answer：Okay, so I need to develop an SQL query that finds the employee with the highest average yearly salary over the last three years from the "salary" table. Hmm, let me think about how to approach this.First, I should understand the structure of the "salary" table. I assume it has columns like employee_id, year, and salary. That makes sense because each entry would represent an employee's salary for a specific year.The goal is to calculate the average salary for each employee over the last three years. So, I need to filter the data to include only the records from the past three years. How do I determine what those years are? Well, if the current year is 2023, the last three years would be 2020, 2021, and 2022. But since the query should be dynamic, maybe I can use the current year minus two to get the starting year.Wait, but in SQL, how do I get the current year? I think in MySQL, it's YEAR(CURDATE()). So, the last three years would be from YEAR(CURDATE()) - 2 to YEAR(CURDATE()). That way, it automatically adjusts each year.Next, I need to group the salaries by employee_id so I can calculate the average for each employee. Using GROUP BY employee_id makes sense here.Then, I calculate the average salary for each employee over those three years using the AVG() function. So, AVG(salary) as average_salary.Now, I want the employee with the highest average salary. To get that, I can order the results in descending order of average_salary and limit the result to just the top one. So, ORDER BY average_salary DESC and LIMIT 1.Putting it all together, the query would select employee_id and the average salary, filter by the last three years, group by employee_id, order by average descending, and limit to one result.Wait, but what if there are multiple employees with the same highest average? The problem says "the employee," implying a single result, so maybe it's assumed there's a unique highest. If not, the query will return the first one in case of a tie.Also, I should ensure that the query only includes employees who have records for all three years. Otherwise, an employee with only two years might have a higher average but isn't consistent over three years. So, I need to add a HAVING clause to check that the count of years is exactly three. That way, only employees with all three years' data are considered.So, adding HAVING COUNT(year) = 3 ensures that we're only looking at employees who have salaries for each of the last three years.Putting it all together, the query should look something like:SELECT employee_id, AVG(salary) as average_salaryFROM salaryWHERE year >= YEAR(CURDATE()) - 2GROUP BY employee_idHAVING COUNT(year) = 3ORDER BY average_salary DESCLIMIT 1;I think that covers all the requirements. It filters the data to the last three years, groups by employee, calculates the average, ensures they have all three years, orders by the highest average, and returns the top employee.

answer：Okay, the user wants to make their SVG pulse or glow. I need to figure out how to achieve that effect. First, I remember that SVGs can use CSS animations. So, I should consider adding a CSS animation to the SVG elements. The two common effects are pulsing and glowing, so I'll need to decide which one to go with or maybe offer both options.Looking at the SVG provided, it's a complex shape with multiple paths. To apply an animation, I can target the entire SVG or specific parts. But since the user wants the whole SVG to pulse or glow, targeting the entire element makes sense.I think about how to create a pulsing effect. Using the `transform` property with `scale` can make the SVG expand and contract, creating a pulsing illusion. For a glow effect, I can use a `drop-shadow` filter that changes the blur radius over time.I should offer both options so the user can choose. I'll start by explaining the pulsing effect. I'll add a CSS class to the SVG with an animation that scales it up and down. Then, I'll do the same for the glow effect using a filter.I also need to make sure the animations are smooth. Using `animation-timing-function: ease-in-out` will help with that. I'll set a reasonable duration, like 1.5 seconds, and make it infinite so it keeps going.In the code, I'll modify the SVG by adding a `class="pulse"` and include the CSS within a `style` tag. Alternatively, I can provide the CSS separately. I'll make sure to explain each step so the user understands how it works.Finally, I'll present both solutions clearly, showing how to implement each effect and offering to adjust parameters if needed. This way, the user can pick the effect they prefer or tweak it further.

