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

• Difficulty Level : Hard
• Last Updated : 11 May, 2021

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 ith 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 ``using` `namespace` `std;` `// Store the current sequence of s``string combination;` `// Store the all the required sequences``set combinations;` `// Function to print all sequences of S``// satisfying the required condition``void` `printSequences(``    ``set 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 combinations = ``new` `LinkedHashSet();` `// Function to print all sequences of S``// satisfying the required condition``static` `void` `printSequences(``    ``HashSet 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 combinations = ``new` `SortedSet();` `// Function to print all sequences of S``// satisfying the required condition``static` `void` `printSequences(``    ``SortedSet 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

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Output:

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

Time Complexity: O(NN)
Auxiliary Space: O(NN)

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