Partition into minimum subsets of consecutive numbers

Last Updated : 06 Jan, 2025

Given an array of distinct positive numbers, the task is to partition the array into minimum number of subsets (or subsequences) such that each subset contains consecutive numbers only.

Examples:

Input: arr[] = [100, 56, 5, 6, 102, 58, 101, 57, 7, 103, 59]
Output: 3
Explanation: [5, 6, 7], [ 56, 57, 58, 59] and [100, 101, 102, 103] are 3 subsets in which numbers are consecutive.

Input: arr[] = [10, 100, 105]
Output: 3
Explanation: [10], [100] and [105] are 3 subsets in which numbers are consecutive.

Table of Content

[Naive Approach] Sorting - O(n*log n) Time and O(1) Space
[Expected Approach] Hashing - O(n) Time and O(n) Space

[Naive Approach] Sorting - O(n*log n) Time and O(1) Space

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 pairs of consecutive numbers such that the difference between them is not equal to one. Each of such pair will belong to a new subset.

C++

// C++ program to find minimum number of subsets
// containing consecutive numbers

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

// Returns count of subsets with consecutive numbers
int minSubsets(vector<int>& arr) {
  
    // Sort the array so that consecutive elements
    // become consecutive in the array.
    sort(arr.begin(), arr.end());

    int count = 1; 
    for (int i = 0; i < arr.size() - 1; i++) {
      
        // Check if there's a break between
        // consecutive numbers
        if (arr[i] + 1 != arr[i + 1])
            count++;
    }

    return count;
}

int main() {
    vector<int> arr = {100, 56, 5, 6, 102, 58, 101, 57, 7, 103, 59};
    cout << minSubsets(arr) << 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 minSubsets(int[] arr) {

        // Sort the array so that consecutive elements
        // become consecutive in the array.
        Arrays.sort(arr);

        int count = 1;
        for (int i = 0; i < arr.length - 1; i++) {

            // Check if there's a break between
            // consecutive numbers
            if (arr[i] + 1 != arr[i + 1])
                count++;
        }

        return count;
    }

    public static void main(String[] args) {
        int[] arr = { 100, 56, 5, 6,   102, 58,
                      101, 57, 7, 103, 59 };
        System.out.println(minSubsets(arr));
    }
}

Python

# Python program to find number of subset
# containing consecutive numbers

def minSubsets(arr):
    
    # Sort the array so that consecutive elements
    # become consecutive in the array.
    arr.sort()

    count = 1
    for i in range(len(arr) - 1):
        
        # Check if there's a break between
        # consecutive numbers
        if arr[i] + 1 != arr[i + 1]:
            count += 1

    return count

if __name__ == "__main__":
    arr = [100, 56, 5, 6, 102, 58, 101, 57, 7, 103, 59]
    print(minSubsets(arr))

// C# program to find number of subset
// containing consecutive numbers
using System;
using System.Collections.Generic;

class GfG {
  
    // Returns count of subsets with consecutive numbers
    static int minSubsets(int[] arr) {
        
        // Sort the array so that consecutive elements
        // become consecutive in the array.
        Array.Sort(arr);

        int count = 1;
        for(int i = 0; i < arr.Length - 1; i++) {
            
            // Check if there's a break between
            // consecutive numbers
            if(arr[i] + 1 != arr[i + 1])
                count++;
        }

        return count;
    }

    static void Main() {
        int[] arr = {100, 56, 5, 6, 102, 58, 101, 57, 7, 103, 59};
        Console.WriteLine(minSubsets(arr));
    }
}

JavaScript

// JavaScript program to find number of subset
// containing consecutive numbers

function minSubsets(arr) {

    // Sort the array so that consecutive elements
    // become consecutive in the array.
    arr.sort((a, b) => a - b);

    let count = 1;
    for (let i = 0; i < arr.length - 1; i++) {

        // Check if there's a break between
        // consecutive numbers
        if (arr[i] + 1 !== arr[i + 1])
            count++;
    }

    return count;
}

// Driver Code
let arr = [ 100, 56, 5, 6, 102, 58, 101, 57, 7, 103, 59 ];
console.log(minSubsets(arr));

