Skip to content
Related Articles

Related Articles

Table of Contents

Improve Article
Save Article
Like Article

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

  • Difficulty Level : Easy
  • Last Updated : 24 Jan, 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++




// C++ program to find number of subset containing
// consecutive numbers
#include <bits/stdc++.h>
using namespace std;
 
// Returns count of subsets with consecutive numbers
int 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 Program
int 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



// Java program to find number of subset
// containing consecutive numbers
import 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.
Python3



# Python program to find number of subset containing
# consecutive numbers
def 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 Program
arr = [ 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#



// C# program to find number of subset
// containing consecutive numbers
using 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
// PHP 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.
    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
?>
Javascript



<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>
Output: 
3
Time Complexity : O(nlogn)
 
This article is contributed by Anuj Chauhan(anuj0503). If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

My Personal Notes
arrow_drop_up
Next

Count sub-sets that satisfy the given condition
Recommended Articles
Page :
Split array into minimum number of subsets such that elements of all pairs are present in different subsets at least once
04, Jan 21
Maximum number of subsets an array can be split into such that product of their minimums with size of subsets is at least K
21, Apr 21
Minimum removal of subsequences of distinct consecutive characters required to empty a given string
24, Nov 20
Maximize count of Decreasing Consecutive Subsequences from an Array
31, Jul 20
Sum of subsets of all the subsets of an array | O(3^N)
30, Oct 19
Sum of subsets of all the subsets of an array | O(2^N)
31, Oct 19
Sum of subsets of all the subsets of an array | O(N)
31, Oct 19
Divide array in two Subsets such that sum of square of sum of both subsets is maximum
07, Feb 20
Partition an array of non-negative integers into two subsets such that average of both the subsets is equal
11, Jul 19
Check if given Array can be divided into subsequences of K increasing consecutive integers
29, Sep 21
Split array into minimum number of subsets with every element of a subset divisible by its minimum
12, Feb 21
Split array into minimum number of subsets having difference between maximum and minimum element at most K
03, Sep 21
Maximize sum of subsets from two arrays having no consecutive values
27, Jan 21
Check if an array can be split into subsets of K consecutive elements
15, Jul 20
Maximise the size of consecutive element subsets in an array
27, Aug 17
Partition array into two subsets with minimum Bitwise XOR between their maximum and minimum
20, Jan 21
Mean of minimum of all possible K-size subsets from first N natural numbers
20, Aug 21
Split array into two subsequences having minimum count of pairs with sum equal to X
09, Oct 20
Count subsequences which contains both the maximum and minimum array element
10, Sep 20
Count of subsequences which consists exactly K prime numbers
21, May 20
Minimize count of Subsets with difference between maximum and minimum element not exceeding K
21, Aug 20
Count non-adjacent subsets from numbers arranged in Circular fashion
29, Oct 19
Count subsets having distinct even numbers
23, May 17
Minimum number of palindromic subsequences to be removed to empty a binary string
08, May 16
Article Contributed By :
https://media.geeksforgeeks.org/auth/avatar.png
GeeksforGeeks
Vote for difficulty
Current difficulty :
Easy





Improved By :
Article Tags :
Practice Tags :
Report Issue

We use cookies to ensure you have the best browsing experience on our website. By using our site, you
acknowledge that you have read and understood our
Cookie Policy &
        Privacy Policy

Lightbox

Start Your Coding Journey Now!