Sarsa(lambda) Algorithm with Eligibility Traces

Implement the Sarsa(lambda) algorithm, which combines temporal difference learning with eligibility traces for on policy control. This algorithm extends one step Sarsa by maintaining a trace for each state action pair, allowing updates to propagate backward through recently visited pairs. Your function should learn an action value function Q(s, a) by interacting with a deterministic environment over multiple episodes. Inputs n states: Total number of states (int) n actions: Total number of actions (int) transitions: A dictionary mapping (state, action) to (next state, reward) tuples representing the deterministic environment dynamics terminal states: A list of terminal state indices gamma: Discount factor (float) alpha: Learning rate (float) lam: Lambda parameter controlling the trace decay (float between 0 and 1) epsilon: Exploration rate for epsilon greedy action selection (float) num episodes: Number of episodes to train (int) seed: Random seed for reproducibility (int, default 42) Algorithm Requirements Initialize Q values to zero At the start of each episode, reset eligibility traces to zero Select a random non terminal starting state uniformly Use epsilon greedy action selection based on current Q values (break ties by choosing the smallest action index) Use accumulating eligibility traces When a terminal state is reached, the episode ends (terminal states have Q value 0) For epsilon greedy: with probability epsilon choose a uniformly random action, otherwise choose greedy Output Return the learned Q table as a 2D list of shape (n states, n actions), with values rounded to 4 decimal places.