Combinations in a String of Digits

Last Updated : 13 Aug, 2024

Given an input string of numbers, find all combinations of numbers that can be formed using digits in the same order.
Examples:

Input : 123 
Output :1 2 3
        1 23
        12 3
        123

Input : 1234
Output : 1 2 3 4 
        1 2 34 
        1 23 4 
        1 234 
        12 3 4 
        12 34 
        123 4 
        1234

The problem can be solved using recursion. We keep track of the current index in the given input string and the length of the output string so far. In each call to the function, if there are no digits remaining in the input string print the current output string and return. Otherwise, copy the current digit to output. From here make two calls, one considering the next digit as part of the next number(including a space in output string) and one considering the next digit as part of the current number( no space included). If there are no digits remaining after the current digit the second call to the function is omitted because a trailing space doesn’t count as a new combination.

C++

// CPP program to find all combination of numbers 
// from a given string of digits
#include <iostream>
#include <cstring>
using namespace std;

// function to print combinations of numbers 
// in given input string
void printCombinations(char* input, int index, 
                     char* output, int outLength)
{
    // no more digits left in input string
    if (input[index] == '\0')
    {
        // print output string & return
        output[outLength] = '\0';
        cout << output << endl;
        return;
    }
    
    // place current digit in input string
    output[outLength] = input[index];
    
    // separate next digit with a space
    output[outLength + 1] = ' ';
    
    printCombinations(input, index + 1, output, 
                                   outLength + 2);
    
    // if next digit exists make a 
    // call without including space
    if(input[index + 1] != '\0')
    printCombinations(input, index + 1, output, 
                                    outLength + 1);
    
}

// driver function to test above function
int main()
{
    char input[] = "1214";
    char *output = new char[100];

    // initialize output with empty string
    output[0] = '\0';
    
    printCombinations(input, 0, output, 0);
    return 0;
}

Java

// Java program to find all combinations
// of numbers from a given string of digits
class GFG
{
    
// function to print combinations of numbers 
// in given input string
static void printCombinations(char[] input,
                              int index, 
                              char[] output, 
                              int outLength)
{
    // no more digits left in input string
    if (input.length == index)
    {
        // print output string & return
        System.out.println(String.valueOf(output));
        return;
    }
    
    // place current digit in input string
    output[outLength] = input[index];
    
    // separate next digit with a space
    output[outLength + 1] = ' ';
    
    printCombinations(input, index + 1, output, 
                                outLength + 2);
    
    // if next digit exists make a 
    // call without including space
    if(input.length!=index + 1)
    printCombinations(input, index + 1, output, 
                                outLength + 1);
}

// Driver Code
public static void main(String[] args) 
{
    char input[] = "1214".toCharArray();
    char []output = new char[100];
    
    printCombinations(input, 0, output, 0);
}
}

// This code is contributed by Rajput-Ji

Python3

# Python3 program to find all combination of numbers 
# from a given string of digits

# function to print combinations of numbers 
# in given input string
def printCombinations(input, index, output, outLength):
    
    # no more digits left in input string
    if (len(input) == index):
        
        # print output string & return
        output[outLength] = '\0'
        print(*output[:outLength], sep = "")
        return
    
    # place current digit in input string
    output[outLength] = input[index]
    
    # separate next digit with a space
    output[outLength + 1] = ' '
    printCombinations(input, index + 1, 
                       output, outLength + 2)
    
    # if next digit exists make a 
    # call without including space
    if(len(input) != (index + 1)):
        printCombinations(input, index + 1, 
                          output, outLength + 1)

# Driver code
input = "1214"
output = [0]*100

# initialize output with empty string
output[0] = '\0'

printCombinations(input, 0, output, 0)

