# Represent a number as the sum of positive numbers ending with 9

Given an integer **N**, the task is to check if **N** can be expressed as a sum of integers having **9** as the last digit (9, 19, 29, 39…), or not. If found to be true, then find the minimum count of such integers required to obtain **N**. Otherwise print **-1**.

**Examples:**

Input:N = 156Output:4Explanation:

156 = 9 + 9 + 9 + 129

Input:N = 60Output:-1Explanation:

No possible way to obtain sum 60 from numbers having 9 as the last digit.

**Naive Approach: **This problem can be viewed as a variation of the Coin change problem. For this problem, the coins can be replaced with [9, 19, 29, 39…. up to the last number smaller than N that ends with 9].

**Time Complexity:** O(N^{2})**Auxiliary Space: **O(N)

**Efficient Approach: **The above approach can be optimized based on the observation that if the **last digit of N is K**, then exactly **(10 – K)** minimum numbers are required to form **N**.

A sum N can be obtained by adding 10 – K numbers, where K is the last digit of N.

Therefore, sum N can be obtained by adding 9, (9 – K) times and adding N – (9 * (9 – K)) finally.

Follow the steps below to solve the problem:

- Extract the last digit of the given number,
**K = N % 10** - Using the above observation, a total of
**(10 – K)**numbers are required. Now, calculate**9 * (9 – K)**, as the first**9 – K**numbers required to obtain**N**is**9**. - Now, calculate
**N – 9 * (9 – K)**and store in a variable, say**z**. If**z**is greater than or equal to**9**and has**9**as its last digit, print**10 – K**as the answer. Otherwise, print**-1**.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the minimum count` `// of numbers ending with 9 to form N` `int` `minCountOfNumbers(` `int` `N)` `{` ` ` `// Extract last digit of N` ` ` `int` `k = N % 10;` ` ` `// Calculate the last digit` ` ` `int` `z = N - (9 * (9 - k));` ` ` `// If the last digit` ` ` `// satisfies the condition` ` ` `if` `(z >= 9 && z % 10 == 9) {` ` ` `return` `10 - k;` ` ` `}` ` ` `else` ` ` `return` `-1;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `N = 156;` ` ` `cout << minCountOfNumbers(N);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` `// Function to find the minimum count` `// of numbers ending with 9 to form N` `static` `int` `minCountOfNumbers(` `int` `N)` `{` ` ` ` ` `// Extract last digit of N` ` ` `int` `k = N % ` `10` `;` ` ` `// Calculate the last digit` ` ` `int` `z = N - (` `9` `* (` `9` `- k));` ` ` `// If the last digit` ` ` `// satisfies the condition` ` ` `if` `(z >= ` `9` `&& z % ` `10` `== ` `9` `)` ` ` `{` ` ` `return` `10` `- k;` ` ` `}` ` ` `else` ` ` `return` `-` `1` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `156` `;` ` ` `System.out.print(minCountOfNumbers(N));` `}` `}` `// This code is contributed by 29AjayKumar` |

## Python3

`# Python3 program for the above approach` `# Function to find the minimum count` `# of numbers ending with 9 to form N` `def` `minCountOfNumbers(N):` ` ` ` ` `# Extract last digit of N` ` ` `k ` `=` `N ` `%` `10` ` ` `# Calculate the last digit` ` ` `z ` `=` `N ` `-` `(` `9` `*` `(` `9` `-` `k))` ` ` `# If the last digit` ` ` `# satisfies the condition` ` ` `if` `(z >` `=` `9` `and` `z ` `%` `10` `=` `=` `9` `):` ` ` `return` `10` `-` `k` ` ` `else` `:` ` ` `return` `-` `1` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `N ` `=` `156` ` ` ` ` `print` `(minCountOfNumbers(N))` `# This code is contributed by mohit kumar 29` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` `// Function to find the minimum count` `// of numbers ending with 9 to form N` `static` `int` `minCountOfNumbers(` `int` `N)` `{` ` ` ` ` `// Extract last digit of N` ` ` `int` `k = N % 10;` ` ` `// Calculate the last digit` ` ` `int` `z = N - (9 * (9 - k));` ` ` `// If the last digit` ` ` `// satisfies the condition` ` ` `if` `(z >= 9 && z % 10 == 9)` ` ` `{` ` ` `return` `10 - k;` ` ` `}` ` ` `else` ` ` `return` `-1;` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `N = 156;` ` ` ` ` `Console.Write(minCountOfNumbers(N));` `}` `}` `// This code is contributed by 29AjayKumar` |

## Javascript

`<script>` `// java script program for the above approach` `// Function to find the minimum count` `// of numbers ending with 9 to form N` `function` `minCountOfNumbers(N){` ` ` ` ` `// Extract last digit of N` ` ` `let k = N % 10;` ` ` `// Calculate the last digit` ` ` `let z = N - (9 * (9 - k));` ` ` `// If the last digit` ` ` `// satisfies the condition` ` ` `if` `(z >= 9 && z % 10 == 9)` ` ` `{` ` ` `return` `10 - k;` ` ` `}` ` ` `else` ` ` `{` ` ` `return` `-1;` ` ` `}` `}` ` ` `// Driver Code ` ` ` `let N = 156;` ` ` `document.write(minCountOfNumbers(N));` `// This code is contributed by sravan kumar` `</script>` |

**Output:**

4

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