给定两个整数N和K ，任务是打印所有由N位数字组成的正数，这些数字的第一位和最后一位之间的差等于K。
例子：
Input: N = 2, K = 0
Output: 11, 22, 33, 44, 55, 66, 77, 88, 99
Input: N = 2, K = 9
Output: 90
方法：想法是使用递归将所有可能的1位数字生成为N位数字，并检查该数字的第一位和最后一位之间的差是否等于K。步骤如下：
- 生成所有可能的长度为1的数字。
- 在每个步骤中，请继续在数字上添加数字，直到数字的长度变为N为止。
- 当数字的长度等于N时，计算数字的第一位和最后一位之间的差，并检查差是否等于N。如果发现是真实的，则打印该数字并继续生成下一个数字。
下面是上述方法的实现：
C++
// C++ program for the above approach
#include
using namespace std;
// Function to store and check the
// difference of digits
void findNumbers(string st, vector& result,
int prev, int n, int K)
{
// Base Case
if (st.length() == n) {
result.push_back(stoi(st));
return;
}
// Last digit of the number to
// check the difference from the
// first digit
if (st.size() == n - 1) {
// Condition to avoid
// repeated values
if (prev - K >= 0) {
string pt = "";
// Update the string pt
pt += prev - K + 48;
// Recursive Call
findNumbers(st + pt, result,
prev - K, n, K);
}
if (K != 0 && prev + K < 10) {
string pt = "";
// Update the string pt
pt += prev + K + 48;
// Recursive Call
findNumbers(st + pt, result,
prev + K, n, K);
}
}
// Any number can come in between
// first and last except the zero
else {
for (int j = 1; j <= 9; j++) {
string pt = "";
pt += j + 48;
// Recursive Call
findNumbers(st + pt, result,
prev, n, K);
}
}
}
// Function to place digit of the number
vector numDifference(int N, int K)
{
vector res;
string st = "";
// When N is 1 and K > 0, then the
// single number will be the first
// and last digit it cannot have
// difference greater than 0
if (N == 1 && K == 0) {
res.push_back(0);
}
else if (N == 1 && K > 0) {
return res;
}
// This loop place the digit at the
// starting
for (int i = 1; i < 10; i++) {
string temp = "";
temp += 48 + i;
// Recursive Call
findNumbers(st + temp, res, i, N, K);
st = "";
}
return res;
}
void numDifferenceUtil(int N, int K)
{
// Vector to store results
vector res;
// Generate all the resultant number
res = numDifference(N, K);
// Print the result
for (int i = 0; i < res.size(); i++) {
cout << res[i] << " ";
}
}
// Driver Code
int main()
{
int N = 2, K = 9;
// Function Call
numDifferenceUtil(N, K);
return 0;
} Java
// Java program for the above approach
import java.util.*;
@SuppressWarnings("unchecked")
class GFG{
// Function to store and check the
// difference of digits
static void findNumbers(String st, ArrayList result,
int prev, int n, int K)
{
// Base Case
if (st.length() == n)
{
result.add(Integer.parseInt(st));
return;
}
// Last digit of the number to
// check the difference from the
// first digit
if (st.length() == n - 1)
{
// Condition to avoid
// repeated values
if (prev - K >= 0)
{
String pt = "";
// Update the String pt
pt += (char)(prev - K + 48);
// Recursive Call
findNumbers(st + pt, result,
prev - K, n, K);
}
if (K != 0 && prev + K < 10)
{
String pt = "";
// Update the String pt
pt += (char)(prev + K + 48);
// Recursive Call
findNumbers(st + pt, result,
prev + K, n, K);
}
}
// Any number can come in between
// first and last except the zero
else
{
for(int j = 1; j <= 9; j++)
{
String pt = "";
pt += (char)(j + 48);
// Recursive Call
findNumbers(st + pt, result,
prev, n, K);
}
}
}
// Function to place digit of the number
static ArrayList numDifference(int N, int K)
{
ArrayList res = new ArrayList();
String st = "";
// When N is 1 and K > 0, then the
// single number will be the first
// and last digit it cannot have
// difference greater than 0
if (N == 1 && K == 0)
{
res.add(0);
}
else if (N == 1 && K > 0)
{
return res;
}
// This loop place the digit at the
// starting
for(int i = 1; i < 10; i++)
{
String temp = "";
temp += (char)(48 + i);
// Recursive Call
findNumbers(st + temp, res, i, N, K);
st = "";
}
return res;
}
static void numDifferenceUtil(int N, int K)
{
// Vector to store results
ArrayList res = new ArrayList();
// Generate all the resultant number
res = numDifference(N, K);
// Print the result
