Maximum games played by winner

30 Apr, 2021
There are N players which are playing a tournament. We need to find the maximum number of games the winner can play. In this tournament, two players are allowed to play against each other only if the difference between games played by them is not more than one.Examples:  
Input  : N = 3
Output : 2
Maximum games winner can play = 2
Assume that player are P1, P2 and P3
First, two players will play let (P1, P2)
Now winner will play against P3, 
making total games played by winner = 2

Input  : N = 4
Output : 2
Maximum games winner can play = 2
Assume that player are P1, P2, P3 and P4
First two pairs will play lets (P1, P2) and 
(P3, P4). Now winner of these two games will 
play against each other, making total games
played by winner = 2
 
We can solve this problem by first computing minimum number of players required such that the winner will play x games. Once this is computed actual problem is just inverse of this. Now assume that dp[i] denotes minimum number of players required so that winner plays i games. We can write a recursive relation among dp values as, dp[i + 1] = dp[i] + dp[i – 1] because if runner up has played (i – 1) games and winner has played i games and all players against which they have played the match are disjoint, total games played by winner will be addition of those two sets of players. Above recursive relation can be written as dp[i] = dp[i – 1] + dp[i – 2] Which is same as the Fibonacci series relation, so our final answer will be the index of the maximal Fibonacci number which is less than or equal to given number of players in the input. 
C++
Java
Python3
C#
PHP
Javascript
// C/C++ program to find maximum number of// games played by winner#include <bits/stdc++.h>using namespace std; // method returns maximum games a winner needs// to play in N-player tournamentint maxGameByWinner(int N){    int dp[N];     // for 0 games, 1 player is needed    // for 1 game, 2 players are required    dp[0] = 1;       dp[1] = 2;         // loop until i-th Fibonacci number is     // less than or equal to N    int i = 2;    do {        dp[i] = dp[i - 1] + dp[i - 2];    } while (dp[i++] <= N);     // result is (i - 2) because i will be    // incremented one extra in while loop    // and we want the last value which is    // smaller than N, so one more decrement    return (i - 2);} // Driver code to test above methodsint main(){    int N = 10;    cout << maxGameByWinner(N) << endl;    return 0;}
// Java program to find maximum number of// games played by winnerclass Max_game_winner {     // method returns maximum games a winner needs    // to play in N-player tournament    static int maxGameByWinner(int N)    {        int[] dp = new int[N];              // for 0 games, 1 player is needed        // for 1 game, 2 players are required        dp[0] = 1;           dp[1] = 2;                  // loop until i-th Fibonacci number is         // less than or equal to N        int i = 2;        do {            dp[i] = dp[i - 1] + dp[i - 2];        } while (dp[i++] <= N);              // result is (i - 2) because i will be        // incremented one extra in while loop        // and we want the last value which is        // smaller than N, so one more decrement        return (i - 2);    }          // Driver code to test above methods    public static void main(String args[])    {        int N = 10;        System.out.println(maxGameByWinner(N));    }}//This code is contributed by Sumit Ghosh
# Python3 program to find maximum# number of games played by winner # method returns maximum games# a winner needs to play in# N-player tournament def maxGameByWinner(N):    dp = [0 for i in range(N)]         # for 0 games, 1 player is needed    # for 1 game, 2 players are required    dp[0] = 1    dp[1] = 2         # loop until i-th Fibonacci    # number is less than or    # equal to N    i = 1    while dp[i] <= N:        i = i + 1        dp[i] = dp[i - 1] + dp[i - 2]             # result is (i - 1) because i will be    # incremented one extra in while loop    # and we want the last value which is    # smaller than N, so    return (i - 1) # Driver codeN = 10print(maxGameByWinner(N)) # This code is contributed# by sahilshelangia
// C# program to find maximum number// of games played by winnerusing System; class GFG {         // method returns maximum games a    // winner needs to play in N-player    // tournament    static int maxGameByWinner(int N)    {        int[] dp = new int[N];             // for 0 games, 1 player is needed        // for 1 game, 2 players are required        dp[0] = 1;        dp[1] = 2;                 // loop until i-th Fibonacci number        // is less than or equal to N        int i = 2;                 do {            dp[i] = dp[i - 1] + dp[i - 2];        } while (dp[i++] <= N);             // result is (i - 2) because i will be        // incremented one extra in while loop        // and we want the last value which is        // smaller than N, so one more decrement        return (i - 2);    }         // Driver code    public static void Main()    {        int N = 10;        Console.Write(maxGameByWinner(N));    }} // This code is contributed by Nitin Mittal.
<?php// PHP program to find maximum number// of games played by winner // Method returns maximum games// a winner needs to play in// N-player tournamentfunction maxGameByWinner($N){    $dp[$N]=0;     // for 0 games, 1 player is needed    // for 1 game, 2 players are required    $dp[0] = 1;    $dp[1] = 2;         // loop until i-th Fibonacci number is    // less than or equal to N    $i = 2;    do    {        $dp[$i] = $dp[$i - 1] + $dp[$i - 2];    } while ($dp[$i++] <= $N);     // result is (i - 2) because i will be    // incremented one extra in while loop    // and we want the last value which is    // smaller than N, so one more decrement    return ($i - 2);}     // Driver Code    $N = 10;    echo maxGameByWinner($N); // This code is contributed by nitin mittal?>
<script> // Javascript program to find maximum number of// games played by winner     // method returns maximum games a winner needs    // to play in N-player tournament    function maxGameByWinner(N)    {        let dp = new Array(N).fill(0);                // for 0 games, 1 player is needed        // for 1 game, 2 players are required        dp[0] = 1;           dp[1] = 2;                    // loop until i-th Fibonacci number is         // less than or equal to N        let i = 2;        do {            dp[i] = dp[i - 1] + dp[i - 2];        } while (dp[i++] <= N);                // result is (i - 2) because i will be        // incremented one extra in while loop        // and we want the last value which is        // smaller than N, so one more decrement        return (i - 2);    } // driver program             let N = 10;        document.write(maxGameByWinner(N)); // This code is contributed by code_hunt.</script>
Output :  
4
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