functions to find minimum
# and maximum of two elements
def min(x, y):
    return x if(x < y) else y

def max(x, y):
    return x if(x > y) else y

# Returns length of the longest
# contiguous subarray
def findLength(arr, n):

    # Initialize result
    max_len = 1
    for i in range(n - 1):

        # Initialize min and max for
        # all subarrays starting with i
        mn = arr[i]
        mx = arr[i]

        # Consider all subarrays starting
        # with i and ending with j
        for j in range(i + 1, n):

            # Update min and max in
            # this subarray if needed
            mn = min(mn, arr[j])
            mx = max(mx, arr[j])

            # If current subarray has
            # all contiguous elements
            if ((mx - mn) == j - i):
                max_len = max(max_len, mx - mn + 1)

    return max_len

# Driver Code
arr = [1, 56, 58, 57, 90, 92, 94, 93, 91, 45]
n = len(arr)
print("Length of the longest contiguous subarray is ",
                                    findLength(arr, n))

# This code is contributed by Anant Agarwal.

C#

using System;

class GFG {

    // Returns length of the longest
    // contiguous subarray
    static int findLength(int []arr, int n)
    {
        int max_len = 1; // Initialize result
        for (int i = 0; i < n - 1; i++)
        {
            // Initialize min and max for all
            // subarrays starting with i
            int mn = arr[i], mx = arr[i];

            // Consider all subarrays starting
            // with i and ending with j
            for (int j = i + 1; j < n; j++)
            {
                // Update min and max in this
                // subarray if needed
                mn = Math.Min(mn, arr[j]);
                mx = Math.Max(mx, arr[j]);

                // If current subarray has all
                // contiguous elements
                if ((mx - mn) == j - i)
                    max_len = Math.Max(max_len,
                                  mx - mn + 1);
            }
        }
        return max_len; // Return result
    }

    public static void Main()
    {

        int []arr = {1, 56, 58, 57, 90, 92,
                               94, 93, 91, 45};
        int n = arr.Length;

        Console.WriteLine("Length of the longest"
                     + " contiguous subarray is "
                           + findLength(arr, n));
    }
}

// This code is contributed by Sam007.

PHP

<?php
// Utility functions to find minimum
// and maximum of two elements
function mins($x, $y)
{
    if($x < $y)
        return $x;
    else
        return $y;
}

function maxi($a, $b)
{
    if($a > $b)
        return $a;
    else
        return $b;
}

// Returns length of the longest
// contiguous subarray
function findLength(&$arr, $n)
{
    $max_len = 1; // Initialize result
    for ($i = 0; $i < $n - 1; $i++)
    {
        // Initialize min and max for all
        // subarrays starting with i
        $mn = $arr[$i];
        $mx = $arr[$i];

        // Consider all subarrays starting
        // with i and ending with j
        for ($j = $i + 1; $j < $n; $j++)
        {
            // Update min and max in this
            // subarray if needed
            $mn = mins($mn, $arr[$j]);
            $mx = maxi($mx, $arr[$j]);

            // If current subarray has all
            // contiguous elements
            if (($mx - $mn) == $j - $i)
                $max_len = maxi($max_len,
                                $mx - $mn + 1);
        }
    }
    return $max_len; // Return result
}

// Driver Code
$arr = array(1, 56, 58, 57, 90,
             92, 94, 93, 91, 45);
$n = sizeof($arr);
echo ("Length of the longest contiguous" .
                         " subarray is ");
echo (findLength($arr, $n));

// This code is contributed
// by Shivi_Aggarwal.
?>

Javascript

<script>

// Utility functions to find minimum
// and maximum of two elements
function min( x, y) { return (x < y)? x : y; }
function max( x, y) { return (x > y)? x : y; }

// Returns length of the longest
// contiguous subarray
function findLength( arr, n)
{
    let max_len = 1;  // Initialize result
    for (let i=0; i<n-1; i++)
    {
        // Initialize min and max for all
        // subarrays starting with i
        let mn = arr[i], mx = arr[i];

        // Consider all subarrays starting
        // with i and ending with j
        for (let j=i+1; j<n; j++)
        {
            // Update min and max in this
            // subarray if needed
            mn = min(mn, arr[j]);
            mx = max(mx, arr[j]);

            // If current subarray has all
            // contiguous elements
            if ((mx - mn) == j-i)
                max_len = Math.max(max_len, mx-mn+1);
        }
    }
    return max_len;  // Return result
}


    // driver code

    let arr = [1, 56, 58, 57, 90, 92, 94, 93, 91, 45];
    let n = arr.length;
    document.write("Length of the longest contiguous subarray is "
         + findLength(arr, n));

</script>

Output

Length of the longest contiguous subarray is 5

Time Complexity of the above solution is O(n²).

Auxiliary Space: O(1) ,since no extra space is used.

We will soon be covering solution for the problem where duplicate elements are allowed in subarray.

Length of the largest subarray with contiguous elements | Set 2