满足给定条件的对数

给定两个整数A和B ，任务是计算对(a，b)的对数，以使1≤a≤A，1≤b≤B以及等式(a * b)+ a + b = concat(a ，b)为true，其中conc(a，b)是a和b的串联(例如，conc(12，23)= 1223，conc(100，11)= 10011)。请注意， a和b不应包含任何前导零。

例子：

Input: A = 1, B = 12
Output: 1
There exists only one pair (1, 9) satisfying
the equation ((1 * 9) + 1 + 9 = 19)

Input: A = 2, B = 8
Output: 0
There doesn’t exist any pair satisfying the equation.

方法：可以观察到，只有当整数≤b的数字仅包含9时，才能满足上述(a * b + a + b = conc(a，b)) 。只需计算仅包含9的位数(≤b)，然后乘以整数a 。

下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
  
// Function to return the number of
// pairs satisfying the equation
int countPair(int a, int b)
{
    // Converting integer b to string
    // by using to_string function
    string s = to_string(b);
  
    // Loop to check if all the digits
    // of b are 9 or not
    int i;
    for (i = 0; i < s.length(); i++) {
  
        // If '9' doesn't appear
        // then break the loop
        if (s[i] != '9')
            break;
    }
  
    int result;
  
    // If all the digits of b contain 9
    // then multiply a with string length
    // else multiply a with string length - 1
    if (i == s.length())
        result = a * s.length();
    else
        result = a * (s.length() - 1);
  
    // Return the number of pairs
    return result;
}
  
// Driver code
int main()
{
    int a = 5, b = 101;
  
    cout << countPair(a, b);
  
    return 0;
}

Java

// Java implementation of the approach
class GFG
{
  
// Function to return the number of
// pairs satisfying the equation
static int countPair(int a, int b)
{
    // Converting integer b to String
    // by using to_String function
    String s = String.valueOf(b);
  
    // Loop to check if all the digits
    // of b are 9 or not
    int i;
    for (i = 0; i < s.length(); i++)
    {
  
        // If '9' doesn't appear
        // then break the loop
        if (s.charAt(i) != '9')
            break;
    }
  
    int result;
  
    // If all the digits of b contain 9
    // then multiply a with String length
    // else multiply a with String length - 1
    if (i == s.length())
        result = a * s.length();
    else
        result = a * (s.length() - 1);
  
    // Return the number of pairs
    return result;
}
  
// Driver code
public static void main(String[] args)
{
    int a = 5, b = 101;
  
    System.out.print(countPair(a, b));
}
}
  
// This code is contributed by PrinciRaj1992

Python

# Python3 implementation of the approach
  
# Function to return the number of
# pairs satisfying the equation
def countPair(a, b):
      
    # Converting integer b to string
    # by using to_function
    s = str(b)
  
    # Loop to check if all the digits
    # of b are 9 or not
    i = 0
    while i < (len(s)):
  
        # If '9' doesn't appear
        # then break the loop
        if (s[i] != '9'):
            break
        i += 1
  
    result = 0
  
    # If all the digits of b contain 9
    # then multiply a with length
    # else multiply a with length - 1
    if (i == len(s)):
        result = a * len(s)
    else:
        result = a * (len(s) - 1)
  
    # Return the number of pairs
    return result
  
# Driver code
a = 5
b = 101
  
print(countPair(a, b))
  
# This code is contributed by mohit kumar 29

C#

// C# implementation of the approach
using System;
  
class GFG
{
  
// Function to return the number of
// pairs satisfying the equation
static int countPair(int a, int b)
{
    // Converting integer b to String
    // by using to_String function
    String s = String.Join("", b);
  
    // Loop to check if all the digits
    // of b are 9 or not
    int i;
    for (i = 0; i < s.Length; i++)
    {
  
        // If '9' doesn't appear
        // then break the loop
        if (s[i] != '9')
            break;
    }
  
    int result;
  
    // If all the digits of b contain 9
    // then multiply a with String length
    // else multiply a with String length - 1
    if (i == s.Length)
        result = a * s.Length;
    else
        result = a * (s.Length - 1);
  
    // Return the number of pairs
    return result;
}
  
// Driver code
public static void Main(String[] args)
{
    int a = 5, b = 101;
  
    Console.Write(countPair(a, b));
}
}
  
// This code is contributed by Rajput-Ji

输出：

10