for(int i = 0; i < res.size(); i++)
{
System.out.print(res.get(i) + " ");
}
}
// Driver Code
public static void main(String []args)
{
int N = 2, K = 9;
// Function Call
numDifferenceUtil(N, K);
}
}
// This code is contributed by pratham76Python3
# Python3 program for
# the above approach
# Function to store and
# check the difference
# of digits
result = []
def findNumbers(st, prev,
n, K):
global result
# Base Case
if (len(st) == n):
result.append(int(st))
return
# Last digit of the number to
# check the difference from the
# first digit
if(len(st) == n - 1):
# Condition to avoid
# repeated values
if (prev - K >= 0):
pt = ""
# Update the string pt
pt += prev - K + 48
# Recursive Call
findNumbers(st + pt,
prev - K,
n, K)
if (K != 0 and
prev + K < 10):
pt = ""
# Update the string pt
pt += prev + K + 48
# Recursive Call
findNumbers(st + pt,
prev + K,
n, K)
# Any number can come in between
# first and last except the zero
else:
for j in range(1, 10, 1):
pt = ""
pt += j + 48
# Recursive Call
findNumbers(st + pt,
prev, n, K)
# Function to place digit
# of the number
def numDifference(N,K):
global result
st = ""
# When N is 1 and K > 0,
# then the single number
# will be the first and
# last digit it cannot have
# difference greater than 0
if (N == 1 and K == 0):
result.append(0)
elif(N == 1 and K > 0):
return result
# This loop place the
# digit at the starting
for i in range(1, 10, 1):
temp = ""
temp += str(48 + i)
# Recursive Call
findNumbers(st + temp,
i, N, K)
st = ""
return result
def numDifferenceUtil(N, K):
# Vector to store results
res = []
# Generate all the
# resultant number
res = numDifference(N, K)
# Print the result
for i in range(1, len(res)):
print(res[i] + 40,
end = " ")
break
# Driver Code
if __name__ == '__main__':
N = 2
K = 9
# Function Call
numDifferenceUtil(N, K)
# This code is contributed by bgangwar59C#
// C# program for the above approach
using System;
using System.Collections;
using System.Collections.Generic;
class GFG
{
// Function to store and check the
// difference of digits
static void findNumbers(string st, ArrayList result,
int prev, int n, int K)
{
// Base Case
if (st.Length == n) {
result.Add(Int32.Parse(st));
return;
}
// Last digit of the number to
// check the difference from the
// first digit
if (st.Length == n - 1) {
// Condition to avoid
// repeated values
if (prev - K >= 0) {
string pt = "";
// Update the string pt
pt += (char)(prev - K + 48);
// Recursive Call
findNumbers(st + pt, result,
prev - K, n, K);
}
if (K != 0 && prev + K < 10) {
string pt = "";
// Update the string pt
pt += (char)(prev + K + 48);
// Recursive Call
findNumbers(st + pt, result,
prev + K, n, K);
}
}
// Any number can come in between
// first and last except the zero
else {
for (int j = 1; j <= 9; j++) {
string pt = "";
pt += (char)(j + 48);
// Recursive Call
findNumbers(st + pt, result,
prev, n, K);
}
}
}
// Function to place digit of the number
static ArrayList numDifference(int N, int K)
{
ArrayList res=new ArrayList();
string st = "";
// When N is 1 and K > 0, then the
// single number will be the first
// and last digit it cannot have
// difference greater than 0
if (N == 1 && K == 0) {
res.Add(0);
}
else if (N == 1 && K > 0) {
return res;
}
// This loop place the digit at the
// starting
for (int i = 1; i < 10; i++) {
string temp = "";
temp += (char)(48 + i);
// Recursive Call
findNumbers(st + temp, res, i, N, K);
st = "";
}
return res;
}
static void numDifferenceUtil(int N, int K)
{
// Vector to store results
ArrayList res=new ArrayList();
// Generate all the resultant number
res = numDifference(N, K);
// Print the result
for (int i = 0; i < res.Count; i++) {
Console.Write(res[i]+" ");
}
}
// Driver Code
public static void Main(string []args)
{
int N = 2, K = 9;
// Function Call
numDifferenceUtil(N, K);
}
}
// This code is contributed by rutvik_56输出：
90时间复杂度： O(2 N )
辅助空间： O(N)