How to populate a backpack table when using recursive dynamic programming

Question

* NOT HOMEWORK *

I implemented a backpack in python and successfully got the best value, but I would like to expand the problem to fill the table with all the appropriate values ​​for the satchel table of all weights and elements.

I implemented it in python, which I am new to, so please tell me if there is anything that I could improve, however the concepts should work in any language.

values, weights, table = [], [], [[]]

def knapsack(i, W):
    global weights, values, table, counter
    if (i < 0):
        # Base case
        return 0
    if (weights[i] > W):
        # Recursion
        return knapsack(i - 1, W)
    else:
        # Recursion
        return max(knapsack(i - 1, W), values[i] + knapsack(i - 1, W - weights[i]))

def main():
    global values, weights, table
    W = int(input())
    values = list(map(int, input().split()))
    weights = list(map(int, input().split()))
    # initalise table with 0's
    table = [[0 for i in range(W)] for i in range(len(values))]
    for i in range(len(values)):
        for j in range(W):
            table[i][j] = 0
    # Fill table
    print("Result: {}".format(knapsack(len(values) - 1, W)))
    printKnapsack(W)

if __name__ == '__main__':
    main()

I also have this print table method, which is not related, but so that you can see that I output it as:

def printLine(W):
    print(" ",end="")
    for i in range(W + 1):
        print("-----",end="")
    print("")

def printKnapsack(W):
    global table
    print("\nKnapsack Table:")
    printLine(W)
    print("| k\w |", end="")
    for i in range(W):
        print("{0: >3} |".format(i + 1), end="")
    print("")
    printLine(W)
    for i in range(len(values)):
        print("|  {}  |".format(i+1), end="")
        for j in range(W):
            print("{0: >3} |".format(table[i][j]), end="")
        print("")
        printLine(W)

This is an example input:

10
18 9 12 25
5 2 4 6

This is what should be output:

Result: 37

Knapsack Table:
 -------------------------------------------------------
| k\w |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 |
 -------------------------------------------------------
|  1  |  0 |  0 |  0 |  0 | 18 | 18 | 18 | 18 | 18 | 18 |
 -------------------------------------------------------
|  2  |  0 |  9 |  9 |  9 | 18 | 18 | 27 | 27 | 27 | 27 |
 -------------------------------------------------------
|  3  |  0 |  9 |  9 | 12 | 18 | 21 | 27 | 27 | 30 | 30 |
 -------------------------------------------------------
|  4  |  0 |  9 |  9 | 12 | 18 | 25 | 27 | 34 | 34 | 37 |
 -------------------------------------------------------

knapsack(i, W), , , , , , .

, .

def knapsack(i, W):
    global weights, values, table, counter
    if (i < 0):
        # Base case
        return 0
    if (weights[i] > W):
        # Recursion
        table[?][?] = ?
        return knapsack(i - 1, W)
    else:
        # Recursion
        table[?][?] = ?
        return max(knapsack(i - 1, W), values[i] + knapsack(i - 1, W - weights[i]))

Answer 1

, :

return max(knapsack(i - 1, W), values[i] + knapsack(i - 1, W - weights[i]))

:

def knapsack(i, W):
    global weights, values, table, counter
    if (i < 0):
        # Base case
        return 0
    if (weights[i] > W):
        # Recursion
        table[i][W-1] = knapsack(i - 1, W)
        return table[i][W-1]
    else:
        # Recursion
        table[i][W-1] = max(knapsack(i - 1, W), values[i] + knapsack(i - 1, W - weights[i]))
        return table[i][W-1]

, . .

,