#795

Medium

auto_awesomeTwo-pointer scanning with invariant tracking

LeetCode Problem Workspace

Number of Subarrays with Bounded Maximum

Count the number of contiguous subarrays with a bounded maximum value using a two-pointer approach.

Problem Statement

Given an integer array nums and two integers left and right, your task is to return the number of contiguous non-empty subarrays such that the maximum element in each subarray falls within the range [left, right].

The array may have multiple subarrays satisfying this condition. To solve the problem efficiently, you should consider techniques like two-pointer scanning to track valid subarrays.

Examples

Example 1

Input: nums = [2,1,4,3], left = 2, right = 3

Output: 3

There are three subarrays that meet the requirements: [2], [2, 1], [3].

Example 2

Input: nums = [2,9,2,5,6], left = 2, right = 8

Output: 7

Example details omitted.

Constraints

1 <= nums.length <= 105
0 <= nums[i] <= 109
0 <= left <= right <= 109

Solution Approach

Two-Pointer Scanning

The key approach for this problem is to use a sliding window or two-pointer technique. We can iterate through the array, expanding the window to include subarrays whose maximum element lies between left and right, and shrinking the window when the maximum element exceeds the right bound.

Counting Valid Subarrays

By keeping track of the number of subarrays that end at each index with a valid maximum, we can calculate the total number of valid subarrays. The key is to efficiently manage the bounds of the window while ensuring the maximum element remains within the desired range.

Avoiding Redundant Calculations

To optimize, we avoid recalculating the maximum for every possible subarray. Instead, maintain two pointers and adjust the range dynamically based on the array values, ensuring that the subarrays' maximums stay within the valid range.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity of this approach is O(n) because each element is processed at most twice by the two pointers. The space complexity is O(1), as only a few variables are required to keep track of the current subarray bounds and counts.

What Interviewers Usually Probe

Candidate demonstrates proficiency with sliding window and two-pointer techniques.
Candidate can clearly explain how the two-pointer technique avoids redundant calculations.
Candidate optimizes their approach to avoid recalculating the maximum for each subarray.

Common Pitfalls or Variants

Common pitfalls

Failing to properly track subarray bounds and missing valid subarrays.
Over-complicating the solution with nested loops or redundant calculations.
Not efficiently managing the sliding window and recalculating the maximum for each subarray.

Follow-up variants

What if the subarrays can contain more than one element with the same maximum value?
What if there were additional constraints on subarray lengths?
How would the solution change if the input array was sorted?

FAQ

What is the primary pattern used to solve the Number of Subarrays with Bounded Maximum problem?

The primary pattern is two-pointer scanning with invariant tracking, where the two pointers help manage subarray bounds and ensure the maximum remains within the specified range.

How does the two-pointer technique help solve this problem efficiently?

The two-pointer technique allows for efficient sliding window management, where the pointers expand and contract based on the maximum element in the current window, avoiding redundant calculations.

Can you describe the time and space complexity of this solution?

The time complexity is O(n) because each element is processed at most twice, and the space complexity is O(1) since only a few variables are used to track the current window state.

What are some common mistakes in solving this problem?

Common mistakes include failing to properly track subarray bounds, recalculating the maximum for each subarray, and not using a sliding window approach effectively.

How can GhostInterview assist in improving my solution to this problem?

GhostInterview provides instant feedback, helping refine your understanding of the two-pointer technique, pointing out inefficiencies, and ensuring optimal subarray calculations.

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Solution

Solution 1

#### Python3

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class Solution:
    def numSubarrayBoundedMax(self, nums: List[int], left: int, right: int) -> int:
        def f(x):
            cnt = t = 0
            for v in nums:
                t = 0 if v > x else t + 1
                cnt += t
            return cnt

        return f(right) - f(left - 1)

Solution 2

#### Python3

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class Solution:
    def numSubarrayBoundedMax(self, nums: List[int], left: int, right: int) -> int:
        def f(x):
            cnt = t = 0
            for v in nums:
                t = 0 if v > x else t + 1
                cnt += t
            return cnt

        return f(right) - f(left - 1)

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