python流控制功能奇怪

Question

我试图使用 DP 解决背包问题。基本上，目标是看看列表中的某些元素的总和是否可以达到总和的一半。

def canPartition(nums):
    """
    :type nums: List[int]
    :rtype: bool
    """
    run_sum = 0
    for num in nums:
        run_sum += num

    if run_sum & 1 == 1:
        return False
    run_sum //= 2

    n = len(nums)
    dp = [[False] * (run_sum+1)] * (n+1)

    for i in range(n+1):
        dp[i][0] = True

    for j in range(1, run_sum+1):
        dp[0][j] = False
    print("initial stage")
    print(dp)

    for i in range(1, 2):
        for j in range(1, run_sum+1):
            dp[i][j] = dp[i-1][j]
            print("inner loop after operation 1:")
            print(dp)
            if j >= nums[i-1]:
                print("inner loop after operation 2:")
                print(i, j)
                dp[i][j] |= dp[i-1][(j - nums[i-1])]
                print(dp)
                print(" ")

    return dp[n][run_sum]

nums = [1, 2, 5]
canPartition(nums)

目标本身在这里并不那么重要。但是最后一个嵌套循环的流程控制表现得非常奇怪。下面是打印结果。

initial stage
[[True, False, False, False, False], [True, False, False, False, False], [True, False, False, False, False], [True, False, False, False, False]]
inner loop after operation 1:
[[True, False, False, False, False], [True, False, False, False, False], [True, False, False, False, False], [True, False, False, False, False]]
inner loop after operation 2:
1 1
[[True, True, False, False, False], [True, True, False, False, False], [True, True, False, False, False], [True, True, False, False, False]]

inner loop after operation 1:
[[True, True, False, False, False], [True, True, False, False, False], [True, True, False, False, False], [True, True, False, False, False]]
inner loop after operation 2:
1 2
[[True, True, True, False, False], [True, True, True, False, False], [True, True, True, False, False], [True, True, True, False, False]]

inner loop after operation 1:
[[True, True, True, False, False], [True, True, True, False, False], [True, True, True, False, False], [True, True, True, False, False]]
inner loop after operation 2:
1 3
[[True, True, True, True, False], [True, True, True, True, False], [True, True, True, True, False], [True, True, True, True, False]]

inner loop after operation 1:
[[True, True, True, True, False], [True, True, True, True, False], [True, True, True, True, False], [True, True, True, True, False]]
inner loop after operation 2:
1 4
[[True, True, True, True, True], [True, True, True, True, True], [True, True, True, True, True], [True, True, True, True, True]]

您可以看到，即使整个嵌套循环中 i 的值为 1，dp[i>1] 的值也会在循环中以某种方式被修改。甚至j也从1修改为4。就像循环内还有另一个“for i in range()”。有谁知道为什么会发生这种情况？我用 python 3.6.1 运行了代码

Answer 1

这一行

dp = [[False] * (run_sum+1)] * (n+1)

创建一个包含 n + 1 个引用的列表，对 False 的相同列表进行引用。一个更简单的例子:

>>> x = [[False]]*3
>>> x
[[False], [False], [False]]
>>> x[0][0] = True
>>> x
[[True], [True], [True]]

你几乎不想将 * 与列表一起使用；使用列表理解来获取独立列表:

dp = [[False for _ in range(run_sum+1)] for _ in range(n+1)]