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

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.

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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 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. 

Python

# 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 
?> 

Output:

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 contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

Java

Python

C#

PHP

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