Is Number of Valid Subarrays easy or hard?

The problem is labeled Hard on LeetCode even though the final algorithm is short. The challenge lies in recognizing the monotonic stack pattern and understanding why the stack size directly represents the number of valid subarrays.

Number of Valid Subarrays Python/Java solution

Most implementations follow the same monotonic stack pattern across languages. Maintain a stack, pop elements while the current value is smaller, push the current value, and add the stack size to the running total. The logic translates directly to Python, Java, C++, Go, and TypeScript.

How to solve Number of Valid Subarrays in O(n)?

Traverse the array while maintaining a monotonic increasing stack. If the current value is smaller than the stack top, pop elements until the stack becomes valid again. Push the current value and add the stack size to the result because each element in the stack forms a valid subarray start. This ensures linear processing of all elements.

What is the best approach for Number of Valid Subarrays?

The optimal solution uses a monotonic increasing stack. As you iterate through the array, you maintain elements in non-decreasing order and pop values when a smaller element appears. The stack size at each step represents how many valid subarrays end at that index. This approach runs in O(n) time and O(n) space.

Is Number of Valid Subarrays asked at Google/Amazon/Meta?

Problems involving monotonic stacks and subarray minimum constraints frequently appear in interviews at companies like Google, Amazon, and Meta. Variants such as Next Smaller Element, Sum of Subarray Minimums, and histogram problems test the same core pattern used in this question.

What data structure is used in Number of Valid Subarrays?

The key data structure is a monotonic stack that maintains elements in non-decreasing order. It allows efficient tracking of ranges where each element remains the minimum of its subarrays. This structure ensures each element is processed only once.

What is the time complexity of Number of Valid Subarrays?

The optimal monotonic stack solution runs in O(n) time because each element is pushed onto the stack once and popped at most once. The space complexity is O(n) for the stack. A naive brute force approach would take O(n²) time by expanding every subarray.

Description Hints 2 Solution Video 28:39

1063. Number of Valid Subarrays

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Given an integer array nums, return the number of non-empty subarrays with the leftmost element of the subarray not larger than other elements in the subarray.

A subarray is a contiguous part of an array.

Example 1:

Input: nums = [1,4,2,5,3]
Output: 11
Explanation: There are 11 valid subarrays: [1],[4],[2],[5],[3],[1,4],[2,5],[1,4,2],[2,5,3],[1,4,2,5],[1,4,2,5,3].

Example 2:

Input: nums = [3,2,1]
Output: 3
Explanation: The 3 valid subarrays are: [3],[2],[1].

Example 3:

Input: nums = [2,2,2]
Output: 6
Explanation: There are 6 valid subarrays: [2],[2],[2],[2,2],[2,2],[2,2,2].

Constraints:

1 <= nums.length <= 5 * 10⁴
0 <= nums[i] <= 10⁵

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Hints open one at a time

Hint 1

Given a data structure that answers queries of the type to find the minimum in a range of an array (Range minimum query (RMQ) sparse table) in O(1) time. How can you solve this problem?

Hint 2

For each starting index do a binary search with an RMQ to find the ending possible position.

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