What is the brute force approach and complexity for Count Subarrays With Fixed Bounds?

Fix each start, grow the end, track min and max with time complexity O(N²) and space complexity O(1).

What is the optimal approach and complexity for Count Subarrays With Fixed Bounds?

For each right, good starts are lastBad+1 … min(lastMin, lastMax) with optimal time complexity O(N) and space complexity O(1).

Count Subarrays With Fixed Bounds

Q: How do you identify the pattern for Count Subarrays With Fixed Bounds?

Look for key signals in the prompt: "count subarrays" indicates For each right end, count a block of good starts.; "minimum is exactly minK, maximum is exactly maxK" indicates "Exactly" again, but on two values at once. It splits into: no value outside the range (monotonic → window) + contains a minK and a maxK (last-seen index).; "values outside the range" indicates Walls. They reset the window: left edge = last wall + 1..

Hard·LeetCode #2444 Pro OnlyTricky / Edge Case

LeetCode

Problem Statement

You are given an integer array nums and two numbers minK and maxK.

A contiguous subarray is a fixed-bound subarray if its smallest value is exactly minK and its largest value is exactly maxK.

Count the fixed-bound subarrays.

This is a LeetCode Hard. It sits at position 4 of the Exactly K sub-pattern because the usual atMost − atMost trick does not fit it directly.

Input

An integer array nums and two integers minK and maxK.

Output

The number of subarrays whose minimum is minK and whose maximum is maxK. The count can be large, so it is returned as a 64-bit number.

Example 1

Input: nums = [1, 3, 5, 2, 7, 5], minK = 1, maxK = 5

Output: 2

The fixed-bound subarrays are [1,3,5] and [1,3,5,2]. Anything that includes the 7 has max 7, and [5] alone has min 5, not 1.

Example 2

Input: nums = [1, 1, 1, 1], minK = 1, maxK = 1

Output: 10

Every subarray has min 1 and max 1. There are 4·5/2 = 10 subarrays.

Constraints

• 2 ≤ nums.length ≤ 10^5
• 1 ≤ nums[i], minK, maxK ≤ 10^6
• The answer can exceed the int range — use a 64-bit type.

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“count subarrays”

→ For each right end, count a block of good starts.

“minimum is exactly minK, maximum is exactly maxK”

→ "Exactly" again, but on two values at once. It splits into: no value outside the range (monotonic → window) + contains a minK and a maxK (last-seen index).

“values outside the range”

→ Walls. They reset the window: left edge = last wall + 1.

Approach Complexity Ladder

Brute Force — try every startO(N²)O(1)

Fix each start, grow the end, track min and max

Optimal — last bad, last min, last maxO(N)O(1)

For each right, good starts are lastBad+1 … min(lastMin, lastMax)

Brute Force Intuition

For every start, move the end right while keeping the running minimum and maximum. If an out-of-range value shows up, stop — every longer subarray contains it too. Count one whenever min = minK and max = maxK.

Recognition rule for this sub-pattern:

"Exactly K" is not monotonic, so a window can't count it directly. Use exactly(K) = atMost(K) − atMost(K − 1).

Remember this · Sliding Window

Trigger

Contiguous subarray / substring + longest, shortest, maximum, count, or "of size K".

Think

Can I keep a valid range and move it, instead of checking every subarray from scratch?

Key question

When is my current window valid?

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