The Hacker News post presents a betting game puzzle where you predict the sum of your neighbors' bets, with the closest guess winning. The challenge is to calculate this sum efficiently when dealing with a large number of players, each choosing a bet from 0 to 9. The author shares a clever algorithm that achieves this in linear time, utilizing a frequency array to avoid redundant calculations. This approach significantly improves performance compared to a naive quadratic solution, making the game scalable for a substantial number of participants.
A Hacker News user has presented a computational puzzle involving a betting game and challenged others to find an efficient solution. The game revolves around a set of N players, each holding a unique binary string of length K. These binary strings represent the players' bets on a series of K coin flips, where '1' predicts heads and '0' predicts tails. After the K coin flips are performed, resulting in a final binary string, the game's objective is to calculate, for each player, the sum of their neighbors' scores. A neighbor is defined as any player whose binary string differs from the given player's string by exactly one bit (also known as a Hamming distance of 1). A player's score is simply the number of correct predictions they made, which can be calculated by comparing their binary string to the outcome string and counting the number of matching positions.
The naive approach to this problem involves iterating through all pairs of players, checking if they are neighbors, and if so, adding the neighbor's score to the current player's neighbor sum. This approach has a time complexity of O(N^2 * K), which becomes computationally expensive for large numbers of players and coin flips. The challenge presented is to devise an algorithm that can calculate these neighbor sums in linear time complexity, specifically O(N*K), which scales much more efficiently. The user has provided sample code in Python demonstrating the naive approach and is soliciting more optimized solutions. They have hinted that a clever application of dynamic programming might be the key to achieving linear time complexity. The underlying problem is essentially efficiently calculating the sum of scores for all Hamming neighbors for each player string within the provided set.
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https://news.ycombinator.com/item?id=43210185
Hacker News users discussed the efficiency and practicality of the presented algorithm for the betting game puzzle. Some questioned the "linear time" claim, pointing out the algorithm's reliance on a precomputed lookup table, the creation of which would not be linear. Others debated the best way to construct such a table efficiently. A few commenters suggested alternative approaches, including using Gray codes or focusing on bit manipulation tricks. There was also discussion about the problem's framing, with some arguing it's more of a dynamic programming exercise than a puzzle. Finally, some users explored variations of the puzzle, such as changing the allowed bet sizes or considering non-integer bets.
The Hacker News post titled "Show HN: Betting game puzzle (Hamming neighbor sum in linear time)" has sparked a discussion with several interesting comments.
Several users engage with the computational aspect of the puzzle. One user points out the potential connection to error correction codes, specifically mentioning Hamming codes, highlighting the relevance of the puzzle to practical applications. Another delves deeper into the computational complexity, discussing how the presented linear-time algorithm provides a significant improvement over a naive exponential approach. This user appreciates the elegance and efficiency of the provided solution, emphasizing the clever use of bit manipulation. They further explore the problem, suggesting a generalization involving arbitrary weights for each neighbor and pondering the existence of efficient solutions for this generalized version.
The discussion also touches upon the mathematical underpinnings of the puzzle. One commenter breaks down the algorithm, explaining how the bitwise XOR operation and subsequent summation effectively calculate the desired neighbor sum. Another user frames the puzzle in the context of graph theory, viewing it as a problem of finding the sum of neighbor values in a hypercube graph.
Furthermore, commenters discuss the presentation and clarity of the puzzle itself. One user expresses appreciation for the clear explanation and the well-structured code. Another suggests potential improvements to the user interface, proposing the addition of interactive elements to enhance engagement. Finally, one commenter expresses interest in exploring variations of the puzzle, suggesting a modified version with different constraints.
Overall, the comments reflect a positive reception of the presented puzzle, with users appreciating its computational challenge, mathematical depth, and clear presentation. The discussion expands upon the original post by connecting the puzzle to related concepts, exploring potential generalizations, and suggesting improvements to its presentation and interactivity.