# Count distinct sum of pairs possible from a given range

Given two positive integers **L** and **R** (* where L â‰¤ R* ), the task is to count the number of distinct integers that can be obtained by adding any pair of integers from the range

**[L, R]**.

**Examples:**

Input:L = 3, R = 5Output:11Explanation:All possible distinct sum of pairs are as follows:

- (3, 3). Sum = 6.
- (3, 4). Sum = 7.
- (3, 5). Sum = 8.
- (4, 5). Sum = 9.
- (5, 5). Sum = 10.
Therefore, the count of distinct sums is 5.

Input:L = 12, R = 14Output:5

**Naive Approach:** The simplest approach to solve the given problem is to find the sum of all possible pairs of numbers from the range **[L, R]** and print the count of all distinct sums obtained.

**Time Complexity:** O((L – R)^{2})**Auxiliary Space:** O(1)

**Efficient Approach:** The above approach can be optimized based on the following observations:

- Since, the given range
**[L, R]**is continuous, the range of numbers obtained by adding will also be continuous. - The minimum and maximum sum of pairs from the range are given by
**2 * L**and**2 * R**respectively. - Therefore, the count distinct sum of pairs is given by
**(2 * R – 2 * L + 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 count distinct sum of` `// pairs possible from the range [L, R]` `int` `distIntegers(` `int` `L, ` `int` `R)` `{` ` ` `// Return the count of` ` ` `// distinct sum of pairs` ` ` `return` `2 * R - 2 * L + 1;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `L = 3, R = 8;` ` ` `cout << distIntegers(L, R);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `class` `GFG{` ` ` `// Function to count distinct sum of` `// pairs possible from the range [L, R]` `static` `int` `distIntegers(` `int` `L, ` `int` `R)` `{` ` ` ` ` `// Return the count of` ` ` `// distinct sum of pairs` ` ` `return` `2` `* R - ` `2` `* L + ` `1` `;` `}` ` ` `// Driver Code` `public` `static` `void` `main (String[] args) ` `{` ` ` `int` `L = ` `3` `, R = ` `8` `;` ` ` ` ` `System.out.println(distIntegers(L, R));` `}` `}` `// This code is contributed by rag2127` |

## Python3

`# Python3 program for the above approach` `# Function to count distinct sum of` `# pairs possible from the range [L, R]` `def` `distIntegers(L, R):` ` ` ` ` `# Return the count of` ` ` `# distinct sum of pairs` ` ` `return` `2` `*` `R ` `-` `2` `*` `L ` `+` `1` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `L, R ` `=` `3` `, ` `8` ` ` `print` `(distIntegers(L, R))` `# This code is contributed by mohit kumar 29.` |

## C#

`// C# program for the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG{` ` ` `// Function to count distinct sum of` `// pairs possible from the range [L, R]` `static` `int` `distIntegers(` `int` `L, ` `int` `R)` `{` ` ` ` ` `// Return the count of` ` ` `// distinct sum of pairs` ` ` `return` `2 * R - 2 * L + 1;` `}` `// Driver Code` `static` `public` `void` `Main()` `{` ` ` `int` `L = 3, R = 8;` ` ` ` ` `Console.Write(distIntegers(L, R));` `}` `}` `// This code is contributed by avijitmondal1998` |

## Javascript

`<script>` ` ` `// Function to count distinct sum of` ` ` `// pairs possible from the range [L, R]` ` ` `function` `distIntegers(L,R)` ` ` `{` ` ` `// Return the count of` ` ` `// distinct sum of pairs` ` ` `return` `2 * R - 2 * L + 1;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `let L = 3, R = 8;` ` ` `document.write(distIntegers(L, R));` ` ` ` ` `// This code is contributed by avanitrachhadiya2155` ` ` `</script>` |

**Output:**

11

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