python中的最小子数组差异

Question

假设我有一个非空整数数组：A0..An。并考虑一个参数P where 0 < P <=n。我需要找到被 P 分割的左右子数组之间的最小绝对差。例如：

  A[0] = 3
  A[1] = 1
  A[2] = 2
  A[3] = 4
  A[4] = 3

P = 1, difference = |3 − 10| = 7 
P = 2, difference = |4 − 9| = 5 
P = 3, difference = |6 − 7| = 1 
P = 4, difference = |10 − 3| = 7

这种情况下的解决方案是1

我完成了下面的代码：

def solution(A):
    lsum, rsum = A[0], sum(A[1:])
    diff = abs(rsum - lsum)
    p = 1
    while True:
        lsum += A[p]
        rsum -= A[p]
        next = abs(rsum - lsum)
        if next < diff:
            diff = next
            p += 1
        else:
            return diff

但我的解决方案有一些错误。它在某些情况下有效，但在某些情况下返回错误答案。例如：在large sequence, numbers from -1 to 1, length = ~100,000这样的条件下，它返回错误的答案

P.S.：我完成了以下解决方案：

 def solution(lst):
    lsum, rsum = lst[0], sum(lst[1:])
    diff = abs(lsum - rsum)
    for i in xrange(1, len(lst) - 1):
        lsum += lst[i]
        rsum -= lst[i]
        ndiff = abs(lsum - rsum)
        diff = min(diff, ndiff)
    return diff

Answer 1

这更简洁但仍然 O(n)：

import itertools

def min_diff(A):
    total = sum(A)
    return min(abs(total - lsum - lsum) for lsum in itertools.accumulate(A))

itertools.accumulate 从 Python 3.2 开始可用。

Answer 2

错误是这样的：

if next < diff:
    diff = next
    p += 1
else:
    return diff

如果next 对diff 没有改进，您将终止。这是错误的，因为您稍后可能会找到更好的解决方案。

除此之外，我认为您的想法朝着正确的方向发展。修复你的错误应该做的是无条件地遍历整个数组，最后只返回diff。 像这样：

def solution(A):
    lsum, rsum = A[0], sum(A[1:])
    diff = abs(rsum - lsum)
    p = 1
    while p < (len(A)-1):
        lsum += A[p]
        rsum -= A[p]
        next = abs(rsum - lsum)
        if next < diff:
            diff = next
        p += 1
    return diff

（注意：我尝试尽可能少地进行修改，即尽可能接近您的代码。另外，我并没有真正对此进行测试。但我希望您明白这一点。）

Answer 3

编辑（以前的解决方案复杂度很高，我的错）

这是你的翻拍，但去掉了列表中的索引 并使用min 内置函数获取最小值。

def solution(a):
    lsum = a[0]
    rsum = sum(a)-lsum
    dfs = [abs(rsum-lsum),]
    for el in a[1:]:
        lsum+=el
        rsum-=el
        dfs.append(abs(rsum-lsum))
    return min(dfs)

调用它

sol = solution([3,1,2,4,3])
print(sol)

生产

1