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feat: add NimGame algorithm with tests #7743

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e93192d
feat: add nim-game algorithm with tests
roshankumar447 Nov 7, 2026
1cc8fab
Merge remote-tracking branch 'upstream/master' into feat/nim-game
roshankumar447 Nov 10, 2026
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23 changes: 23 additions & 0 deletions src/main/java/com/thealgorithms/maths/NimGame.java
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package com.thealgorithms.maths;

/**
* Nim Game: Two players take turns removing 1 to 3 stones from a pile.
* The player who removes the last stone wins. Returns true if the first
* player can guarantee a win given n stones.
*
* <p>Key insight: if n is a multiple of 4, the second player always wins
* because whatever the first player takes (1-3), the second player can
* always take enough to leave another multiple of 4.
*
* <p>Time complexity: O(1), Space complexity: O(1)
*
* @see <a href="https://leetcode.com/problems/nim-game/">LeetCode #292</a>
*/
public final class NimGame {
private NimGame() {
}

public static boolean canWinNim(int n) {
return n % 4 != 0;
}
}
24 changes: 24 additions & 0 deletions src/test/java/com/thealgorithms/maths/NimGameTest.java
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package com.thealgorithms.maths;

import static org.junit.jupiter.api.Assertions.assertFalse;
import static org.junit.jupiter.api.Assertions.assertTrue;

import org.junit.jupiter.api.Test;

public class NimGameTest {

@Test
public void testFirstPlayerWins() {
assertTrue(NimGame.canWinNim(1));
assertTrue(NimGame.canWinNim(2));
assertTrue(NimGame.canWinNim(3));
assertTrue(NimGame.canWinNim(5));
}

@Test
public void testSecondPlayerWins() {
assertFalse(NimGame.canWinNim(4));
assertFalse(NimGame.canWinNim(8));
assertFalse(NimGame.canWinNim(12));
}
}
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