# This code is contributed by SHUBHAMSINGH10

// C# program to find all combinations
// of numbers from a given string of digits
using System;
    
class GFG
{
    
// function to print combinations of numbers 
// in given input string
static void printCombinations(char[] input,
                              int index, 
                              char[] output, 
                              int outLength)
{
    // no more digits left in input string
    if (input.Length == index)
    {
        // print output string & return
        Console.WriteLine(String.Join("", 
                                output));
        return;
    }
    
    // place current digit in input string
    output[outLength] = input[index];
    
    // separate next digit with a space
    output[outLength + 1] = ' ';
    
    printCombinations(input, index + 1, output, 
                                outLength + 2);
    
    // if next digit exists make a 
    // call without including space
    if(input.Length!=index + 1)
    printCombinations(input, index + 1, output, 
                                outLength + 1);
}

// Driver Code
public static void Main(String[] args) 
{
    char []input = "1214".ToCharArray();
    char []output = new char[100];
    
    printCombinations(input, 0, output, 0);
}
}

// This code is contributed by 29AjayKumar

JavaScript

<script>
// Javascript program to find all combinations
// of numbers from a given string of digits

    // function to print combinations of numbers
// in given input string
    function printCombinations(input,index,output,outLength)
    {
    
        // no more digits left in input string
    if (input.length == index)
    {
    
        // print output string & return
        document.write(output.join("")+"<br>");
        return;
    }
     
    // place current digit in input string
    output[outLength] = input[index];
     
    // separate next digit with a space
    output[outLength + 1] = ' ';
     
    printCombinations(input, index + 1, output,
                                outLength + 2);
     
    // if next digit exists make a
    // call without including space
    if(input.length != index + 1)
    printCombinations(input, index + 1, output,
                                outLength + 1);
    }
    
    // Driver Code
    let input = "1214".split("");
    let output = new Array(100);
    printCombinations(input, 0, output, 0);
    
    // This code is contributed by avanitrachhadiya2155
</script>

Output:

Time complexity : O(2^n)

Space complexity : O(n^2)
Alternative Solution:

C++

// CPP program to find all combination of
// numbers from a given string of digits
// using bit algorithm used same logic
// as to print power set of string
#include <bits/stdc++.h>
using namespace std;

// function to print combinations of 
// numbers in given input string
void printCombinations(char s[]){
    
    // find length of char array
    int l = strlen(s);

    // we can give space between characters 
    // ex. ('1' & '2') or ('2' & '3') or
    // ('3' & '4') or ('3' & '4') or all
    // that`s why here we have maximum 
    // space length - 1
    for(int i = 0; i < pow(2, l - 1); i++){
        int k = i, x = 0;
        
        // first character will be printed
        // as well
        cout << s[x];
        x++;
        for(int j = 0; j < strlen(s) - 1; j++){
            
            // if bit is set, means provide
            // space
            if(k & 1)
                cout << " ";
            k = k >> 1;
            cout << s[x];
            
            // always increment index of 
            // input string
            x++;
        }
        cout << "\n";
    }
}

// driver code
int main() {

    char input[] = "1214";
    printCombinations(input);
    
    return 0;
}
// This code is contributed by PRINCE Gupta 2

Java

// Java program to find all combination of
// numbers from a given string of digits
// using bit algorithm used same logic
// as to print power set of string
import java.util.*;

class GFG
{

// function to print combinations of 
// numbers in given input string
static void printCombinations(char s[])
{
    
    // find length of char array
    int l = s.length;

    // we can give space between characters 
    // ex. ('1' & '2') or ('2' & '3') or
    // ('3' & '4') or ('3' & '4') or all
    // that`s why here we have maximum 
    // space length - 1
    for(int i = 0; 
            i < Math.pow(2, l - 1); i++)
    {
        int k = i, x = 0;
        
        // first character will be printed
        // as well
        System.out.print(s[x]);
        x++;
        for(int j = 0; 
                j < s.length - 1; j++)
        {
            
            // if bit is set, means provide
            // space
            if(k % 2 == 1)
                System.out.print(" ");
            k = k >> 1;
            System.out.print(s[x]);
            
