Pythonic Psuedo-code of Dynamic Programming

dynamic_programming.py

def minimize_fuel_consumption(num_timesteps, velocity, acceleration, fuel_consumption_function):
    # Initialize the cost function with a large value for all states
    cost = [[float('inf') for _ in range(len(velocity))] for _ in range(num_timesteps)]

    # Define the set of actions
    actions = ['accelerate', 'decelerate', 'maintain constant speed']

    # Initialize the cost for the initial state to zero
    cost[0][0] = 0

    # Iterate over all timesteps
    for t in range(1, num_timesteps):
        # Iterate over all states
        for i, (v, a) in enumerate(zip(velocity, acceleration)):
            # Iterate over all predecessor states
            for j, (v_prev, a_prev) in enumerate(zip(velocity, acceleration)):
                # Check if the current state can be reached from the predecessor state by applying an action
                if (a_prev == a and v_prev <= v) or (a_prev < a):
                    # Update the cost for the current state if it is lower than the current value
                    cost[t][i] = min(cost[t][i], cost[t-1][j] + fuel_consumption_function(v, a))

    # The optimal sequence of actions can be obtained by tracking the actions taken at each time step
    action_sequence = []
    s = (velocity[0], acceleration[0])  # Initialize the state to the initial state
    for t in range(num_timesteps-1, 0, -1):
        # Find the action that minimizes the cost to reach the current state
        min_cost = float('inf')
        best_action = None
        for action in actions:
            # Compute the successor state for the current action
            if action == 'accelerate':
                s_next = (s[0]+1, s[1]+1)
            elif action == 'decelerate':
                s_next = (s[0]-1, s[1]-1)
            else:
                s_next = (s[0], s[1])
            # Check if the successor state is a valid state and has a lower cost than the current minimum
            if s_next[0] >= 0 and s_next[0] < len(velocity) and s_next[1] >= 0 and s_next[1] < len(acceleration) and cost[t][s_next[0]] < min_cost:
                min_cost = cost[t][s_next[0]]
                best_action = action
                s = s_next
        action_sequence.append(best_action)

    return action_sequence[::-1]  # Reverse the action sequence to get the sequence in the correct order