3409. Longest Subsequence With Decreasing Adjacent Difference

You are given an array of integers nums.

Your task is to find the length of the longest subsequence seq of nums, such that the absolute differences between consecutive elements form a non-increasing sequence of integers. In other words, for a subsequence seq0, seq1, seq2, …, seqm of nums, |seq1 - seq0| >= |seq2 - seq1| >= ... >= |seqm - seqm - 1|.

Return the length of such a subsequence.

A subsequence is an non-empty array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

3408. Design Task Manager

There is a task management system that allows users to manage their tasks, each associated with a priority. The system should efficiently handle adding, modifying, executing, and removing tasks.

Implement the TaskManager class:

• TaskManager(vector<vector<int>>& tasks) initializes the task manager with a list of user-task-priority triples. Each element in the input list is of the form [userId, taskId, priority], which adds a task to the specified user with the given priority.
• void add(int userId, int taskId, int priority) adds a task with the specified taskId and priority to the user with userId. It is guaranteed that taskId does not exist in the system.
• void edit(int taskId, int newPriority) updates the priority of the existing taskId to newPriority. It is guaranteed that taskId exists in the system.
• void rmv(int taskId) removes the task identified by taskId from the system. It is guaranteed that taskId exists in the system.
• int execTop() executes the task with the highest priority across all users. If there are multiple tasks with the same highest priority, execute the one with the highest taskId. After executing, the taskId is removed from the system. Return the userId associated with the executed task. If no tasks are available, return -1.

Note that a user may be assigned multiple tasks.

3407. Substring Matching Pattern

You are given a string s and a pattern string p, where p contains exactly one '*' character.

The '*' in p can be replaced with any sequence of zero or more characters.

Return true if p can be made a substring of s, and false otherwise.

A substring is a contiguous non-empty sequence of characters within a string.

F - Falling Bars

E - 11/22 Subsequence

3405. Count the Number of Arrays with K Matching Adjacent Elements

You are given three integers n, m, k. A good array arr of size n is defined as follows:

• Each element in arr is in the inclusive range [1, m].
• Exactly k indices i (where 1 <= i < n) satisfy the condition arr[i - 1] == arr[i].

Return the number of good arrays that can be formed.

Since the answer may be very large, return it modulo 109 + 7.

3404. Count Special Subsequences

You are given an array nums consisting of positive integers.

A special subsequence is defined as a subsequence of length 4, represented by indices (p, q, r, s), where p < q < r < s. This subsequence must satisfy the following conditions:

• nums[p] * nums[r] == nums[q] * nums[s]
• There must be at least one element between each pair of indices. In other words, q - p > 1, r - q > 1 and s - r > 1.

A subsequence is a sequence derived from the array by deleting zero or more elements without changing the order of the remaining elements.

Return the number of different special subsequences in nums.

3403. Find the Lexicographically Largest String From the Box I

You are given a string word, and an integer numFriends.

Alice is organizing a game for her numFriends friends. There are multiple rounds in the game, where in each round:

• word is split into numFriends non-empty strings, such that no previous round has had the exact same split.
• All the split words are put into a box.

Find the lexicographically largest string from the box after all the rounds are finished.

A string a is lexicographically smaller than a string b if in the first position where a and b differ, string a has a letter that appears earlier in the alphabet than the corresponding letter in b.
If the first min(a.length, b.length) characters do not differ, then the shorter string is the lexicographically smaller one.

3402. Minimum Operations to Make Columns Strictly Increasing

You are given a m x n matrix grid consisting of non-negative integers.

In one operation, you can increment the value of any grid[i][j] by 1.

Return the minimum number of operations needed to make all columns of grid strictly increasing.

3399. Smallest Substring With Identical Characters II

You are given a binary string s of length n and an integer numOps.

You are allowed to perform the following operation on s at most numOps times:

• Select any index i (where 0 <= i < n) and flip s[i]. If s[i] == '1', change s[i] to '0' and vice versa.

You need to minimize the length of the longest substring of s such that all the characters in the substring are identical.

Return the minimum length after the operations.

A substring is a contiguous non-empty sequence of characters within a string.