Count minimum number of subsets (or subsequences) with consecutive numbers

06 Jul, 2022
Given an array of distinct positive numbers, the task is to calculate the number of subsets (or subsequences) from the array such that each subset contains consecutive numbers.
Examples: 
Input :  arr[] = {100, 56, 5, 6, 102, 58, 
                            101, 57, 7, 103, 59}
Output : 3
{5, 6, 7}, { 56, 57, 58, 59}, {100, 101, 102, 103}
are 3 subset in which numbers are consecutive.

Input :  arr[] = {10, 100, 105}
Output : 3
{10}, {100} and {105} are 3 subset in which 
numbers are consecutive. 
The idea is to sort the array and traverse the sorted array to count the number of such subsets. To count the number of such subsets, we need to count the consecutive numbers such that the difference between them is not equal to one.
Following is the algorithm for the finding number of subset containing consecutive numbers: 
1. Sort the array arr[ ] and count = 1.
2. Traverse the sorted array and for each element arr[i].
   If arr[i] + 1 != arr[i+1], 
       then increment the count by one.
3. Return the count. 
Below is the implementation of this approach :  
C++
Java
Python3
C#
PHP
Javascript
// C++ program to find number of subset containing// consecutive numbers#include <bits/stdc++.h>using namespace std; // Returns count of subsets with consecutive numbersint numofsubset(int arr[], int n){    // Sort the array so that elements which are    // consecutive in nature became consecutive    // in the array.    sort(arr, arr + n);     int count = 1; // Initialize result    for (int i = 0; i < n - 1; i++) {        // Check if there is beginning of another        // subset of consecutive number        if (arr[i] + 1 != arr[i + 1])            count++;    }     return count;} // Driven Programint main(){    int arr[] = { 100, 56, 5, 6, 102, 58, 101,                  57, 7, 103, 59 };    int n = sizeof(arr) / sizeof(arr[0]);    cout << numofsubset(arr, n) << endl;    return 0;}
// Java program to find number of subset// containing consecutive numbersimport java.util.*;class GFG {     // Returns count of subsets with consecutive numbers    static int numofsubset(int arr[], int n)    {        // Sort the array so that elements        // which are consecutive in nature        // became consecutive in the array.        Arrays.sort(arr);         // Initialize result        int count = 1;        for (int i = 0; i < n - 1; i++) {            // Check if there is beginning            // of another subset of            // consecutive number            if (arr[i] + 1 != arr[i + 1])                count++;        }         return count;    }     // Driven Program    public static void main(String[] args)    {        int arr[] = { 100, 56, 5, 6, 102, 58, 101,                      57, 7, 103, 59 };        int n = arr.length;        System.out.println(numofsubset(arr, n));    }} // This code is contributed by prerna saini.
# Python program to find number of subset containing# consecutive numbersdef numofsubset(arr, n):   # Sort the array so that elements which are consecutive  # in nature became consecutive in the array.  x = sorted(arr)    count = 1    for i in range(0, n-1):     # Check if there is beginning of another subset of    # consecutive number    if (x[i] + 1 != x[i + 1]):      count = count + 1    return count # Driven Programarr = [ 100, 56, 5, 6, 102, 58, 101, 57, 7, 103, 59 ]n = len(arr)print (numofsubset(arr, n)) # This code is contributed by Afzal Ansari.
// C# program to find number of subset// containing consecutive numbersusing System; class GFG {     // Returns count of subsets with    // consecutive numbers    static int numofsubset(int[] arr, int n)    {        // Sort the array so that elements        // which are consecutive in nature        // became consecutive in the array.        Array.Sort(arr);         // Initialize result        int count = 1;        for (int i = 0; i < n - 1; i++) {                         // Check if there is beginning            // of another subset of            // consecutive number            if (arr[i] + 1 != arr[i + 1])                count++;        }         return count;    }     // Driven Program    public static void Main()    {        int[] arr = { 100, 56, 5, 6, 102, 58, 101,                                 57, 7, 103, 59 };        int n = arr.Length;        Console.WriteLine(numofsubset(arr, n));    }} // This code is contributed by vt_m.
<?php// PHP program to find number// of subset containing// consecutive numbers // Returns count of subsets// with consecutive numbersfunction numofsubset( $arr, $n){         // Sort the array so that    // elements which are    // consecutive in nature    // became consecutive    // in the array.    sort($arr);     // Initialize result    $count = 1;    for ($i = 0; $i < $n - 1; $i++)    {                 // Check if there is        // beginning of another        // subset of consecutive        // number        if ($arr[$i] + 1 != $arr[$i + 1])            $count++;    }     return $count;}     // Driver Code    $arr = array(100, 56, 5, 6, 102, 58, 101,                 57, 7, 103, 59 );    $n = sizeof($arr);    echo numofsubset($arr, $n);     // This code is contributed by Anuj_67?>
<script>// javascript program to find number of subset// containing consecutive numbers     // Returns count of subsets with consecutive numbers    function numofsubset(arr , n) {        // Sort the array so that elements        // which are consecutive in nature        // became consecutive in the array.        arr.sort((a,b)=>a-b);         // Initialize result        var count = 1;        for (i = 0; i < n - 1; i++) {            // Check if there is beginning            // of another subset of            // consecutive number            if (arr[i] + 1 != arr[i + 1])                count++;        }         return count;    }     // Driven Program             var arr = [ 100, 56, 5, 6, 102, 58, 101, 57, 7, 103, 59 ];        var n = arr.length;        document.write(numofsubset(arr, n)); // This code contributed by Rajput-Ji</script>
3

Time Complexity : O(nlogn)
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