# Find maximum unreachable height using two ladders

Given two ladders of height h1 and h2. The task is to find the maximum height that can’t be reached using any possible combination by the two ladders. If it is possible to reach all the heights then print 0.

Examples:

Input: H1 = 2, H2 = 11
Output: 9
We cannot reach heights 1, 3, 5, 7 and 9.
So, the maximum possible height is 9.

Input: H1 = 7, H2 = 5
Output: 23

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: For the given numbers a and b, the maximum number c such that ax + by = c is not possible where x ≥ 0 and y ≥ 0 is Frobenius number which is equal to (a * b) – a – b.

Below is the implementation of the above approach:

## CPP

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the maximum height ` `// which can't be reached ` `int` `maxHeight(``int` `h1, ``int` `h2) ` `{ ` `    ``return` `((h1 * h2) - h1 - h2); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `h1 = 7, h2 = 5; ` ` `  `    ``cout << max(0, maxHeight(h1, h2)); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach  ` `class` `GFG ` `{ ` ` `  `    ``// Function to return the maximum height  ` `    ``// which can't be reached  ` `    ``static` `int` `maxHeight(``int` `h1, ``int` `h2)  ` `    ``{  ` `        ``return` `((h1 * h2) - h1 - h2);  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main(String args[]) ` `    ``{  ` `        ``int` `h1 = ``7``, h2 = ``5``;  ` `     `  `        ``System.out.println(Math.max(``0``, maxHeight(h1, h2)));  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python

 `# Python3 implementation of the approach ` ` `  `# Function to return the maximum height ` `# which can't be reached ` `def` `maxHeight(h1, h2): ` `    ``return` `((h1 ``*` `h2) ``-` `h1 ``-` `h2) ` ` `  `# Driver code ` `h1 ``=` `7` `h2 ``=` `5` ` `  `print``(``max``(``0``, maxHeight(h1, h2))) ` ` `  `# This code is contributed by mohit kumar 29 `

## C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `    ``// Function to return the maximum height  ` `    ``// which can't be reached  ` `    ``static` `int` `maxHeight(``int` `h1, ``int` `h2)  ` `    ``{  ` `        ``return` `((h1 * h2) - h1 - h2);  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main() ` `    ``{  ` `        ``int` `h1 = 7, h2 = 5;  ` `     `  `        ``Console.WriteLine(Math.Max(0, maxHeight(h1, h2)));  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```23
```

Time Complexity: O(1)

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Improved By : mohit kumar 29, AnkitRai01