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# Organizing Tournament Problem

• Difficulty Level : Medium
• Last Updated : 12 Aug, 2021

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 = 1
Output: Possible
Explanation:
In 1st half hours Players { p1, p2 } played the game against { p3 }.
In 2d half hours Players { p2, P3 } played the game against { p1
Since all players played the game against each other within T(=1) hours. Therefore, the required output is “Possible”.

Input: N = 4, T = 0.5
Output: Not Possible
Explanation:
In 1st half hours Players { p1, p2 } played the game against { p3, p4 }.
Since player p1 did not play the game against p2 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 – 1 times.
• In each game, If one of the team have N / 2 players and other team have (N + 1) / 2 then the game must be played (N + 1) / 2 times.

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 ``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`

## Java

 `// Java program for the above approach``import` `java.io.*;` `class` `GFG {` `// Function to find the N players``// the game against each other or not``static` `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``public` `static` `void` `main(String[] args)``{``    ``int` `N = ``6``, T = ``2``;``  ` `    ``// function call``    ``System.out.println(calculate(N, T));``}``}` `// This code is contributed by sanjoy_62.`

## 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)`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to find the N players``// the game against each other or not``static` `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``public` `static` `void` `Main(String[] args)``{``    ``int` `N = 6, T = 2;``  ` `  ``// function call``    ``Console.WriteLine(calculate(N, T));``}``}` `// This code is contributed by splevel62.`

## Javascript

 ``
Output:
`Possible`

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

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