给定一个由N位数字组成的字符串整数X和一个整数K ，任务是找到大于或等于X的最小整数，它是K周期(K <= N) 。
例子：
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.
方法：
为了解决这个问题，我们的想法是让X i = X ik对所有i > K 。然后按照以下步骤解决问题：
- 检查X 是否大于或等于初始整数。如果是，则打印当前字符串作为答案。
- 否则，从右向左遍历，找到第一个不等于9 的数字。然后将该数字加1，并用名为pos的变量标记该位置。
- 然后将pos之后的所有数字设置为第K个数字为0 。再次使X i = X ik对所有i > K 。
下面是上述方法的实现：
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 sapnasingh4991Python3
# 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 avanitrachhadiya2155C#
// 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 sapnasingh4991Javascript
输出：
1313时间复杂度： O(N)
辅助空间： O(N)
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