Check if a numeric string can be split into substrings having difference between consecutive numbers equal to K

Given a numeric string S consisting of N digits and a positive integer K, the task is to check if the given string can be split into more than one substrings with difference between consecutive substrings equal to K.

Examples:

Input: S = “8642”, K = 2
Output: Yes
Explanation: Split the given string as {“8”, “6”, “4”, “2”}. Now, the difference between the consecutive substrings is K(= 2).

Input: S = “1009896”, K = 0
Output: No

Approach: The given problem can be solved by generating all possible substring of the given string and check if the concatenation of any subset of the generated substring is equal to the given string S and the consecutive difference of the number as a substring is K, then print Yes. Otherwise, print No. Follow the below steps to solve the problem:

• Iterate over the range [1, N/2] using the variable i and perform the following steps:
  • Store the substring of length i and starting from 0 in a variable X.
  • Generate the sequence of size N starting with this number X where the difference of consecutive terms is K. Store this string in a variable test.
  • If both the strings test and S are equal, then update the value of ans as true and break out of the loop.
• After completing the above steps, if the value of ans is false, print “No”. Otherwise, print “Yes”.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to check if a numeric string
// can be split into substrings such that
// the difference between the consecutive
// substrings is K
void isPossible(string s, int K)
{
    bool valid = false;
    long firstx = -1;

    // Stores the size of the string
    int n = s.length();

    // Iterate over the range [1, N] and
    // try each possible starting number
    for (int i = 1; i <= n / 2; ++i) {

        long x = stol(s.substr(0, i));
        firstx = x;

        // Convert the number to string
        string test = to_string(x);

        // Build up a sequence
        // starting with the number
        while (test.length() < s.length()) {
            x -= K;
            test += to_string(x);
        }

        // Compare it with the
        // original string s
        if (test == s) {
            valid = true;
            break;
        }
    }

    // Print the result
    cout << ((valid == true) ? "Yes " : "No");
}

// Driver Code
int main()
{
    string S = "8642";
    int K = 2;
    isPossible(S, K);

    return 0;
}

Java

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

class GFG {

  // Function to check if a numeric String
  // can be split into subStrings such that
  // the difference between the consecutive
  // subStrings is K
  static void IsPossible(String s, int k)
  {
    boolean valid = false;
    long firstx = -1;

    // Stores the size of the String
    int n = s.length();

    // Iterate over the range [1, N] and
    // try each possible starting number
    for (int i = 1; i <= n / 2; ++i) {
      long x = Long.valueOf(s.substring(0, i));
      firstx = x;

      // Convert the number to String
      String test = String.valueOf(x);

      // Build up a sequence
      // starting with the number
      while (test.length() < s.length()) {
        x -= k;
        test += String.valueOf(x);
      }

      // Compare it with the
      // original String s
      if (test.equals(s)) {
        valid = true;
        break;
      }
    }

    // Print the result
    System.out.println(valid ? "Yes" : "No");
  }

  // Driver code
  public static void main(String[] args)
  {
    String S = "8642";
    int K = 2;

    // Function call
    IsPossible(S, K);
  }
}

// This code is contributed by phasing17.

Python3

# python 3 program for the above approach

# Function to check if a numeric string
# can be split into substrings such that
# the difference between the consecutive
# substrings is K
def isPossible(s,K):
    valid = False
    firstx = -1

    # Stores the size of the string
    n = len(s)

    # Iterate over the range [1, N] and
    # try each possible starting number
    for i in range(1,n//2+1,1):
        x = int(s[0:i])
        firstx = x

        # Convert the number to string
        test = str(x)

        # Build up a sequence
        # starting with the number
        while (len(test) < len(s)):
            x -= K
            test += str(x)

        # Compare it with the
        # original string s
        if (test == s):
            valid = True
            break

    # Print the result
    print("Yes") if valid == True else print("No")

# Driver Code
if __name__ == '__main__':
    S = "8642"
    K = 2
    isPossible(S, K)

    # This code is contributed by ipg2016107.

C#

// C# program for the above approach
using System;

class GFG {

  // Function to check if a numeric string
  // can be split into substrings such that
  // the difference between the consecutive
  // substrings is K
  static void IsPossible(string s, int k)
  {
    bool valid = false;
    long firstx = -1;

    // Stores the size of the string
    int n = s.Length;

    // Iterate over the range [1, N] and
    // try each possible starting number
    for (int i = 1; i <= n / 2; ++i) {
      long x = Convert.ToInt64(s.Substring(0, i));
      firstx = x;

      // Convert the number to string
      string test = x.ToString();

      // Build up a sequence
      // starting with the number
      while (test.Length < s.Length) {
        x -= k;
        test += x.ToString();
      }

      // Compare it with the
      // original string s
      if (test == s) {
        valid = true;
        break;
      }
    }

    // Print the result
    Console.WriteLine(valid == true ? "Yes" : "No");
  }

  // Driver code
  static void Main(string[] args)
  {
    string S = "8642";
    int K = 2;

    // Function call
    IsPossible(S, K);
  }
}

// This code is contributed by phasing17.

Javascript

<script>

// JavaScript program for the above approach

// Function to check if a numeric string
// can be split into substrings such that
// the difference between the consecutive
// substrings is K
function isPossible(s, K)
{
    let valid = false;
    let firstx = -1;

    // Stores the size of the string
    let n = s.length;

    // Iterate over the range [1, N] and
    // try each possible starting number
    for (let i = 1; i <= n / 2; ++i) {

        let x = (s.substr(0, i));
        firstx = x;

        // Convert the number to string
        let test = x.toString();

        // Build up a sequence
        // starting with the number
        while (test.length < s.length) {
            x -= K;
            test += x.toString();
        }

        // Compare it with the
        // original string s
        if (test == s) {
            valid = true;
            break;
        }
    }

    // Print the result
    document.write((valid == true) ? "Yes " : "No");
}
// Driver Code

    let S = "8642";
    let K = 2;
    isPossible(S, K);

</script>

Output:

Yes

Time Complexity: O(N²)
Auxiliary Space: O(N)