x̄ - >Optimization problem - To minimize Sum of distances between cities

 def min_total_travel_time(A):

    MOD = 10**9 + 7

    N = len(A)

    # Calculate the total travel time without building any motorways

    total_time = A[N-1] - A[0]

    # Initialize an array to store the minimum travel time for each city

    min_travel_time = [float('inf')] * N

    # Traverse the cities from left to right and find the minimum travel time to the easternmost city

    for i in range(N):

        for j in range(i + 1, N):

            min_travel_time[j] = min(min_travel_time[j], A[j] - A[i])

    # Initialize an array to store the maximum travel time for each city

    max_travel_time = [0] * N

    # Traverse the cities from right to left and find the maximum travel time to the easternmost city

    for i in range(N - 1, -1, -1):

        for j in range(i - 1, -1, -1):

            max_travel_time[j] = max(max_travel_time[j], A[i] - A[j])

    # Initialize the minimum total travel time

    min_total_time = total_time

    # Find the minimum total travel time with a motorway

    for i in range(1, N - 1):

        min_total_time = min(min_total_time, total_time - max_travel_time[i] + min_travel_time[i])

    return min_total_time % MOD

# Example usage:

A = [0, 1, 3, 6, 7, 9]

result = min_total_travel_time(A)

print(result)