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The knapsack problem is a combinatorial optimization problem of choosing items with weights and values to maximize the total value within a given capacity. The unbounded knapsack problem allows unlimited copies of each item, while the bounded knapsack problem limits the number of copies to a positive integer.
1.b) The side that was heavier the first time is lighter the second time. This means that one of the three coins that went from the lighter side to the heavier side is the light coin. For the third attempt, weigh two of these coins against each other: if one is lighter, it is the unique coin; if they balance, the third coin is the light one.
A mathematical problem of calculating the number of grains of wheat on a chessboard if each square has twice as many grains as the previous one. Learn about its origins, solutions, and applications in exponential growth, compound interest, and technology strategy.
A decision boundary is a hypersurface that partitions the vector space into two sets for each class in a statistical-classification problem. Learn about different types of decision boundaries, their applications, and how they are learned by neural networks and support vector machines.
Learn about the optimization problem of packing items of different sizes into a fixed number of bins, and its applications, variations, and algorithms. Find out the hardness, approximation, and online versions of the problem, and their complexity and performance.
The Potter Box is a framework for ethical analysis developed by Ralph B. Potter, Jr., a Harvard Divinity School professor. It consists of four steps: facts, values, principles, and loyalties, and can be applied to any moral dilemma.
Newcomb's paradox is a thought experiment involving a game between two players, one of whom is able to predict the future. The paradox arises from the conflict between two game-theory strategies that give different answers to the question of what choice maximizes the player's payout.
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. Learn how to find the optimal decision using utility, expected utility, and probabilistic approaches.