查找数字总和为N的最小数字

给定正整数N ，任务是找到位数之和为N的最小数字。
例子：

Input: N = 10
Output: 19
Explanation:
1 + 9 = 10 = N

Input: N = 18
Output: 99
Explanation:
9 + 9 = 18 = N

天真的方法：

• 天真的方法是从0开始运行i的循环，找到i的数字总和，然后检查它是否等于N。

下面是上述方法的实现。

C++

// C++ program to find the smallest
// number whose sum of digits is also N
#include 
#include 
using namespace std;
 
// Function to get sum of digits
int getSum(int n)
{
    int sum = 0;
    while (n != 0) {
        sum = sum + n % 10;
        n = n / 10;
    }
    return sum;
}
 
// Function to find the smallest
// number whose sum of digits is also N
void smallestNumber(int N)
{
    int i = 1;
    while (1) {
        // Checking if number has
        // sum of digits = N
        if (getSum(i) == N) {
            cout << i;
            break;
        }
        i++;
    }
}
 
// Driver code
int main()
{
    int N = 10;
    smallestNumber(N);
 
    return 0;
}

Java

// Java program to find the smallest
// number whose sum of digits is also N
class GFG{
 
// Function to get sum of digits
static int getSum(int n)
{
    int sum = 0;
    while (n != 0)
    {
        sum = sum + n % 10;
        n = n / 10;
    }
    return sum;
}
 
// Function to find the smallest
// number whose sum of digits is also N
static void smallestNumber(int N)
{
    int i = 1;
    while (1 != 0)
    {
        // Checking if number has
        // sum of digits = N
        if (getSum(i) == N)
        {
            System.out.print(i);
            break;
        }
        i++;
    }
}
 
// Driver code
public static void main(String[] args)
{
    int N = 10;
    smallestNumber(N);
}
}
 
// This code is contributed
// by shivanisinghss2110

Python3

# Python3 program to find the smallest
# number whose sum of digits is also N
 
# Function to get sum of digits
def getSum(n):
 
    sum1 = 0;
    while (n != 0):
        sum1 = sum1 + n % 10;
        n = n // 10;
     
    return sum1;
 
# Function to find the smallest
# number whose sum of digits is also N
def smallestNumber(N):
 
    i = 1;
    while (1):
        # Checking if number has
        # sum of digits = N
        if (getSum(i) == N):
            print(i);
            break;
         
        i += 1;
     
# Driver code
N = 10;
smallestNumber(N);
 
# This code is contributed by Code_Mech

C#

// C# program to find the smallest
// number whose sum of digits is also N
using System;
 
class GFG{
 
// Function to get sum of digits
static int getSum(int n)
{
    int sum = 0;
    while (n != 0)
    {
        sum = sum + n % 10;
        n = n / 10;
    }
    return sum;
}
 
// Function to find the smallest
// number whose sum of digits is also N
static void smallestNumber(int N)
{
    int i = 1;
    while (1 != 0)
    {
         
        // Checking if number has
        // sum of digits = N
        if (getSum(i) == N)
        {
            Console.Write(i);
            break;
        }
        i++;
    }
}
 
// Driver code
public static void Main(String[] args)
{
    int N = 10;
     
    smallestNumber(N);
}
}
 
// This code is contributed by Amit Katiyar

Javascript

 
//Javascript program to find /the smallest
// number whose sum of digits is also N
  
// Function to get sum of digits
function getSum(n)
{
    let sum = 0;
    while (n != 0) {
        sum = sum + n % 10;
        n = Math.floor(n / 10);
    }
    return sum;
}
  
// Function to find the smallest
// number whose sum of digits is also N
function smallestNumber(N)
{
    let i = 1;
    while (1) {
        // Checking if number has
        // sum of digits = N
        if (getSum(i) == N) {
            document.write(i);
            break;
        }
        i++;
    }
}
  
// Driver code
 
    let N = 10;
    smallestNumber(N);
  
     
// This code is contributed by Mayank Tyagi
 

输出

19

时间复杂度： O(N)。
高效方法：

• 解决此问题的有效方法是观察。让我们看一些例子。
  • 如果N = 10，则ans = 19
  • 如果N = 20，则ans = 299
  • 如果N = 30，则ans = 3999
• 因此，很明显答案将除第一个数字外的所有数字均为9，因此我们得到的数字最小。
• 因此，第N个项将是=

$(N \bmod 9 + 1) * 10^\frac{N}{9} - 1$

下面是上述方法的实现

C++

// C++ program to find the smallest
// number whose sum of digits is also N
#include 
#include 
using namespace std;
 
// Function to find the smallest
// number whose sum of digits is also N
void smallestNumber(int N)
{
    cout << (N % 9 + 1)
                    * pow(10, (N / 9))
                - 1;
}
 
// Driver code
int main()
{
    int N = 10;
    smallestNumber(N);
 
    return 0;
}

Java

// Java program to find the smallest
// number whose sum of digits is also N
class GFG{
  
// Function to find the smallest
// number whose sum of digits is also N
static void smallestNumber(int N)
{
    System.out.print((N % 9 + 1) *
            Math.pow(10, (N / 9)) - 1);
}
  
// Driver code
public static void main(String[] args)
{
    int N = 10;
    smallestNumber(N);
}
}
 
// This code is contributed by sapnasingh4991

Python3

# Python3 program to find the smallest
# number whose sum of digits is also N
 
# Function to find the smallest
# number whose sum of digits is also N
def smallestNumber(N):
 
    print((N % 9 + 1) * pow(10, (N // 9)) - 1)
 
# Driver code
N = 10
smallestNumber(N)
 
# This code is contributed by Code_Mech

C＃

// C# program to find the smallest
// number whose sum of digits is also N
using System;
class GFG{
 
// Function to find the smallest
// number whose sum of digits is also N
static void smallestNumber(int N)
{
    Console.WriteLine((N % 9 + 1) *
             Math.Pow(10, (N / 9)) - 1);
}
 
// Driver code
public static void Main()
{
    int N = 10;
     
    smallestNumber(N);
}
}
 
// This code is contributed by Ritik Bansal

Java脚本

 
    // Javascript program to find the smallest
    // number whose sum of digits is also N
     
    // Function to find the smallest
    // number whose sum of digits is also N
    function smallestNumber(N)
    {
        document.write( (N % 9 + 1) * Math.pow(10, parseInt(N / 9, 10)) - 1 );
    }
     
    let N = 10;
    smallestNumber(N);
     

输出

19