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Smallest number greater than X which is K-periodic
• Last Updated : 31 May, 2021

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++

 `// C++ Program to find the``// smallest K periodic``// integer greater than X``#include ``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

 ``
Output:
`1313`

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

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