# Organizing Tournament Problem

Given a positive integer **N** representing the count of players playing the game. The game is played between two teams such that each team consists of at least one player but the total count of players in the game must be **N**. The game lasts in exactly **30 minutes**, the task is to check if all players will play the game against each other or not If the game can be played up to **T** hours and it is allowed to play the game more than **1** times. If found to be true then print **“Possible”**. Otherwise, print **“Not Possible”**.

**Examples:**

Input:N = 3, T = 1Output:PossibleExplanation:

In 1st half hours Players { p_{1}, p_{2}} played the game against { p_{3}}.

In 2d half hours Players { p_{2}, P_{3}} played the game against { p_{1}}

Since all players played the game against each other within T(=1) hours. Therefore, the required output is “Possible”.

Input:N = 4, T = 0.5Output:Not PossibleExplanation:

In 1st half hours Players { p_{1}, p_{2}} played the game against { p_{3}, p_{4}}.

Since player p_{1}did not play the game against p_{2}within T(=0.5) hours. Therefore, the required output is “Not Possible”.

**Approach:** The problem can be solved using Greedy technique. Following are the observations:

- In each game, if one of the two teams has only one player then the game must be played
N – 1times.- In each game, If one of the team have
N / 2players and other team have(N + 1) / 2then the game must be played(N + 1) / 2times.

Follow the steps below to solve the problem:

- If total time to play the game
**N-1**times is less than or equal to**T**, then print**“Possible”**. - If total time to play the game
**(N + 1) / 2**times is less than or equal to**T**, then print**“Possible”**. - Otherwise, print
**“Not Possible”**.

Below is the implementation of the above approach:

## C++

`// C++ Program for the above approach` `#include <iostream>` `using` `namespace` `std;` `// Function to find the N players` `// the game against each other or not` `string calculate(` `int` `N, ` `int` `T)` `{` ` ` ` ` `// Base Case` ` ` `if` `(N <= 1 || T <= 0) {` ` ` ` ` `// Return -1 if not valid` ` ` `return` `"-1"` `;` ` ` `}` ` ` ` ` `// Converting hours into minutes` ` ` `int` `minutes = T * 60;` ` ` ` ` `// Calculating maximum games that` ` ` `// can be played.` ` ` `int` `max_match = N - 1;` ` ` ` ` `// Time required for conducting` ` ` `// maximum games` ` ` `int` `max_time = max_match * 30;` ` ` `// Checking if it is possible` ` ` `// to conduct maximum games` ` ` `if` `(max_time <= minutes) {` ` ` ` ` `// Return possible` ` ` `return` `"Possible"` `;` ` ` `}` ` ` `// Calculating minimum games` ` ` `int` `min_match = N / 2;` ` ` `min_match = N - min_match;` ` ` ` ` `// Time required for conducting` ` ` `// minimum games` ` ` `int` `min_time = min_match * 30;` ` ` `// Checking if it is possible` ` ` `// to conduct minimum games` ` ` `if` `(min_time <= minutes) {` ` ` ` ` `// Return possible` ` ` `return` `"Possible"` `;` ` ` `}` ` ` `// Return not possible if time` ` ` `// is less than required time` ` ` `return` `"Not Possible"` `;` `}` ` ` `// Driver Code` ` ` `// Total count of players` `int` `main()` `{` ` ` `int` `N = 6, T = 2;` ` ` ` ` `// function call` ` ` `cout << calculate(N, T);` ` ` `return` `0;` `}` `// This code is contributed by Parth Manchanda` |

## Python3

`# Python program for the above problem` `# Function to find the N players` `# the game against each other or not` `def` `calculate(N, T):` ` ` `# Base Case` ` ` `if` `N <` `=` `1` `or` `T <` `=` `0` `:` ` ` `# Return -1 if not valid` ` ` `return` `-` `1` ` ` `# Converting hours into minutes` ` ` `minutes ` `=` `T ` `*` `60` ` ` `# Calculating maximum games that` ` ` `# can be played.` ` ` `max_match ` `=` `N ` `-` `1` ` ` `# Time required for conducting` ` ` `# maximum games` ` ` `max_time ` `=` `max_match ` `*` `30` ` ` `# Checking if it is possible` ` ` `# to conduct maximum games` ` ` `if` `max_time <` `=` `minutes:` ` ` `# Return possible` ` ` `return` `"Possible"` ` ` `# Calculating minimum games` ` ` `min_match ` `=` `N` `/` `/` `2` ` ` `min_match ` `=` `N ` `-` `min_match` ` ` `# Time required for conducting` ` ` `# minimum games` ` ` `min_time ` `=` `min_match ` `*` `30` ` ` `# Checking if it is possible` ` ` `# to conduct minimum games` ` ` `if` `min_time <` `=` `minutes:` ` ` `# Return possible` ` ` `return` `"Possible"` ` ` `# Return not possible if time` ` ` `# is less than required time` ` ` `return` `"Not Possible"` `# Driver Code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `# Total count of players` ` ` `N ` `=` `6` ` ` `# Given hours` ` ` `T ` `=` `2` ` ` `# Function call` ` ` `ans ` `=` `calculate(N, T)` ` ` `# Print ans` ` ` `print` `(ans)` |

## Javascript

`<script>` ` ` `// JavaScript Program for the above approach` ` ` `// Function to find the N players` ` ` `// the game against each other or not` ` ` `function` `calculate(N, T)` ` ` `{` ` ` `// Base Case` ` ` `if` `(N <= 1 || T <= 0)` ` ` `{` ` ` `// Return -1 if not valid` ` ` `return` `-1;` ` ` `}` ` ` `// Converting hours into minutes` ` ` `let minutes = T * 60;` ` ` `// Calculating maximum games that` ` ` `// can be played.` ` ` `let max_match = N - 1` ` ` `// Time required for conducting` ` ` `// maximum games` ` ` `max_time = max_match * 30` ` ` `// Checking if it is possible` ` ` `// to conduct maximum games` ` ` `if` `(max_time <= minutes)` ` ` `{` ` ` ` ` `// Return possible` ` ` `return` `"Possible"` `;` ` ` `}` ` ` `// Calculating minimum games` ` ` `min_match = Math.floor(N / 2);` ` ` `min_match = N - min_match` ` ` `// Time required for conducting` ` ` `// minimum games` ` ` `min_time = min_match * 30;` ` ` `// Checking if it is possible` ` ` `// to conduct minimum games` ` ` `if` `(min_time <= minutes)` ` ` `{` ` ` ` ` `// Return possible` ` ` `return` `"Possible"` `;` ` ` `// Return not possible if time` ` ` `// is less than required time` ` ` `return` `"Not Possible"` `;` ` ` `}` ` ` `}` ` ` `// Driver Code` ` ` `// Total count of players` ` ` `let N = 6` ` ` `// Given hours` ` ` `let T = 2` ` ` `// Function call` ` ` `let ans = calculate(N, T)` ` ` `// Print ans` ` ` `document.write(ans);` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output:**

Possible

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

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the **Essential Maths for CP Course** at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**