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 X_i = X_i-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 K^th digit to 0. Again make X_i = X_i-k for all i >K.

Below is the implementation of the above approach:

C++

// 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;
}

Java

// 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

Python3

# Python3 program to find the smallest
# K periodic integer greater than X

# Function to find the
# smallest K periodic
# integer greater than X
def Kperiodicinteger(X, N, K):

    X = list(X)

    # Stores the number
    # in a temporary string
    temp = X.copy()

    # Set X[i]=X[i-k] for
    # i>k
    for i in range(K):

        # Start from the current
        # index
        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

    POS = 0

    # Find the first digit
    # not equal to 9
    for i in range(K - 1, -1, -1):
        if (X[i] != '9'):

            # Increment X[i]
            X[i] = str(int(X[i]) + 1)

            # Set POS to
            # current index
            POS = i
            break

    # Change X[i] to 0
    # for all indices
    # from POS+1 to K
    for i in range(POS + 1, K):
        X[i] = '0'

    # Set X[i]=X[i-k] for
    # i>k
    for i in range(K):
        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
N = 4
K = 2
X = "1215"

print(*Kperiodicinteger(X, N, K), sep = '')

# This code is contributed by avanitrachhadiya2155

C#

// 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

Javascript

<script>

// Javascript Program to find the
// smallest K periodic
// integer greater than X

// Function to find the
// smallest K periodic
// integer greater than X
function Kperiodicinteger(X, N, K)
{
    // Stores the number
    // in a temporary string
    var temp = X

    // Set X[i]=X[i-k] for
    // i>k
    for (var i = 0; i < K; i++)

    {
        // Start from
        // the current
        // index
        var 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 (parseInt(X.join('')) < parseInt(temp.join(''))) {

        return X.join('');
    }

    var POS;

    // Find the first
    // digit not equal to 9
    for (var i = K - 1; i >= 0; i--) {
        if (X[i] != '9') {

        // Increment X[i]
            X[i] = String.fromCharCode(X[i].charCodeAt(0) + 1);

            // Set POS to
            // current index
            POS = i;

            break;
        }
    }

    // Change X[i] to 0
    // for all indices
    // from POS+1 to K
    for (var i = POS + 1; i < K; i++) {
        X[i] = '0';
    }

    // Set X[i]=X[i-k] for
    // i>k
    for (var i = 0; i < K; i++)

    {
        var 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.join('');
}

// Driver Code
var N = 4, K = 2;
var X = "1215";
document.write( Kperiodicinteger(X.split(''), N, K));

// This code is contributed by itsok.
</script>

Output:

1313

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