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Problem Statement:Nim is a popular two-player game with simple rules:Start with several piles of stones, each pile may have a different number of stones.Players take turns picking 1 or more stones from any single pile.The player who takes the last stone wins.Your task is to determine who wins the game given the number of piles and the number of stones in each pile, assuming both players play optimally.Input Format:The first line contains an integer n representing the total number of piles.The second line contains n space-separated integers representing the number of stones in each pile.Constraints:1 <= n <= 1001 <= pile[i] <= 100Output Format:Print the winner.Example:Imagine a game with 3 piles of stones: [3, 2, 4]. Here's how the game might go:Player 1 takes 2 stones from pile 1, leaving [3, 4].Player 2 takes 2 stones from pile 1, leaving [3, 2].Player 1 takes 1 stone from pile 0, leaving [2, 2].Player 2 takes 1 stone from pile 0, leaving [1, 2].Player 1 takes 1 stone from pile 1, leaving [1, 1].Player 2 takes 1 stone from pile 0, leaving [0, 1].Player 1 takes 1 stone from pile 1, winning the game.Sample Test CasesTest Case 1:Expected Output:33 2 4Player·1Test Case 2:Expected Output:21 1Player·2

Question

Problem Statement:Nim is a popular two-player game with simple rules:Start with several piles of stones, each pile may have a different number of stones.Players take turns picking 1 or more stones from any single pile.The player who takes the last stone wins.Your task is to determine who wins the game given the number of piles and the number of stones in each pile, assuming both players play optimally.Input Format:The first line contains an integer n representing the total number of piles.The second line contains n space-separated integers representing the number of stones in each pile.Constraints:1 <= n <= 1001 <= pile[i] <= 100Output Format:Print the winner.Example:Imagine a game with 3 piles of stones: [3, 2, 4]. Here's how the game might go:Player 1 takes 2 stones from pile 1, leaving [3, 4].Player 2 takes 2 stones from pile 1, leaving [3, 2].Player 1 takes 1 stone from pile 0, leaving [2, 2].Player 2 takes 1 stone from pile 0, leaving [1, 2].Player 1 takes 1 stone from pile 1, leaving [1, 1].Player 2 takes 1 stone from pile 0, leaving [0, 1].Player 1 takes 1 stone from pile 1, winning the game.Sample Test CasesTest Case 1:Expected Output:33 2 4Player·1Test Case 2:Expected Output:21 1Player·2

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Solution

The problem is asking to determine the winner of the game Nim. The game Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap or pile. The goal of the game is to avoid being the player who must remove the last object.

Here is a step-by-step solution:

Step 1: Understand the problem. The problem is asking to determine the winner of the game Nim. The game Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap or pile. The goal of the game is to avoid being the player who must remove the last object.

Step 2: The key to solve this problem is understanding the concept of "Nim-Sum". The Nim-Sum is calculated by taking the binary representation of the size of each pile, and performing the bitwise XOR operation on them. If the Nim-Sum is 0, then the first player will lose if both players play optimally. If the Nim-Sum is not 0, then the first player will win if both players play optimally.

Step 3: Implement the solution. First, read the number of piles. Then, read the size of each pile. Calculate the Nim-Sum by performing the bitwise XOR operation on the size of each pile. If the Nim-Sum is 0, print "Player 2". Otherwise, print "Player 1".

Here is a Python code snippet that implements the above steps:

n = int(input())
piles = list(map(int, input().split()))
nim_sum = 0
for pile in piles:
    nim_sum ^= pile
if nim_sum == 0:
    print("Player 2")
else:
    print("Player 1")

This code first reads the number of piles and the size of each pile. It then calculates the Nim-Sum by performing the bitwise XOR operation on the size of each pile. If the Nim-Sum is 0, it prints "Player 2". Otherwise, it prints "Player 1".

This problem has been solved

Similar Questions

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