Python中的动态编程实现

Question

I am trying to solve this problem

This is the Python code and I am having trouble figuring out dp[i][j]. This is supposed to be the minimum cost for the first j city centers with i shops.

# A an integer array for city centers
# k an integer number of shops
# return  an integer
def groceryShops(A, k):
    # Write your code here
    if not A:
        return 0

    n = len(A) # n is the number of city centers.

    if k >= n: # we should not have more shops than city centers.
        return 0

    A.sort()
    cost = [[0 for _ in range(n + 1)] for _ in range(n + 1)]

    """
    cost[i][j] is the minimum cost to build a shop between city centers i and j
    This shop should be in the median of the city centers.
    """
    for i in range(n):
        for j in range(i, n):
            mid = int(i + (j - i) / 2)
            print("i= ", i, " j= ", j, "Median is: ", mid, " Center:",  A[mid], "\n")

            for r in range(i, mid + 1):
                cost[i + 1][j + 1] += A[mid] - A[r]
                print("dist of ", A[mid] ," --to-> " ,  A[r], " Right ", cost[i + 1][j + 1])
            for r in range(mid + 1, j + 1):
                cost[i + 1][j + 1] += A[r] - A[mid]
                print("dist of ",  A[mid] ," <--to-- " ,  A[r], " Left ", cost[i + 1][j + 1])
            print("COST: ", "(", A[i ], "," ,A[j], " )", cost[i + 1][j + 1], "\n\n")


    # print("cost")
    # for row in cost:
    #   for c in row:
    #     print(c, end = " ")
    #   print()
    """
    dp[i][j] is the minimum cost for the first j city centers with i shops.
    """
    dp = [[float('inf') for _ in range(n + 1)] for _ in range(k + 1)]
    dp[0][0] = 0

    for i in range(1, k + 1):
        for j in range(1, n + 1):
            for r in range(j):
                dp[i][j] = ???  # only fill this gap :), min or max of some values using i, j and r?

    # print("\n\nDP Table")
    # for row in dp:
    #   for c in row:
    #     print(c, end = "       ")
    #   print("\n")

    return dp[-1][-1]

The following input k = 5, a = [1, 2, 3, 6, 7, 9, 11, 21, 40, 50] should produce an output of 9.

Answer 1

As @Kenny Ostrom said, you have to get into the code by actually going through the debugger and checking your data structures while you do that and compare it with the actual task you wanted it to do.

Although, I did read the code and the time complexity is O(nk) :)