# Maximum number of distinct positive integers that can be used to represent N

Given an integer **N**, the task is to find the maximum number of distinct positive integers that can be used to represent **N**.

**Examples:**

Input:N = 5Output:2

5 can be represented as 1 + 4, 2 + 3, 3 + 2, 4 + 1 and 5.

So maximum integers that can be used in the representation are 2.

Input:N = 10Output:4

**Approach:** We can always greedily choose distinct integers to be as small as possible to maximize the number of distinct integers that can be used. If we are using the first x natural numbers, let their sum be f(x).

So we need to find a maximum x such that f(x) < = n.

1 + 2 + 3 + … n < = n

x*(x+1)/2 < = n

x^2+x-2n < = 0

We can solve the above equation by using quadratic formula X = (-1 + sqrt(1+8*n))/2.

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 required count` `int` `count(` `int` `n)` `{` ` ` `return` `int` `((-1 + ` `sqrt` `(1 + 8 * n)) / 2);` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 10;` ` ` `cout << count(n);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the approach` `class` `GFG` `{` ` ` `// Function to return the required count` ` ` `static` `int` `count(` `int` `n)` ` ` `{` ` ` `return` `(` `int` `)(-` `1` `+ Math.sqrt(` `1` `+ ` `8` `* n)) / ` `2` `;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `10` `;` ` ` ` ` `System.out.println(count(n));` ` ` `}` `}` `// This code is contributed by ihritik` |

## Python3

`# Python3 implementation of the approach` `from` `math ` `import` `sqrt` `# Function to return the required count` `def` `count(n) :` ` ` `return` `(` `-` `1` `+` `sqrt(` `1` `+` `8` `*` `n)) ` `/` `/` `2` `;` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `n ` `=` `10` `;` ` ` `print` `(count(n));` `# This code is contributed by AnkitRai01` |

## C#

`// C# implementation of approach` `using` `System;` `class` `GFG` `{` ` ` ` ` `// Function to return the required count` ` ` `public` `static` `int` `count(` `int` `n)` ` ` `{` ` ` `return` `(-1 + (` `int` `)Math.Sqrt(1 + 8 * n)) / 2;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 10;` ` ` ` ` `Console.Write(count(n));` ` ` `}` `}` `// This code is contributed by Mohit Kumar` |

## Javascript

`<script>` `// Javascript implementation of the approach` `// Function to return the required count` `function` `count(n)` `{` ` ` `return` `parseInt((-1 + Math.sqrt(1 + 8 * n)) / 2);` `}` `// Driver code` `var` `n = 10;` `document.write(count(n));` `// This code is contributed by rutvik_56` `</script>` |

**Output:**

4

**Time Complexity:** O(1)

**Auxiliary Space: **O(1)