Game of Nim

class Solution {
    public boolean playNimGame(int[] stones) {
        int totalXOR = 0;
        for (int stoneCount : stones) {
            totalXOR ^= stoneCount;
        }
        return totalXOR != 0;
    }
}

This solution implements the classic problem known as the "Game of Nim" using Java. In this game, the function playNimGame receives an array stones, where each element represents the count of stones in each pile.

To determine the winner under the optimal strategies for both players, utilize the XOR operation. XOR all elements of the stones array sequentially. The result stored in totalXOR will be analyzed to decide the outcome:

• If totalXOR equals zero, it indicates a losing position, so the function returns false.
• If totalXOR is non-zero, the current player can force a win, making the function return true.

This method effectively evaluates the winnability of a Nim game state using bitwise operations, providing a quick and efficient solution.

function calculateNim(pileArray) {
    let result = 0;
    for (let pile of pileArray) {
        result ^= pile;
    }
    return result !== 0;
}

The "Game of Nim" solution provided is implemented in JavaScript. It calculates the winning move based on a given set of piles represented in an array. Review the key aspects of the solution:

• The function calculateNim accepts an array pileArray, where each integer represents the number of items in a pile.
• A variable result initializes to zero. This variable accumulates the result of a bitwise XOR operation performed on each pile from the array.
• Iterate over each pile in pileArray using a for loop. Inside the loop, update result by performing a bitwise XOR (^= operator) of result with the number of items (pile) in the current pile.
• Finally, the function evaluates whether result is non-zero. If result is non-zero (result !== 0), it returns true, indicating a winning possibility for the player starting the game. Otherwise, it returns false.

The XOR operation is crucial here as it applies the mathematical foundation of the Nim-sum, which determines the winning strategy in the Game of Nim:

• If the Nim-sum (result) at the beginning of the turn is zero, the player is destined to lose if the opponent plays optimally.
• Conversely, a non-zero starting Nim-sum allows for a possible winning strategy with optimal play.

Utilize this function by passing an array of integers where each integer counts the items in respective piles, and it will aid in strategizing the next move in the game.

class Solution:
    def canWinNim(self, stones: List[int]) -> bool:
        xor_result = 0
        for stone in stones:
            xor_result ^= stone
        return xor_result != 0

The provided Python solution addresses the problem of determining the winning strategy in the Nim game given an array of integers where each integer represents the number of stones in piles. The solution follows a bit manipulation approach using XOR to determine the outcome:

• Utilize a loop to iterate through each pile of stones.
• Accumulate the result of XOR operation on all the piles.
• Return True if the resultant XOR is not zero, indicating the starting player can ensure a win with optimal play; otherwise, return False.

This method effectively utilizes properties of the XOR operation to evaluate the game state in linear time complexity, making it efficient for handling large inputs. Ensure to include the List import from typing to avoid errors during execution.