find a maximum sum of a compact subsequence of array elements.
Task description
A non-empty array A consisting of N integers is given. A pair of integers (P, Q), such that 0 ≤ P ≤ Q < N, is called a slice of array A. The sum of a slice (P, Q) is the total of A[P] + A[P+1] + ... + A[Q].
Write a function:
def solution(A)
that, given an array A consisting of N integers, returns the maximum sum of any slice of A.
For example, given array A such that:
A[0] = 3 A[1] = 2 A[2] = -6
A[3] = 4 A[4] = 0
the function should return 5 because:
(3, 4) is a slice of A that has sum 4,
(2, 2) is a slice of A that has sum −6,
(0, 1) is a slice of A that has sum 5,
no other slice of A has sum greater than (0, 1).
Write an efficient algorithm for the following assumptions:
N is an integer within the range [1..1,000,000];
each element of array A is an integer within the range [−1,000,000..1,000,000];
the result will be an integer within the range [−2,147,483,648..2,147,483,647].
思路:我们计算到每个位置的最大和。假设在第i元素有最大的和max_ending。那么在i+1时,最大的和= max{a_{i+1}, max_ending+a_{i+1}}。max_slice存储最大值。
def solution(A):
# write your code in Python 3.6
max_slice = A[0]
max_ending = 0
#在i有最大值
for i in A:
max_ending = max(i,max_ending + i)
max_slice = max(max_slice,max_ending)
return max_slice
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