What is the optimal solution for the Sum of Variable Length Subarrays problem?

The optimal solution uses prefix sums to calculate the sum of elements for each subarray efficiently, reducing redundant calculations.

How can brute force be applied to the Sum of Variable Length Subarrays?

Brute force involves calculating the sum of elements in each subarray independently, which can be slow but works due to small constraints.

What role does prefix sum play in solving this problem?

Prefix sum helps by allowing quick calculation of subarray sums, improving the solution from brute force's O(n^2) to O(n).

Can the Sum of Variable Length Subarrays be solved using dynamic programming?

While dynamic programming is not necessary, it can be used to store intermediate results to avoid redundant calculations, similar to prefix sums.

What are the time and space complexities of the optimal solution?

The optimal solution with prefix sums has a time complexity of O(n) and a space complexity of O(n), where n is the length of the array.

#3427

Easy

auto_awesome前缀和

LeetCode 题解工作台

变长子数组求和

给你一个长度为 n 的整数数组 nums 。对于每个下标 i （ 0 ），定义对应的子数组 nums[start ... i] （ start = max(0, i - nums[i]) ）。返回为数组中每个下标定义的子数组中所有元素的总和。子数组是数组中的一个连续、非空的元素序列。 …

数组前缀和

题目描述

给你一个长度为 n 的整数数组 nums 。对于每个下标 i（0 <= i < n），定义对应的子数组 nums[start ... i]（start = max(0, i - nums[i])）。

返回为数组中每个下标定义的子数组中所有元素的总和。

子数组 是数组中的一个连续、非空的元素序列。

示例 1：

输入：nums = [2,3,1]

输出：11

解释：

下标 i	子数组	和
0	`nums[0] = [2]`	2
1	`nums[0 ... 1] = [2, 3]`	5
2	`nums[1 ... 2] = [3, 1]`	4
总和		11

总和为 11 。因此，输出 11 。

示例 2：

输入：nums = [3,1,1,2]

输出：13

解释：

下标 i	子数组	和
0	`nums[0] = [3]`	3
1	`nums[0 ... 1] = [3, 1]`	4
2	`nums[1 ... 2] = [1, 1]`	2
3	`nums[1 ... 3] = [1, 1, 2]`	4
总和		13

总和为 13 。因此，输出为 13 。

提示：

1 <= n == nums.length <= 100
1 <= nums[i] <= 1000

lightbulb

解题思路

方法一

1

2

3

4

5

class Solution:
    def subarraySum(self, nums: List[int]) -> int:
        s = list(accumulate(nums, initial=0))
        return sum(s[i + 1] - s[max(0, i - x)] for i, x in enumerate(nums))

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Candidate demonstrates understanding of prefix sums.
question_mark
Candidate chooses an appropriate approach based on problem constraints.
question_mark
Candidate avoids unnecessary recalculations in the solution.

warning

常见陷阱

外企场景

error
Forgetting to calculate the subarray's starting index properly.
error
Not considering the optimization potential with prefix sums.
error
Using inefficient algorithms for larger arrays without considering the constraints.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Given larger arrays, how can we optimize the brute force approach further?
arrow_right_alt
What would happen if the array elements were negative? How would this affect the subarray calculations?
arrow_right_alt
Can the solution be adjusted to return a different value, such as the maximum or minimum sum of the subarrays?

help

常见问题

外企场景

继续练习

#3425 最长特殊路径 #3432 统计元素和差值为偶数的分区方案 #3434 子数组操作后的最大频率