Minimum number of consecutive sequences that can be formed in an array

Given an array of integers. The task is to find the minimum number of consecutive sequences that can be formed using the elements of the array. 
Examples:

Input: arr[] = { -3, -2, -1, 0, 2 }
Output: 2
Consecutive sequences are (-3, -2, -1, 0), (2).

Input: arr[] = { 3, 4, 0, 2, 6, 5, 10 }
Output: 3
Consecutive sequences are (0), {2, 3, 4, 5, 6} and {10}

Approach:

• Sort the array.
• Iterate the array, and check if current element is just 1 smaller than the next element. 
  
• If it is then increment the count by 1.
• Return the final count of consecutive sequences.

Below is the implementation of above approach :

C++

// C++ program find the minimum number of consecutive
// sequences in an array
#include <bits/stdc++.h>
using namespace std;

int countSequences(int arr[], int n)
{
    int count = 1;

    sort(arr, arr + n);

    for (int i = 0; i < n - 1; i++)
        if (arr[i] + 1 != arr[i + 1])
            count++;

    return count;
}

// Driver program
int main()
{
    int arr[] = { 1, 7, 3, 5, 10 };
    int n = sizeof(arr) / sizeof(arr[0]);

    // function call to print required answer
    cout << countSequences(arr, n);
    return 0;
}

Java

// Java  program find the minimum number of consecutive
// sequences in an array

import java.util.Arrays;
import java.io.*;

class GFG {

static int countSequences(int arr[], int n)
{
    int count = 1;

    Arrays.sort(arr);

    for (int i = 0; i < n - 1; i++)
        if (arr[i] + 1 != arr[i + 1])
            count++;

    return count;
}

// Driver program
    public static void main (String[] args) {

    int arr[] = { 1, 7, 3, 5, 10 };
    int n = arr.length;
    // function call to print required answer
    System.out.println( countSequences(arr, n));

    }
//This code is contributed by ajit.
}

Python3

# Python3 program find the minimum number of consecutive
# sequences in an array

def countSequences(arr, n) :
    count = 1

    arr.sort()

    for i in range( n -1) :
        if (arr[i] + 1 != arr[i + 1]) :
            count += 1

    return count


# Driver program
if __name__ == "__main__" :

    arr = [ 1, 7, 3, 5, 10 ]
    n = len(arr)

    # function call to print required answer
    print(countSequences(arr, n))

# This code is contributed by Ryuga

C#

// C# program find the minimum number of consecutive
// sequences in an array
 using System;
class GFG {

static int countSequences(int []arr, int n)
{
    int count = 1;

    Array.Sort(arr);

    for (int i = 0; i < n - 1; i++)
        if (arr[i] + 1 != arr[i + 1])
            count++;

    return count;
}

// Driver program
    static public void Main (String []args) {

    int []arr = { 1, 7, 3, 5, 10 };
    int n = arr.Length;
    // function call to print required answer
    Console.WriteLine( countSequences(arr, n));

    }
}
//This code is contributed by Arnab Kundu

PHP

<?php
// PHP program find the minimum number
// of consecutive sequences in an array

function countSequences($arr, $n)
{
    $count = 1;

    sort($arr);

    for ($i = 0; $i < $n - 1; $i++)
        if ($arr[$i] + 1 != $arr[$i + 1])
            $count++;

    return $count;
}

// Driver Code
$arr = array( 1, 7, 3, 5, 10 );
$n = count($arr);

// function call to print required answer
echo countSequences($arr, $n);

// This code is contributed by inder_verma
?>

Javascript

<script>

    // Javascript program find the
    // minimum number of consecutive
    // sequences in an array

    function countSequences(arr, n)
    {
        let count = 1;

        arr.sort(function(a, b){return a - b});

        for (let i = 0; i < n - 1; i++)
            if (arr[i] + 1 != arr[i + 1])
                count++;

        return count;
    }

    let arr = [ 1, 7, 3, 5, 10 ];
    let n = arr.length;

    // function call to print required answer
    document.write(countSequences(arr, n));

</script>

Output:

5

Time Complexity: O(n log n), where n is the size of the array.

Auxiliary Space: O(1)