Pen Distribution Problem

Given an integer N denoting the number of boxes in a pen, and two players P1 and P2 playing a game of distributing N pens among themselves as per the following rules:

• P1 makes the first move by taking 2^X pens. (Initially, X = 0)
• P2 takes 3^X pens.
• Value of X increases by 1 after each move.
• P1 and P2 makes move alternatively.
• If the current player has to take more pens than the number of pens remaining in the box, then they quit.
• The game will be over when both the players quit or when the box becomes empty.

The task to print the following details once the game is over:

1. The number of pens remaining in the box.
2. The number of pens collected by P1.
3. The number of pens collected by P2.

Examples: 
 

Input: N = 22
Output: 
Number of pens remaining in the box: 14
Number of pens collected by P1 : 5
Number of pens collected by P2 : 3
Explanation:

• Move 1: X = 0, P1 takes 1 pen from the box. Therefore, N = 22 - 1 = 21.
• Move 2: X = 1, P2 takes 3 pens from the box. Therefore, N = 21 - 3 = 18.
• Move 3: X = 2, P1 takes 4 pens from the box. Therefore, N = 18 - 4 = 14.
• Move 4: X = 3, P2 quits as 27 > 14.
• Move 5: X = 4, P1 quits as 16 > 14.
• Game Over! Both players have quit.

Input: N = 1
Output: 
Number of pens remaining in the box : 0
Number of pens collected by P1 : 1
Number of pens collected by P2 : 0

Approach: The idea is to use Recursion. Follow the steps to solve the problem: 
 

1. Define a recursive function: 
 

Game_Move(N, P1, P2, X, Move, QuitP1, QuitP2) 
where, 
N : Total number of Pens 
P1 : Score of P1 
P2 : Score of P2 
X : Initialized to zero 
Move = 0 : P1's turn 
Move = 1 : P2's turn 
QuitP1 : Has P1 quit 
QuitP2 : Has P2 quit 

2. Finally, print the final values after the game has ended

Below is the implementation of the above-mentioned approach:
 

Number of pens remaining in the box: 14
Number of pens collected by P1: 5
Number of pens collected by P2: 3

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