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# Minimum count of numbers required with unit digit X that sums up to N

• Last Updated : 11 May, 2021

Given two integers N and X, the task is to find the minimum count of integers with sum N and having unit digit X. If no such representation exists then print -1.
Examples:

Input: N = 38, X = 9
Output:
Explanation:
Minimum two integers are required with unit digit as X to represent as a sum equal to 38.
38 = 19 + 19 or 38 = 29 + 9
Input: N = 6, X = 4
Output: -1
Explanation:
No such representation of

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Approach:
Follow the steps below to solve the problem:

• Obtain the unit digit of N and check if it achieved by the sum of numbers whose unit digits are X.
• If it is possible, check if N ? X * ( Minimum number of times a number with unit digit X needs to be added to get sum N).
• If the above condition is satisfied then print the minimum number of times a number with unit digit X needs to be added to get sum N. Otherwise, print -1.

Below is the implementation of the above approach:

## C++

 `// C++ Program to implement``// the above approach``#include ``using` `namespace` `std;` `// Function to calculate and return``// the minimum number of times a number``// with unit digit X needs to be added``// to get a sum N``int` `check(``int` `unit_digit, ``int` `X)``{``    ``int` `times, digit;` `    ``// Calculate the number of``    ``// additions required to get unit``    ``// digit of N``    ``for` `(``int` `times = 1; times <= 10;``         ``times++) {``        ``digit = (X * times) % 10;``        ``if` `(digit == unit_digit)``            ``return` `times;``    ``}` `    ``// If unit digit of N``    ``// cannot be obtained``    ``return` `-1;``}` `// Function to return the minimum``// number required to represent N``int` `getNum(``int` `N, ``int` `X)``{``    ``int` `unit_digit;` `    ``// Stores unit digit of N``    ``unit_digit = N % 10;` `    ``// Stores minimum addition``    ``// of X required to``    ``// obtain unit digit of N``    ``int` `times = check(unit_digit, X);` `    ``// If unit digit of N``    ``// cannot be obtained``    ``if` `(times == -1)``        ``return` `times;` `    ``// Otherwise``    ``else` `{` `        ``// If N is greater than``        ``// or equal to (X*times)``        ``if` `(N >= (times * X))` `            ``// Minimum count of numbers``            ``// that needed to represent N``            ``return` `times;` `        ``// Representation not``        ``// possible``        ``else``            ``return` `-1;``    ``}``}` `// Driver Code``int` `main()``{``    ``int` `N = 58, X = 7;``    ``cout << getNum(N, X) << endl;``    ``return` `0;``}`

## Java

 `// Java Program to implement``// the above approach``class` `GFG{``    ` `// Function to calculate and return``// the minimum number of times a number``// with unit digit X needs to be added``// to get a sum N``static` `int` `check(``int` `unit_digit, ``int` `X)``{``    ``int` `times, digit;` `    ``// Calculate the number of``    ``// additions required to get unit``    ``// digit of N``    ``for` `(times = ``1``; times <= ``10``;``                    ``times++)``    ``{``        ``digit = (X * times) % ``10``;``        ``if` `(digit == unit_digit)``            ``return` `times;``    ``}` `    ``// If unit digit of N``    ``// cannot be obtained``    ``return` `-``1``;``}` `// Function to return the minimum``// number required to represent N``static` `int` `getNum(``int` `N, ``int` `X)``{``    ``int` `unit_digit;` `    ``// Stores unit digit of N``    ``unit_digit = N % ``10``;` `    ``// Stores minimum addition``    ``// of X required to``    ``// obtain unit digit of N``    ``int` `times = check(unit_digit, X);` `    ``// If unit digit of N``    ``// cannot be obtained``    ``if` `(times == -``1``)``        ``return` `times;` `    ``// Otherwise``    ``else``    ``{` `        ``// If N is greater than``        ``// or equal to (X*times)``        ``if` `(N >= (times * X))` `            ``// Minimum count of numbers``            ``// that needed to represent N``            ``return` `times;` `        ``// Representation not``        ``// possible``        ``else``            ``return` `-``1``;``    ``}``}` `// Driver Code``public` `static` `void` `main(String []args)``{``    ``int` `N = ``58``, X = ``7``;``    ``System.out.println( getNum(N, X));``}``}` `// This code is contributed by Ritik Bansal`

## Python3

 `# Python3 program to implement``# the above approach` `# Function to calculate and return``# the minimum number of times a number``# with unit digit X needs to be added``# to get a sum N``def` `check(unit_digit, X):``    ` `    ``# Calculate the number of additions``    ``# required to get unit digit of N``    ``for` `times ``in` `range``(``1``, ``11``):``        ``digit ``=` `(X ``*` `times) ``%` `10``        ``if` `(digit ``=``=` `unit_digit):``            ``return` `times``            ` `    ``# If unit digit of N``    ``# cannot be obtained``    ``return` `-``1` `# Function to return the minimum``# number required to represent N``def` `getNum(N, X):``    ` `    ``# Stores unit digit of N``    ``unit_digit ``=` `N ``%` `10` `    ``# Stores minimum addition``    ``# of X required to``    ``# obtain unit digit of N``    ``times ``=` `check(unit_digit, X)` `    ``# If unit digit of N``    ``# cannot be obtained``    ``if` `(times ``=``=` `-``1``):``        ``return` `times` `    ``# Otherwise``    ``else``:` `        ``# If N is greater than``        ``# or equal to (X*times)``        ``if` `(N >``=` `(times ``*` `X)):` `            ``# Minimum count of numbers``            ``# that needed to represent N``            ``return` `times` `        ``# Representation not``        ``# possible``        ``else``:``            ``return` `-``1` `# Driver Code``N ``=` `58``X ``=` `7` `print``(getNum(N, X))` `# This code is contributed by Sanjit_Prasad`

## C#

 `// C# Program to implement``// the above approach``using` `System;``class` `GFG{``    ` `// Function to calculate and return``// the minimum number of times a number``// with unit digit X needs to be added``// to get a sum N``static` `int` `check(``int` `unit_digit, ``int` `X)``{``    ``int` `times, digit;` `    ``// Calculate the number of``    ``// additions required to get unit``    ``// digit of N``    ``for` `(times = 1; times <= 10;``                    ``times++)``    ``{``        ``digit = (X * times) % 10;``        ``if` `(digit == unit_digit)``            ``return` `times;``    ``}` `    ``// If unit digit of N``    ``// cannot be obtained``    ``return` `-1;``}` `// Function to return the minimum``// number required to represent N``static` `int` `getNum(``int` `N, ``int` `X)``{``    ``int` `unit_digit;` `    ``// Stores unit digit of N``    ``unit_digit = N % 10;` `    ``// Stores minimum addition``    ``// of X required to``    ``// obtain unit digit of N``    ``int` `times = check(unit_digit, X);` `    ``// If unit digit of N``    ``// cannot be obtained``    ``if` `(times == -1)``        ``return` `times;` `    ``// Otherwise``    ``else``    ``{` `        ``// If N is greater than``        ``// or equal to (X*times)``        ``if` `(N >= (times * X))` `            ``// Minimum count of numbers``            ``// that needed to represent N``            ``return` `times;` `        ``// Representation not``        ``// possible``        ``else``            ``return` `-1;``    ``}``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `N = 58, X = 7;``    ``Console.Write(getNum(N, X));``}``}` `// This code is contributed by Code_Mech`

## Javascript

 ``
Output:
`4`

Time Complexity: O(1)
Auxiliary Space: O(1)

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