Python中的01背包动态编程

Question

def printtable(arr):
    for row in arr:
        print(row)
    return

items = [(3,2),(4,3),(5,4),(6,5)]
W = 5

arr = [[0]*(W+1)]*(len(items)+1)

for i in range(1,len(items)+1,1):
    val,wt = items[i-1]
    for w in range(1,W+1,1):
        if wt <= w:
            arr[i][w] = max(arr[i-1][w] , val + arr[i-1][w-wt])
        else:
            arr[i][w] = arr[i-1][w]

printtable(arr)

The output is:

[0, 0, 3, 4, 6, 7]
[0, 0, 3, 4, 6, 7]
[0, 0, 3, 4, 6, 7]
[0, 0, 3, 4, 6, 7]
[0, 0, 3, 4, 6, 7]

I don't know what is the issue in this code ? The values are wrong. But the logic in the code is correct.

Expected output is:

0 0 0 0 0 0
0 0 3 3 3 3
0 0 3 4 4 7
0 0 3 4 5 7
0 0 3 4 5 7

Answer 1

The issue is in how you create the list of lists . When you do -

arr = [[0]*(W+1)]*(len(items)+1)

This creates a single inner list and each list in the outer list is a reference to the same list. Example to show this issue -

>>> a = [[0]*5]*5
>>> print(a)
[[0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0]]
>>> a[0][0] = 1
>>> print(a)
[[1, 0, 0, 0, 0],
 [1, 0, 0, 0, 0],
 [1, 0, 0, 0, 0],
 [1, 0, 0, 0, 0],
 [1, 0, 0, 0, 0]]

---

You should use list comprehension instead -

arr = [[0 for _ in range(W+1)] for _ in range(len(items)+1)]