Print all combinations generated by characters of a numeric string which does not exceed N

Given a numeric string S of length M and an integer N, the task is to find all distinct combinations of S (repetitions allowed) that are at most N.

Examples:

Input: S = “124”, N = 100
Output: 1, 11, 12, 14, 2, 21, 22, 24, 4, 41, 42, 44
Explanation: Combinations “111”, “112”, “122”, “124”, “412” are greater than 100. Therefore, these combinations are excluded from the output.

Input: S = “345”, N = 400
Output: 3, 33, 333, 334, 335, 34, 343, 344, 345, 35, 353, 354, 355, 4, 43, 44, 45, 5, 53, 54, 55

Approach: The idea is to generate all the numbers possible using Backtracking and then print those numbers which does not exceed N. Follow the steps below to solve the problem:

• Initialize a Set of strings, say combinations[], to store all distinct combinations of S that numerically does not exceed N.
• Initialize a string ans to store the current combination of numbers possible from S.
• Declare a function generateCombinations() to generate all required combinations whose values are less than the given value N and the function is defined as:
  • Traverse the string S over the range [0, M] using the variable i and do the following:
    • Push the current character S[i] to ans and convert the current string ans to the number and store it in x.
    • If x is less than or equal to N then push the string ans into combinations[] and recursively call the function generateCombinations().
  • Backtrack to its previous state by removing the i^th character from ans.
• After completing the above steps, print the set of all strings stored in combinations[].

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Store the current sequence of s
string combination;

// Store the all the required sequences
set<string> combinations;

// Function to print all sequences of S
// satisfying the required condition
void printSequences(
    set<string> combinations)
{
    // Print all strings in the set
    for (string s : combinations) {
        cout << s << ' ';
    }
}

// Function to generate all sequences
// of string S that are at most N
void generateCombinations(string& s, int n)
{

    // Iterate over string s
    for (int i = 0; i < s.size(); i++) {

        // Push ith character to combination
        combination.push_back(s[i]);

        // Convert the string to number
        long x = stol(combination);

        // Check if the condition is true
        if (x <= n) {

            // Push the current string to
            // the final set of sequences
            combinations.insert(combination);

            // Recursively call function
            generateCombinations(s, n);
        }

        // Backtrack to its previous state
        combination.pop_back();
    }
}

// Driver Code
int main()
{
    string S = "124";
    int N = 100;

    // Function Call
    generateCombinations(S, N);

    // Print required sequences
    printSequences(combinations);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Store the current sequence of s
static String combination = "";

// Store the all the required sequences
static HashSet<String> combinations = new LinkedHashSet<String>();

// Function to print all sequences of S
// satisfying the required condition
static void printSequences(
    HashSet<String> combinations)
{

    // Print all Strings in the set
    for(String s : combinations)
    {
        System.out.print(s + " ");
    }
}

// Function to generate all sequences
// of String S that are at most N
static void generateCombinations(String s, int n)
{

    // Iterate over String s
    for(int i = 0; i < s.length(); i++)
    {

        // Push ith character to combination
        combination += (s.charAt(i));

        // Convert the String to number
        long x = Integer.valueOf(combination);

        // Check if the condition is true
        if (x <= n)
        {

            // Push the current String to
            // the final set of sequences
            combinations.add(combination);

            // Recursively call function
            generateCombinations(s, n);
        }

        // Backtrack to its previous state
        combination = combination.substring(
            0, combination.length() - 1);
    }
}

// Driver Code
public static void main(String[] args)
{
    String S = "124";
    int N = 100;

    // Function Call
    generateCombinations(S, N);

    // Print required sequences
    printSequences(combinations);
}
}

// This code is contributed by Amit Katiyar

Python3

# Python3 program for the above approach

# Store the current sequence of s
combination = "";

# Store the all the required sequences
combinations = [];

# Function to print all sequences of S
# satisfying the required condition
def printSequences(combinations) :

    # Print all strings in the set
    for s in (combinations) :
        print(s, end = ' ');

# Function to generate all sequences
# of string S that are at most N
def generateCombinations(s, n) :
    global combination;

    # Iterate over string s
    for i in range(len(s)) :

        # Push ith character to combination
        combination += s[i];

        # Convert the string to number
        x = int(combination);

        # Check if the condition is true
        if (x <= n) :

            # Push the current string to
            # the final set of sequences
            combinations.append(combination);

            # Recursively call function
            generateCombinations(s, n);

        # Backtrack to its previous state
        combination = combination[:-1];

# Driver Code
if __name__ == "__main__" :

    S = "124";
    N = 100;

    # Function Call
    generateCombinations(S, N);

    # Print required sequences
    printSequences(combinations);

    # This code is contributed by AnkThon

C#

// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG
{

// Store the current sequence of s
static String combination = "";

// Store the all the required sequences
static SortedSet<String> combinations = new SortedSet<String>();

// Function to print all sequences of S
// satisfying the required condition
static void printSequences(
    SortedSet<String> combinations)
{

    // Print all Strings in the set
    foreach(String s in combinations)
    {
        Console.Write(s + " ");
    }
}

// Function to generate all sequences
// of String S that are at most N
static void generateCombinations(String s, int n)
{

    // Iterate over String s
    for(int i = 0; i < s.Length; i++)
    {

        // Push ith character to combination
        combination += (s[i]);

        // Convert the String to number
        long x = Int32.Parse(combination);

        // Check if the condition is true
        if (x <= n)
        {

            // Push the current String to
            // the readonly set of sequences
            combinations.Add(combination);

            // Recursively call function
            generateCombinations(s, n);
        }

        // Backtrack to its previous state
        combination = combination.Substring(
            0, combination.Length - 1);
    }
}

// Driver Code
public static void Main(String[] args)
{
    String S = "124";
    int N = 100;

    // Function Call
    generateCombinations(S, N);

    // Print required sequences
    printSequences(combinations);
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>
      // JavaScript program for the above approach
      // Store the current sequence of s
      var combination = "";

      // Store the all the required sequences
      var combinations = [];

      // Function to print all sequences of S
      // satisfying the required condition
      function printSequences(combinations) {
        // Print all Strings in the set
        for (var s of combinations) {
          document.write(s + " ");
        }
      }

      // Function to generate all sequences
      // of String S that are at most N
      function generateCombinations(s, n) {
        // Iterate over String s
        for (var i = 0; i < s.length; i++) {
          // Push ith character to combination
          combination += s[i];

          // Convert the String to number
          var x = parseInt(combination);

          // Check if the condition is true
          if (x <= n) {
            // Push the current String to
            // the readonly set of sequences
            combinations.push(combination);

            // Recursively call function
            generateCombinations(s, n);
          }

          // Backtrack to its previous state
          combination = combination.substring(0, combination.length - 1);
        }
      }

      // Driver Code
      var S = "124";
      var N = 100;

      // Function Call
      generateCombinations(S, N);

      // Print required sequences
      printSequences(combinations);
    </script>

Output:

1 11 12 14 2 21 22 24 4 41 42 44

Time Complexity: O(N^N)
Auxiliary Space: O(N^N)