Smallest number greater than X which is K-periodic

Given a string integer X consisting of N digits and an integer K, the task is to find the smallest integer greater than or equal to X which is K periodic (K <= N)
Examples: 

Input: K = 2, X = “1215” 
Output: 1313 
Explanation: 
1313 is 2-periodic since digits at positions 1, 3 are ‘1’ and digits at positions 2, 4 are ‘3’. This is the smallest 2-periodic integer greater than or equal to “1215”.
Input: K = 3, X = “299398” 
Output: 300300 
Explanation: 
300300 is the smallest possible 3 periodic number. 

Approach: 
To solve the problem, the idea is to make Xi = Xi-k for all i > K. Then follow the steps below to solve the problem:

  • Check if X greater than or equal to the initial integer. If so, then print the current string as the answer.
  • Otherwise, traverse from right to left and find the first digit which is not equal to 9. Then increment that digit by 1 and mark the position by a variable called pos.
  • Then set all digits after pos up to the Kth digit to 0. Again make Xi = Xi-k for all i >K.

Below is the implementation of the above approach:

C++

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// C++ Program to find the 
// smallest K periodic 
// integer greater than X 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to find the 
// smallest K periodic 
// integer greater than X 
string Kperiodicinteger(string X, int N, 
                        int K) 
    // Stores the number 
    // in a temporary string 
    string temp = X; 
  
    // Set X[i]=X[i-k] for 
    // i>k 
    for (int i = 0; i < K; i++) 
  
    
        // Start from 
        // the current 
        // index 
        int j = i; 
  
        // Loop upto N 
        // change 
        // X[j] to X[i] 
        while (j < N) { 
            X[j] = X[i]; 
            j += K; 
        
    
  
    // Return X if current 
    // Value is greater 
    // than original value 
    if (X >= temp) { 
  
        return X; 
    
  
    int POS; 
  
    // Find the first 
    // digit not equal to 9 
    for (int i = K - 1; i >= 0; i--) { 
        if (X[i] != '9') { 
              
        // Increment X[i] 
            X[i]++; 
  
            // Set POS to 
            // current index 
            POS = i; 
  
            break
        
    
  
    // Change X[i] to 0 
    // for all indices 
    // from POS+1 to K 
    for (int i = POS + 1; i < K; i++) { 
        X[i] = '0'
    
  
    // Set X[i]=X[i-k] for 
    // i>k 
    for (int i = 0; i < K; i++) 
  
    
        int j = i; 
        // Loop upto N 
        // change 
        // X[j] to X[i] 
  
        while (j < N) { 
            X[j] = X[i]; 
            j += K; 
        
    
  
    // Return the 
    // final string 
    return X; 
  
// Driver Code 
int main() 
  
    int N = 4, K = 2; 
  
    string X = "1215"
  
    cout << Kperiodicinteger(X, N, K); 
  
    return 0; 
}

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Java

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// Java program to find the smallest 
// K periodic integer greater than X 
import java.util.*; 
  
class GFG{ 
  
// Function to find the 
// smallest K periodic 
// integer greater than X 
static String Kperiodicinteger(char []X, 
                            int N, int K) 
      
    // Stores the number 
    // in a temporary String 
    String temp = String.valueOf(X); 
  
    // Set X[i]=X[i-k] for 
    // i>k 
    for(int i = 0; i < K; i++) 
    
          
        // Start from the current 
        // index 
        int j = i; 
  
        // Loop upto N change 
        // X[j] to X[i] 
        while (j < N) 
        
            X[j] = X[i]; 
            j += K; 
        
    
  
    // Return X if current 
    // Value is greater 
    // than original value 
    if (String.valueOf(X).compareTo(temp) >= 0
    
        return String.valueOf(X); 
    
  
    int POS = 0
  
    // Find the first 
    // digit not equal to 9 
    for(int i = K - 1; i >= 0; i--) 
    
        if (X[i] != '9'
        
              
            // Increment X[i] 
            X[i]++; 
  
            // Set POS to 
            // current index 
            POS = i; 
            break
        
    
  
    // Change X[i] to 0 
    // for all indices 
    // from POS+1 to K 
    for(int i = POS + 1; i < K; i++) 
    
        X[i] = '0'
    
  
    // Set X[i]=X[i-k] for 
    // i>k 
    for(int i = 0; i < K; i++) 
    
        int j = i; 
          
        // Loop upto N change 
        // X[j] to X[i] 
        while (j < N) 
        
            X[j] = X[i]; 
            j += K; 
        
    
  
    // Return the 
    // final String 
    return String.valueOf(X); 
  
// Driver Code 
public static void main(String[] args) 
    int N = 4, K = 2
    String X = "1215"
  
    System.out.print(Kperiodicinteger( 
            X.toCharArray(), N, K)); 
  
// This code is contributed by sapnasingh4991 

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C#

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// C# program to find the smallest
// K periodic integer greater than X
using System;
  
class GFG{
  
// Function to find the
// smallest K periodic
// integer greater than X
static String Kperiodicinteger(char[] X, 
                               int N, int K)
{
  
    // Stores the number
    // in a temporary String
    String temp = String.Join("", X);
  
    // Set X[i]=X[i-k] for
    // i>k
    for(int i = 0; i < K; i++)
    {
  
        // Start from the current
        // index
        int j = i;
  
        // Loop upto N change
        // X[j] to X[i]
        while (j < N) 
        {
            X[j] = X[i];
            j += K;
        }
    }
  
    // Return X if current
    // Value is greater
    // than original value
    if (String.Join("", X).CompareTo(temp) >= 0) 
    {
        return String.Join("", X);
    }
  
    int POS = 0;
  
    // Find the first
    // digit not equal to 9
    for(int i = K - 1; i >= 0; i--) 
    {
        if (X[i] != '9')
        {
  
            // Increment X[i]
            X[i]++;
  
            // Set POS to
            // current index
            POS = i;
            break;
        }
    }
  
    // Change X[i] to 0
    // for all indices
    // from POS+1 to K
    for(int i = POS + 1; i < K; i++)
    {
        X[i] = '0';
    }
  
    // Set X[i]=X[i-k] for
    // i>k
    for(int i = 0; i < K; i++)
    {
        int j = i;
  
        // Loop upto N change
        // X[j] to X[i]
        while (j < N)
        {
            X[j] = X[i];
            j += K;
        }
    }
  
    // Return the
    // readonly String
    return String.Join("", X);
}
  
// Driver Code
public static void Main(String[] args)
{
    int N = 4, K = 2;
    String X = "1215";
  
    Console.Write(Kperiodicinteger(
          X.ToCharArray(), N, K));
}
}
  
// This code is contributed by sapnasingh4991

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Output: 

1313

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

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