Given two integers A and B, the task is to calculate the number of pairs (a, b) such that 1 ? a ? A, 1 ? b ? B and the equation (a * b) + a + b = concat(a, b) is true where conc(a, b) is the concatenation of a and b (for example, conc(12, 23) = 1223, conc(100, 11) = 10011). Note that a and b should not contain any leading zeroes.
Examples:
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.
Approach: It can be observed that the above (a * b + a + b = conc(a, b)) will only be satisfied when the digits of an integer ? b contains only 9. Simply, calculate the number of digits (? b) containing only 9 and multiply with the integer a.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to return the number of// pairs satisfying the equationint 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 codeint main(){ int a = 5, b = 101; cout << countPair(a, b); return 0;} |
Java
// Java implementation of the approachclass GFG{// Function to return the number of// pairs satisfying the equationstatic 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 codepublic static void main(String[] args){ int a = 5, b = 101; System.out.print(countPair(a, b));}}// This code is contributed by PrinciRaj1992 |
Python3
# Python3 implementation of the approach# Function to return the number of# pairs satisfying the equationdef 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 codea = 5b = 101print(countPair(a, b))# This code is contributed by mohit kumar 29 |
C#
// C# implementation of the approachusing System;class GFG{// Function to return the number of// pairs satisfying the equationstatic 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 codepublic static void Main(String[] args){ int a = 5, b = 101; Console.Write(countPair(a, b));}}// This code is contributed by Rajput-Ji |
Javascript
<script>// Javascript implementation of the approach// Function to return the number of// pairs satisfying the equationfunction countPair(a, b){ // Converting integer b to string // by using to_string function var s = (b.toString()); // Loop to check if all the digits // of b are 9 or not var i; for(i = 0; i < s.length; i++) { // If '9' doesn't appear // then break the loop if (s[i] != '9') break; } var 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 codevar a = 5, b = 101;document.write(countPair(a, b));// This code is contributed by rutvik_56</script> |
Output:
10
Time Complexity: O(b)
Auxiliary Space: O(1)
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