            // always increment index of 
            // input string
            x++;
        }
        System.out.print("\n");
    }
}

// Driver Code
public static void main(String[] args) 
{
    char input[] = "1214".toCharArray();
    printCombinations(input);
}
}

// This code is contributed by PrinciRaj1992

Python

# Python 3 program to find all
# combination of numbers from 
# a given string of digits using 
# bit algorithm used same logic
# as to print power set of string

# Function to print combinations of 
# numbers in given input string
def printCombinations(s):
    
    # find length of char array
    l = len(s);

    # we can give space between 
    # characters ex. ('1' & '2')
    # or ('2' & '3') or ('3' & '4')
    # or ('3' & '4') or all that`s 
    # why here we have maximum 
    # space length - 1
    for i in range(pow(2, l - 1)):
        k = i
        x = 0
        
        # first character will 
        # be printed as well
        print(s[x], end = "")
        x += 1
        
        for j in range(len(s) - 1):
            
            # if bit is set, means 
            # provide space
            if(k & 1):
                print(" ", end = "")
            k = k >> 1
            print(s[x], end = "")
            
            # always increment index of 
            # input string
            x += 1
        
        print()

# Driver code
if __name__ == "__main__":

    inp = "1214";
    printCombinations(inp);

# This code is contributed by Chitranayal

// C# program to find all combination of
// numbers from a given string of digits
// using bit algorithm used same logic
// as to print power set of string
using System;
    
class GFG
{

// function to print combinations of 
// numbers in given input string
static void printCombinations(char []s)
{
    
    // find length of char array
    int l = s.Length;

    // we can give space between characters 
    // ex. ('1' & '2') or ('2' & '3') or
    // ('3' & '4') or ('3' & '4') or all
    // that`s why here we have maximum 
    // space length - 1
    for(int i = 0; 
            i < Math.Pow(2, l - 1); i++)
    {
        int k = i, x = 0;
        
        // first character will be printed
        // as well
        Console.Write(s[x]);
        x++;
        for(int j = 0; 
                j < s.Length - 1; j++)
        {
            
            // if bit is set, means provide
            // space
            if(k % 2 == 1)
                Console.Write(" ");
            k = k >> 1;
            Console.Write(s[x]);
            
            // always increment index of 
            // input string
            x++;
        }
        Console.Write("\n");
    }
}

// Driver Code
public static void Main(String[] args) 
{
    char []input = "1214".ToCharArray();
    printCombinations(input);
}
}

// This code is contributed by Rajput-Ji

JavaScript

<script>

// Javascript program to find all combination of
// numbers from a given string of digits
// using bit algorithm used same logic
// as to print power set of string
    
    // function to print combinations of
    // numbers in given input string
    function printCombinations(s)
    {
        // find length of char array
    let l = s.length;
 
    // we can give space between characters
    // ex. ('1' & '2') or ('2' & '3') or
    // ('3' & '4') or ('3' & '4') or all
    // that`s why here we have maximum
    // space length - 1
    for(let i = 0;
            i < Math.pow(2, l - 1); i++)
    {
        let k = i, x = 0;
         
        // first character will be printed
        // as well
        document.write(s[x]);
        x++;
        for(let j = 0;
                j < s.length - 1; j++)
        {
             
            // if bit is set, means provide
            // space
            if(k % 2 == 1)
                document.write(" ");
            k = k >> 1;
            document.write(s[x]);
             
            // always increment index of
            // input string
            x++;
        }
        document.write("<br>");
    }
    }
    
    // Driver Code
    let input= "1214".split("");
    printCombinations(input);
    
    // This code is contributed by rag2127
    
</script>

Output:

Time Complexity : O(n * 2^n)

Space Complexity : O(n)

Maximise product of each array element with their indices by rearrangement

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Combinations in a String of Digits

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