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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def solve(self, method='policy_iteration', v_init=None, epsilon=None, max_iter=None, k=20):
 """ Solve the dynamic programming problem. Parameters method : str, optinal(default='policy_iteration') Solution method, str in {'value_iteration', 'vi', 'policy_iteration', 'pi', 'modified_policy_iteration', 'mpi'}. v_init : array_like(float, ndim=1), optional(default=None) Initial value function, of length n. If None, `v_init` is set such that v_init(s) = max_a r(s, a) for value iteration and policy iteration; for modified policy iteration, v_init(s) = min_(s_next, a) r(s_next, a)/(1 - beta) to guarantee convergence. epsilon : scalar(float), optional(default=None) Value for epsilon-optimality. If None, the value stored in the attribute `epsilon` is used. max_iter : scalar(int), optional(default=None) Maximum number of iterations. If None, the value stored in the attribute `max_iter` is used. k : scalar(int), optional(default=20) Number of iterations for partial policy evaluation in modified policy iteration (irrelevant for other methods). Returns ------- res : DPSolveResult Optimization result represetned as a DPSolveResult. See `DPSolveResult` for details. """

        if method in ['value_iteration', 'vi']:
            res = self.value_iteration(v_init=v_init,
                                       epsilon=epsilon,
                                       max_iter=max_iter)
        elif method in ['policy_iteration', 'pi']:
            res = self.policy_iteration(v_init=v_init,
                                        max_iter=max_iter)
        elif method in ['modified_policy_iteration', 'mpi']:
            res = self.modified_policy_iteration(v_init=v_init,
                                                 epsilon=epsilon,
                                                 max_iter=max_iter,
                                                 k=k)
        else:
            raise ValueError('invalid method')

        return res