Is Sum of Subarray Ranges easy or hard?

The problem is rated Medium on LeetCode. Understanding the brute force solution is straightforward, but deriving the O(n) monotonic stack approach requires familiarity with subarray contribution techniques and boundary discovery.

How to solve Sum of Subarray Ranges in O(n)?

Compute the contribution of each element as both a maximum and a minimum. Use monotonic stacks to find the previous and next greater elements for maximum contribution and previous and next smaller elements for minimum contribution. Multiply the distances to count how many subarrays include that element as the boundary.

What is the best approach for Sum of Subarray Ranges?

The optimal solution uses a monotonic stack to compute how many subarrays treat each element as a maximum and as a minimum. By calculating these contributions separately and subtracting them, the total range sum can be derived in O(n) time. This avoids enumerating every subarray.

Is Sum of Subarray Ranges asked at Google/Amazon/Meta?

Sum of Subarray Ranges represents a common interview pattern involving monotonic stacks and subarray contribution counting. Variants of this pattern frequently appear in interviews at companies like Amazon, Google, and Meta because they test deeper understanding of array boundaries and stack techniques.

What data structure is used in Sum of Subarray Ranges?

The optimal solution uses a monotonic stack. The stack maintains indices in increasing or decreasing order to efficiently find previous and next greater or smaller elements in linear time.

What is the time complexity of Sum of Subarray Ranges?

The brute force method runs in O(n^2) time because it checks every subarray while tracking the current minimum and maximum. The optimal monotonic stack approach runs in O(n) time since each element is pushed and popped from the stack at most once.

Sum of Subarray Ranges Python or Java solution approach

Python and Java implementations typically follow the same pattern: compute contributions for maximum values using a decreasing monotonic stack, then compute contributions for minimum values using an increasing stack. Both passes run in O(n) time and store indices in the stack.

Description Hints 2 Solution Video 10:34

2104. Sum of Subarray Ranges

Medium61.6% acceptance9 companies

You are given an integer array nums. The range of a subarray of nums is the difference between the largest and smallest element in the subarray.

Return the sum of all subarray ranges of nums.

A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input: nums = [1,2,3]
Output: 4
Explanation: The 6 subarrays of nums are the following:
[1], range = largest - smallest = 1 - 1 = 0 
[2], range = 2 - 2 = 0
[3], range = 3 - 3 = 0
[1,2], range = 2 - 1 = 1
[2,3], range = 3 - 2 = 1
[1,2,3], range = 3 - 1 = 2
So the sum of all ranges is 0 + 0 + 0 + 1 + 1 + 2 = 4.

Example 2:

Input: nums = [1,3,3]
Output: 4
Explanation: The 6 subarrays of nums are the following:
[1], range = largest - smallest = 1 - 1 = 0
[3], range = 3 - 3 = 0
[3], range = 3 - 3 = 0
[1,3], range = 3 - 1 = 2
[3,3], range = 3 - 3 = 0
[1,3,3], range = 3 - 1 = 2
So the sum of all ranges is 0 + 0 + 0 + 2 + 0 + 2 = 4.

Example 3:

Input: nums = [4,-2,-3,4,1]
Output: 59
Explanation: The sum of all subarray ranges of nums is 59.

Constraints:

1 <= nums.length <= 1000
-10⁹ <= nums[i] <= 10⁹

Follow-up: Could you find a solution with O(n) time complexity?

Asked at 9 companies

Chubb D. E. Shaw PhonePe Amazon Meta

Google Microsoft Bloomberg Apple

Topics

Hints open one at a time

Hint 1

Can you get the max/min of a certain subarray by using the max/min of a smaller subarray within it?

Hint 2

Notice that the max of the subarray from index i to j is equal to max of (max of the subarray from index i to j-1) and nums[j].

10:34

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