adjacent-increasing-subarrays-detection-ii

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Algorithms

Given an array <code>nums</code> of <code>n</code> integers, your task is to find the maximum value of <code>k</code> for which there exist two adjacent subarrays of length <code>k</code> each, such that both subarrays are strictly increasing. Specifically, check if there are two subarrays of length <code>k</code> starting at indices <code>a</code> and <code>b</code> (<code>a &lt; b</code>), where:

<ul>
	<li>Both subarrays <code>nums[a..a + k - 1]</code> and <code>nums[b..b + k - 1]</code> are strictly increasing.</li>
	<li>The subarrays must be adjacent, meaning <code>b = a + k</code>.</li>
</ul>

Return the maximum possible value of <code>k</code>.

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

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [2,5,7,8,9,2,3,4,3,1]

Output: 3

Explanation:

<ul>
	<li>The subarray starting at index 2 is <code>[7, 8, 9]</code>, which is strictly increasing.</li>
	<li>The subarray starting at index 5 is <code>[2, 3, 4]</code>, which is also strictly increasing.</li>
	<li>These two subarrays are adjacent, and 3 is the maximum possible value of <code>k</code> for which two such adjacent strictly increasing subarrays exist.</li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: nums = [1,2,3,4,4,4,4,5,6,7]

Output: 2

Explanation:

<ul>
	<li>The subarray starting at index 0 is <code>[1, 2]</code>, which is strictly increasing.</li>
	<li>The subarray starting at index 2 is <code>[3, 4]</code>, which is also strictly increasing.</li>
	<li>These two subarrays are adjacent, and 2 is the maximum possible value of <code>k</code> for which two such adjacent strictly increasing subarrays exist.</li>
</ul>
</div>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= nums.length &lt;= 2 * 105</code></li>
	<li><code>-109 &lt;= nums[i] &lt;= 109</code></li>
</ul>

maxIncreasingSubarrays

Adjacent Increasing Subarrays Detection II

Array

Binary Search

给你一个由 <code>n</code> 个整数组成的数组 <code>nums</code> ，请你找出 <code>k</code> 的 最大值，使得存在 两个 相邻 且长度为 <code>k</code> 的 严格递增 子数组。具体来说，需要检查是否存在从下标 <code>a</code> 和 <code>b</code> (<code>a &lt; b</code>) 开始的 两个 子数组，并满足下述全部条件：

<ul>
	<li>这两个子数组 <code>nums[a..a + k - 1]</code> 和 <code>nums[b..b + k - 1]</code> 都是 严格递增 的。</li>
	<li>这两个子数组必须是 相邻的，即 <code>b = a + k</code>。</li>
</ul>

返回 <code>k</code> 的 最大可能 值。

子数组 是数组中的一个连续 非空 的元素序列。

&nbsp;

示例 1：

<div class="example-block">
输入：nums = [2,5,7,8,9,2,3,4,3,1]

输出：3

解释：

<ul>
	<li>从下标 2 开始的子数组是 <code>[7, 8, 9]</code>，它是严格递增的。</li>
	<li>从下标 5 开始的子数组是 <code>[2, 3, 4]</code>，它也是严格递增的。</li>
	<li>这两个子数组是相邻的，因此 3 是满足题目条件的 最大 <code>k</code> 值。</li>
</ul>
</div>

示例 2：

<div class="example-block">
输入：nums = [1,2,3,4,4,4,4,5,6,7]

输出：2

解释：

<ul>
	<li>从下标 0 开始的子数组是 <code>[1, 2]</code>，它是严格递增的。</li>
	<li>从下标 2 开始的子数组是 <code>[3, 4]</code>，它也是严格递增的。</li>
	<li>这两个子数组是相邻的，因此 2 是满足题目条件的 最大 <code>k</code> 值。</li>
</ul>
</div>

&nbsp;

提示：

<ul>
	<li><code>2 &lt;= nums.length &lt;= 2 * 105</code></li>
	<li><code>-109 &lt;= nums[i] &lt;= 109</code></li>
</ul>