Specify House-Selection Constraints Before Choosing a Robbery Dynamic Program

Discuss a house-robbery optimization problem in which a set of houses has values and some choices cannot be combined. Explain which constraints must be clarified and how the structure of those constraints determines the algorithm. ### Constraints Only the problem family is supplied; house layout, compatibility rules, value range, and output contract are unresolved. Do not infer a circular layout from a variant label. For an illustrative analysis, you may assume a linear row of nonnegative house values where adjacent houses cannot both be chosen, but label that model explicitly. ### Clarifying Questions - Are houses arranged in a line, a circle, a tree, or a more general graph? - Which pairs or groups cannot be selected together? - Are values nonnegative, may all houses be skipped, and is the output a total or the selected indices? - Are there cardinality limits, tie rules, or other constraints? ```hint Define a state that preserves the last relevant choice For a linear adjacency rule, the best answer for a prefix can be separated according to whether its final house is selected. ``` ### What a Strong Answer Covers - Explicit unresolved layout and compatibility semantics. - A correct conditional dynamic-programming recurrence and base cases for the illustrative linear model. - An explanation of how circular or other dependencies change the state or decomposition. ### Follow-up Questions - If the first and last houses are also incompatible, how would you adapt the linear solution? - What additional information is needed to return chosen indices instead of only the maximum total?