Output

[Expected Approach] Hashing - O(n) Time and O(n) Space

The idea is to use Hashing. We first insert all elements in a Hash Set. Then, traverse over all the elements and check if the current element can be a starting element of a consecutive subsequence. If it is then increment count by 1 and and remove elements X, X + 1, X + 2 …. till all consecutive numbers of this subset are removed.
To check if the current element, say X can be a starting element, check if (X – 1) is present in the set. If (X – 1) is present in the set, then X cannot be starting of a consecutive subsequence.

C++

// C++ program to find number of subset containing
// consecutive numbers using Hash Map

#include <iostream>
#include <vector>
#include <unordered_set>
using namespace std;

int minSubsets(vector<int>& arr) {
  
    unordered_set<int> s(arr.begin(), arr.end());    
    
    int count = 0;
    for(int x : arr) {
      
        // Check for the start of a new subset 
        if(s.find(x - 1) == s.end()) {
            count++;
        }
    }
    return count;
}

int main() {
    vector<int> arr = {100, 56, 5, 6, 102, 58, 101, 57, 7, 103};
    cout << minSubsets(arr) << endl;
    return 0;
}

Java

// Java program to find number of subset containing
// consecutive numbers using Hash Map in O(n)
import java.util.*;

class GfG {
    static int minSubsets(int[] arr) {
        
        // Create a HashSet from the array
        Set<Integer> s = new HashSet<>();
        for(int num : arr){
            s.add(num);
        }
        
        int count = 0;
        for(int x : arr){
            
            // Check for the start of a new subset 
            if(!s.contains(x - 1)){
                count++;
            }
        }
        return count;
    }
    
    public static void main(String[] args){
        int[] arr = {100, 56, 5, 6, 102, 58, 101, 57, 7, 103};
        System.out.println(minSubsets(arr));
    }
}

Python

# Python program to find number of subset containing
# consecutive numbers using Hash Map in O(n)
def minSubsets(arr):
    
    # Create a set from the list
    s = set(arr)
    
    count = 0
    for x in arr:
        
        # Check for the start of a new subset 
        if (x - 1) not in s:
            count += 1
    return count

if __name__ == "__main__":
    arr = [100, 56, 5, 6, 102, 58, 101, 57, 7, 103, 59]
    print(minSubsets(arr))

// C# program to find number of subset containing
// consecutive numbers using Hash Map in O(n)
using System;
using System.Collections.Generic;

class GfG {
    static int countSubsets(int[] arr) {
        
        // Create a HashSet from the list
        HashSet<int> s = new HashSet<int>(arr);
        
        int count = 0;
        foreach(int x in arr){
            
            // Check for the start of a new subset 
            if(!s.Contains(x - 1)){
                count++;
            }
        }
        return count;
    }
    
    static void Main(){
        int[] arr = {100, 56, 5, 6, 102, 58, 101, 57, 7, 103};
        Console.WriteLine(countSubsets(arr));
    }
}

JavaScript

// JavaScript program to find number of subset containing
// consecutive numbers using Hash Map in O(n)

function minSubsets(arr) {
    
    // Create a Set from the array
    let s = new Set(arr);
    
    let count = 0;
    for(let x of arr){
        
        // Check for the start of a new subset 
        if(!s.has(x - 1)){
            count++;
        }
    }
    return count;
}

// Driver Code
let arr = [100, 56, 5, 6, 102, 58, 101, 57, 7, 103];
console.log(minSubsets(arr));

Output

Choose m elements having minimum difference between max and min

Anuj Chauhan(anuj0503)

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Article Tags :

Practice Tags :

Partition into minimum subsets of consecutive numbers

[Naive Approach] Sorting - O(n*log n) Time and O(1) Space

[Expected Approach] Hashing - O(n) Time and O(n) Space

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