发现的最大时间间隔总和在实数的列表 [英] Find the maximum interval sum in a list of real numbers

问题描述

下面是一个面试问题，一个同事问一个编程的位置。我认为这是伟大的看受访者认为它通过。我很想得到的反应如何多所社区想到了。

Here's an interview questions that a colleague asked for a programming position. I thought this was great for watching the interviewee think it through. I'd love to get responses for how the SO community thinks of it.

鉴于长度为N实数的清单，说 [A_1，A_2，...，A_N] ，什么是找到了最大值M的复杂性其中存在指数1＆LT; = I＆LT; = J＆LT; = N使得

Given a list of real numbers of length N, say [a_1, a_2, ..., a_N], what is the complexity of finding the maximum value M for which there exist indices 1 <= i <= j <= N such that

A_I + A_ {I + 1} + ... + a_j = M ？

我的道歉，如果这是一个经典的CS问题。

My apologies if this is a classic CS problem.

推荐答案

的复杂性是只是为O（n）的Kadane算法：

该算法跟踪试探性最大子的（maxSum，maxStartIndex，maxEndIndex）。它积累了部分和在 currentMaxSum 和更新的最佳范围时，这部分的总和变得比 maxSum 大。

The algorithm keeps track of the tentative maximum subsequence in (maxSum, maxStartIndex, maxEndIndex). It accumulates a partial sum in currentMaxSum and updates the optimal range when this partial sum becomes larger than maxSum.

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