2013寒假练习 1027 一个人的旅行 1028 Constructing Roads 1032 Trees Made to Order
以下是一个简单的 Python 代码，可以将输入的原问题转换为对偶问题，但不会对问题进行求解： ```python def dual_problem(primal_problem): """ Converts a given primal problem to its corresponding dual problem """ # Extracting the objective function coefficients from the primal problem primal_c = primal_problem['c'] # Extracting the constraint coefficients from the primal problem primal_A = primal_problem['A'] # Extracting the right-hand side values from the primal problem primal_b = primal_problem['b'] # Transposing the constraint coefficients matrix dual_A = primal_A.T # Extracting the number of variables and constraints from the primal problem num_vars = primal_A.shape[1] num_constraints = primal_A.shape[0] # Constructing the dual objective function coefficients dual_c = -primal_b # Constructing the dual constraint coefficients dual_b = -primal_c # Constructing the dual right-hand side values dual_lb = np.zeros(num_constraints) dual_ub = np.ones(num_constraints) * np.inf # Constructing the dual problem dictionary dual_problem = {'c': dual_c, 'A': dual_A, 'b': dual_b, 'lb': dual_lb, 'ub': dual_ub} return dual_problem ``` 注意：这个代码假定输入的原问题是线性规划问题，并使用 NumPy 库来进行矩阵操作。如果输入的原问题不是线性规划问题，或者没有安装 NumPy 库，则需要进行适当的修改。
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