count-the-number-of-incremovable-subarrays-ii

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Algorithms

You are given a 0-indexed array of positive integers <code>nums</code>.

A subarray of <code>nums</code> is called incremovable if <code>nums</code> becomes strictly increasing on removing the subarray. For example, the subarray <code>[3, 4]</code> is an incremovable subarray of <code>[5, 3, 4, 6, 7]</code> because removing this subarray changes the array <code>[5, 3, 4, 6, 7]</code> to <code>[5, 6, 7]</code> which is strictly increasing.

Return the total number of incremovable subarrays of <code>nums</code>.

Note that an empty array is considered strictly increasing.

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

&nbsp;
Example 1:

<pre>
Input: nums = [1,2,3,4]
Output: 10
Explanation: The 10 incremovable subarrays are: [1], [2], [3], [4], [1,2], [2,3], [3,4], [1,2,3], [2,3,4], and [1,2,3,4], because on removing any one of these subarrays nums becomes strictly increasing. Note that you cannot select an empty subarray.
</pre>

Example 2:

<pre>
Input: nums = [6,5,7,8]
Output: 7
Explanation: The 7 incremovable subarrays are: [5], [6], [5,7], [6,5], [5,7,8], [6,5,7] and [6,5,7,8].
It can be shown that there are only 7 incremovable subarrays in nums.
</pre>

Example 3:

<pre>
Input: nums = [8,7,6,6]
Output: 3
Explanation: The 3 incremovable subarrays are: [8,7,6], [7,6,6], and [8,7,6,6]. Note that [8,7] is not an incremovable subarray because after removing [8,7] nums becomes [6,6], which is sorted in ascending order but not strictly increasing.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 109</code></li>
</ul>

incremovableSubarrayCount

Count the Number of Incremovable Subarrays II

Shortest Subarray to be Removed to Make Array Sorted

shortest-subarray-to-be-removed-to-make-array-sorted

删除最短的子数组使剩余数组有序

Array

Two Pointers

Binary Search

给你一个下标从 0&nbsp;开始的 正&nbsp;整数数组&nbsp;<code>nums</code>&nbsp;。

如果 <code>nums</code>&nbsp;的一个子数组满足：移除这个子数组后剩余元素 严格递增&nbsp;，那么我们称这个子数组为 移除递增&nbsp;子数组。比方说，<code>[5, 3, 4, 6, 7]</code>&nbsp;中的 <code>[3, 4]</code>&nbsp;是一个移除递增子数组，因为移除该子数组后，<code>[5, 3, 4, 6, 7]</code>&nbsp;变为&nbsp;<code>[5, 6, 7]</code>&nbsp;，是严格递增的。

请你返回 <code>nums</code>&nbsp;中 移除递增&nbsp;子数组的总数目。

注意&nbsp;，剩余元素为空的数组也视为是递增的。

子数组 指的是一个数组中一段连续的元素序列。

&nbsp;

示例 1：

<pre>
输入：nums = [1,2,3,4]
输出：10
解释：10 个移除递增子数组分别为：[1], [2], [3], [4], [1,2], [2,3], [3,4], [1,2,3], [2,3,4] 和 [1,2,3,4]。移除任意一个子数组后，剩余元素都是递增的。注意，空数组不是移除递增子数组。
</pre>

示例 2：

<pre>
输入：nums = [6,5,7,8]
输出：7
解释：7&nbsp;个移除递增子数组分别为：[5], [6], [5,7], [6,5], [5,7,8], [6,5,7] 和 [6,5,7,8] 。
nums 中只有这 7 个移除递增子数组。
</pre>

示例 3：

<pre>
输入：nums = [8,7,6,6]
输出：3
解释：3 个移除递增子数组分别为：[8,7,6], [7,6,6] 和 [8,7,6,6] 。注意 [8,7] 不是移除递增子数组因为移除 [8,7] 后 nums 变为 [6,6] ，它不是严格递增的。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 109</code></li>
</ul>