1. **Focus on the process, not the result**: Instead of trying to come up with a direct solution to find the final modified array, focus on understanding the process of replacing adjacent non-coprime numbers with their LCM. Break down the problem into smaller steps and analyze each step carefully.
2. **Use a loop to iterate through the array**: Since the process involves replacing adjacent non-coprime numbers, you'll need to iterate through the array multiple times. Use a loop to do this, and keep track of the changes made to the array in each iteration.
3. **Check for adjacent non-coprime numbers**: In each iteration, check if there are any adjacent non-coprime numbers in the array. You can do this by using the GCD function to check if the GCD of two adjacent numbers is greater than 1.
4. **Calculate the LCM**: If you find adjacent non-coprime numbers, calculate their LCM using the formula `lcm(a, b) = |a*b| / gcd(a, b)`. Replace the two numbers with their LCM in the array.
5. **Keep track of changes**: As you modify the array, keep track
Here are some hints to get you started:
**Hint 1:**
When initializing the `FoodRatings` class, consider using a data structure that can efficiently store and retrieve food items based on their ratings and cuisines. You might want to think about using a combination of data structures, such as a hashmap and a priority queue.
**Hint 2:**
When implementing the `changeRating` method, think about how you can update the rating of a specific food item without affecting the overall structure of the data. You might want to consider using a separate data structure to keep track of the rating changes.
**Hint 3:**
When implementing the `highestRated` method, think about how you can efficiently find the food item with the highest rating for a given cuisine. You might want to consider using a priority queue or a hashmap to store the food items by their ratings and cuisines.
**Hint 4:**
When there are multiple food items with the same highest rating, think about how you can break the tie by considering the lexicographically smaller name. You might want to consider using a custom comparator or a hashmap to store the food items by their ratings and cuisines.
**Hint 5:**
When implementing the `Food
**Hint 1:** Think about how you can efficiently store and manage the tasks for each user. You might consider using a data structure that allows you to quickly locate and update tasks for a specific user.
**Hint 2:** The `add`, `edit`, and `rmv` methods all operate on a specific task, so consider how you can use these methods to maintain a data structure that keeps track of tasks for each user.
**Hint 3:** The `execTop` method needs to find the task with the highest priority across all users and execute it. Think about how you can use your data structure to efficiently find the task with the highest priority.
**Hint 4:** When executing a task, you need to remove it from the system. Consider how you can use your data structure to keep track of which tasks have been executed and need to be removed.
**Hint 5:** The problem statement guarantees that `taskId` will be valid for all `add`, `edit`, and `rmv` methods. This means you don't need to worry about handling invalid `taskId`s.
**Hint 6:** Think about how you can use the `tasks` parameter in the constructor to initialize your data
**Hint 1:**
Start by designing a data structure to represent the spreadsheet. You can use a 2D array or a hash map to store the cell values. Consider using a separate data structure to store the cell references and their corresponding values.
**Hint 2:**
When implementing the `setCell` method, think about how you can efficiently update the value of a cell. You may want to consider using a hash map to store the cell references and their corresponding values.
**Hint 3:**
When implementing the `getValue` method, think about how you can evaluate a formula. You can break down the formula into smaller parts, such as parsing the formula to extract the cell references and values, and then evaluating the formula using a recursive or iterative approach.
**Hint 4:**
When implementing the `resetCell` method, think about how you can reset the value of a cell. You may want to consider using a hash map to store the cell references and their corresponding values, and then updating the value of the cell to 0.
**Hint 5:**
When designing the `getValue` method, consider handling the following edge cases:
* What happens if the formula references a cell
Here are some hints to help you tackle this challenge:
**Hint 1: Understand the requirements**
* The `Router` class needs to efficiently manage data packets with a fixed memory limit.
* Packets have three attributes: `source`, `destination`, and `timestamp`.
* The `addPacket` method adds a new packet, and if the memory limit is exceeded, the oldest packet is removed.
* The `forwardPacket` method returns the next packet in FIFO order and removes it from storage.
* The `getCount` method returns the number of packets with a specific destination and timestamp range.
**Hint 2: Choose a data structure**
* Consider using a combination of data structures to efficiently manage the packets.
* You might need a data structure to store the packets, and another to keep track of the oldest packet (for removal).
* Think about using a queue (e.g., a FIFO queue) to store the packets, as it will help with the `forwardPacket` method.
**Hint 3: Handle packet duplicates**
* When adding a new packet, check if a packet with the same `source`, `destination`, and `timestamp` already exists in the router.
