Find the Winning Player in Coin Game - Problem

You are given two positive integers x and y, denoting the number of coins with values 75 and 10 respectively.

Alice and Bob are playing a game. Each turn, starting with Alice, the player must pick up coins with a total value of exactly 115. If the player is unable to do so, they lose the game.

Return the name of the player who wins the game if both players play optimally.

Input & Output

Example 1 — Basic Case

$ Input: x = 2, y = 8

› Output: Bob

💡 Note: Maximum turns = min(2, 8÷4) = min(2, 2) = 2. Since 2 is even, Bob wins.

Example 2 — Alice Wins

$ Input: x = 4, y = 11

› Output: Bob

💡 Note: Maximum turns = min(4, 11÷4) = min(4, 2) = 2. Since 2 is even, Bob wins.

Example 3 — Insufficient Coins

$ Input: x = 1, y = 3

› Output: Bob

💡 Note: Need 1×75 + 4×10 = 115, but only have 3 ten-coins (need 4). Alice can't make first move, so Bob wins.

Constraints

1 ≤ x, y ≤ 100

Visualization

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Asked in

G Google 15 a Amazon 12

Brief HTML summary: The key insight is that there's only one way to make 115: using 1×75-coin + 4×10-coins. Best approach is mathematical calculation: find max_turns = min(x, y÷4), if odd Alice wins, if even Bob wins. Time: O(1), Space: O(1)

Common Approaches

✓ Mathematical Approach

⏱️ Time: O(1) Space: O(1)

Since there's only one way to make 115 (1×75 + 4×10), we can directly calculate the maximum number of turns possible. The limiting factor is min(x, y/4). If this number is odd, Alice wins (she gets the last turn). If even, Bob wins.

Simulation Approach

⏱️ Time: O(min(x, y/4)) Space: O(1)

Try each player's turn by checking if they can form exactly 115. The only way to make 115 is with 1 coin of value 75 and 4 coins of value 10 (1×75 + 4×10 = 115). Alternate between players until one can't make a valid move.

Mathematical Approach — Algorithm Steps

Step 1: Calculate max turns = min(x, y÷4)
Step 2: If max turns is odd, Alice wins
Step 3: If max turns is even, Bob wins

Visualization

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Step-by-Step Walkthrough

Formula

max_turns = min(x, y÷4)

Calculate

For x=2, y=8: min(2, 8÷4) = min(2, 2) = 2

Determine Winner

2 is even → Bob wins

Code -

solution.c — C

#include <stdio.h>

int min(int a, int b) {
    return a < b ? a : b;
}

char* solution(int x, int y) {
    int maxTurns = min(x, y / 4);
    return maxTurns % 2 == 1 ? "Alice" : "Bob";
}

int main() {
    int x, y;
    scanf("%d", &x);
    scanf("%d", &y);
    char* result = solution(x, y);
    printf("%s\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Only performs simple arithmetic operations

✓ Linear Growth

Space Complexity

O(1)

Uses only constant extra space for calculation

✓ Linear Space

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Find the Winning Player in Coin Game - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Mathematical Approach — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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