* If a duplicate packet is found, return `false
Here are some hints to help you tackle this challenge:
**Hint 1: Understand the problem structure**
The problem involves managing a movie renting system with multiple shops. Each shop has a limited number of movies, and each movie has a unique ID. The system needs to support searching for movies, renting movies, dropping off rented movies, and generating a report of the currently rented movies.
**Hint 2: Break down the problem into smaller components**
To solve this problem, you'll need to break it down into smaller components. For example, you can create separate functions for:
* `search`: Find the cheapest 5 shops that have an unrented copy of a given movie.
* `rent`: Rent a movie from a given shop.
* `drop`: Drop off a previously rented movie at a given shop.
* `report`: Generate a report of the currently rented movies.
**Hint 3: Use data structures to store movie information**
You'll need to use a data structure to store information about each movie, such as its ID, the shops that have it, and the rental price. A hashmap or a dictionary could be a good choice for this.
**Hint 4: Implement the search function**
For the `search` function,
**Hint 1:** Start by thinking about how you can count the frequency of each element in the array. You can use a data structure like a hash map or a dictionary to store the frequency of each element.
**Hint 2:** Once you have the frequency of each element, think about how you can find the maximum frequency. You can use a variable to keep track of the maximum frequency and update it as you iterate through the frequency counts.
**Hint 3:** Now that you have the maximum frequency, think about how you can count the number of elements that have this maximum frequency. You can use the frequency counts to do this. For example, you can iterate through the frequency counts and count the number of elements that have a frequency equal to the maximum frequency.
**Hint 4:** Consider using a two-pointer approach to solve this problem. You can use one pointer to iterate through the frequency counts and another pointer to keep track of the number of elements that have the maximum frequency.
**Hint 5:** Think about how you can optimize your solution. For example, you can use a single pass through the array to count the frequency of each element, rather than using a two-pointer approach.
By following these hints
1. **Split the version strings into arrays of integers**: Think about how you can split the version strings into arrays of integers, where each integer represents a revision. You can use the dot (.) as a delimiter to split the string. This will make it easier to compare the revisions.
2. **Pad the shorter array with zeros**: Since the problem states that missing revision values should be treated as 0, you'll need to pad the shorter array with zeros to ensure both arrays have the same length. This will make it easier to compare the revisions.
3. **Compare the arrays of integers**: Once you have the arrays of integers, you can compare them directly. You can use a loop to iterate through the arrays and compare the integers. If you find a mismatch, you can return the appropriate result (-1, 1, or 0).
4. **Use a data structure to keep track of the comparison**: Consider using a data structure like a stack or a queue to keep track of the comparison. This can help you avoid writing nested if-else statements and make the code more readable.
5. **Think about edge cases**: Don't forget to test your code with edge cases, such as version strings
**Hint 1:** Think about how you would solve this problem manually. How would you convert a fraction to a decimal string? You might want to consider using long division or a similar approach.
**Hint 2:** Notice that the problem statement mentions "the fractional part is repeating, enclose the repeating part in parentheses." This suggests that you'll need to identify the repeating part of the decimal expansion. How might you do that?
**Hint 3:** Consider using a string to build up the decimal representation of the fraction. You could start with the whole part, then add the fractional part. When do you know when to stop adding digits to the fractional part?
**Hint 4:** Think about how you can use a data structure like a queue or a stack to keep track of the digits of the decimal expansion. This might help you identify the repeating part more easily.
**Hint 5:** Don't forget to handle the case where the denominator is 1 (i.e., the input is just a single integer). In this case, the output should be a simple string representation of the integer.
**Hint 6:** Consider using a loop to repeatedly divide the numerator by the denominator and add the remainder
**Hint 1:** Think about the problem as a dynamic programming problem. You need to find the minimum path sum from top to bottom, which means you need to consider the sum of the current cell and the minimum path sum of the cell above it.
**Hint 2:** Notice that the problem has a recursive structure. You can think of each cell as having two children: the cell to the left and the cell to the right. The minimum path sum of each cell is the sum of the current cell and the minimum path sum of one of its children.
**Hint 3:** To avoid using extra space, consider using a bottom-up approach. Start from the bottom row and work your way up. For each cell, calculate the minimum path sum by considering the sum of the current cell and the minimum path sum of one of its children.
**Hint 4:** Think about how you can use the triangle's structure to your advantage. Since each row has one more cell than the previous row, you can use the previous row's minimum path sums to calculate the current row's minimum path sums.
**Hint 5:** Consider using a 1D array to store the minimum path sums. You can use indices to