answer：Okay, I have this problem to solve: Cheapest Flights Within K Stops with Time Constraints. Hmm, let's see what it's about. So, there are n cities connected by m flights. Each flight has a source u, destination v, a price w, and takes t time. I need to find the cheapest price from the starting city src to the destination dst, but with two constraints: up to k stops and the total time must be within T. If no such route exists, I return -1.Let me think about the examples to understand better. In the first example, n is 3, and the edges are given. The src is 0, dst is 2, k is 1, and T is 2. The output is 200. So, the path is 0->1->2, which costs 100+100=200 and takes 1+1=2 time. That's within the constraints. The other option is 0->2 directly, which costs 500 and takes 2 time, but since k is 1, that's allowed as it's 0 stops, but the price is higher. So, the first path is better.In the second example, k is 0, so the only option is the direct flight, which costs 500 and takes 2 time. So, that's the answer.So, the problem is to find the minimum cost path from src to dst with at most k stops and total time <= T.How do I approach this? Well, it's a variation of the shortest path problem but with two constraints: the number of stops and the total time. So, I need to track both the cost and the time as I traverse the graph.I remember that for the standard problem of finding the cheapest flight with up to k stops, people often use BFS with a priority queue, but considering the number of stops. But here, we have an additional constraint on time. So, I need to model this in a way that keeps track of both the cost and the time.Wait, maybe a dynamic programming approach would work here. Let's think about it. For each city, I can keep track of the minimum cost to reach it with a certain number of stops and the total time taken. But since the number of stops can vary, and the time can vary, this might get a bit complex.Alternatively, perhaps a modified Dijkstra's algorithm could be used. Dijkstra's is good for finding the shortest path in terms of cost, but here we have two constraints: the number of stops and the time. So, each state in the priority queue would need to include the current city, the number of stops taken so far, the total cost, and the total time. Then, when considering the next flight, we can check if adding it would exceed the k stops or the T time.But how do we manage the states efficiently? Because for each city, there might be multiple ways to reach it with different numbers of stops and different times and costs. We need to keep track of the minimum cost for each (city, stops, time) combination, but that's a lot of states.Wait, perhaps we can model it as a state (current city, number of stops used, total time so far). For each state, we track the minimum cost to reach it. Then, when we process a state, we can explore all possible outgoing flights, updating the stops, time, and cost accordingly.But the problem is that the number of possible states could be quite large. For example, n is up to 100, k is up to 99, and T is up to 100*100=10,000. So, the state space is 100 * 100 * 10,000 = 100,000,000. That's a lot, but perhaps manageable with some optimizations.Alternatively, maybe we can optimize by keeping for each city and number of stops, the minimum time and cost. Wait, but that might not be sufficient because even if you have a higher cost but lower time, it might allow for better paths in the future.Hmm, perhaps the way to go is to use a priority queue where each element is a tuple of (current cost, current city, number of stops, total time). The priority is the current cost, so we always process the cheapest path first. For each state, when we process it, we can explore all adjacent flights. For each flight, we calculate the new number of stops (stops + 1), the new total time (time + flight time), and the new cost (cost + flight price). If the new stops are <= k and the new time <= T, then we can consider adding this new state to the queue.But wait, we also need to make sure that we don't process the same state multiple times unnecessarily. So, for each city, and for each possible number of stops, we can keep track of the minimum time and cost. If a new state arrives at a city with the same number of stops but a higher cost and higher time, it's not useful, so we can skip it.Wait, but how to manage that. For example, for a given city and number of stops, if a new state has a higher cost than a previously recorded state, but a lower time, it might still be useful because it could lead to a better overall path. So, we can't just ignore it based on cost alone.This seems complicated. Maybe a better approach is to model this as a state where for each city, we track the minimum cost for each possible number of stops and time. But that might be too memory-intensive.Alternatively, perhaps we can use a BFS approach with a priority queue, but for each state, we only keep track of the minimum cost for a given (city, stops, time). Wait, but that's not straightforward.Let me think differently. The problem is similar to the standard BFS where we track the number of stops, but with an added time constraint. So, perhaps for each node, we can keep a 2D array: dp[stops][time] = min_cost. But that's a lot of memory, especially since time can be up to 100*100=10,000.Wait, but for each node, the maximum number of stops is k, which is up to 99. So, for each node, we can have a 2D array of size (k+1) x (T_max), where T_max is up to 10,000. That's 100 * 100 * 10,000 = 100,000,000 entries. That's a lot, but perhaps manageable with some optimizations.Wait, but for each node, the maximum time we can have is T. So, for each node, the time can't exceed T. So, for each node, the time dimension is up to T, which is up to 10,000. So, for each node, the array is (k+1) x T.Hmm, but 100 nodes * 100 stops * 10,000 time = 100,000,000 entries. That's a lot, but perhaps manageable in Python with some optimizations.So, the plan is:1. Initialize a 3D array (or a list of 2D arrays) for each city, where dp[stops][time] represents the minimum cost to reach that city with exactly 'stops' stops and 'time' time.2. For the starting city src, the initial state is 0 stops, 0 time, and 0 cost. So, dp[0][0] = 0.3. For all other cities, the initial cost is infinity.4. Use a priority queue (like Dijkstra's) to process the states in order of increasing cost. Each state is (current_cost, current_city, stops_so_far, time_so_far).5. For each state, if current_city is dst, check if the time_so_far is <= T and stops_so_far <=k. If so, update the answer if this is the minimum cost found so far.6. For each flight from current_city to next_city, calculate new_stops = stops_so_far + 1, new_time = time_so_far + flight_time, new_cost = current_cost + flight_price.7. If new_stops <=k and new_time <= T, and if the new_cost is less than the current recorded cost for (next_city, new_stops, new_time), then update the dp and add the new state to the priority queue.Wait, but how do we manage the dp array? Because for each next_city, new_stops, new_time, we need to check if the new_cost is better than any existing cost for that state.Alternatively, perhaps for each city, we can have a 2D array where for each possible number of stops (up to k), we track the minimum time and cost. But I'm not sure.Alternatively, perhaps for each state (city, stops), we track the minimum time and cost. So, for each (city, stops), we can have the minimum time and cost. Then, when considering a flight, if the new_time is within T, and the new_stops is within k, we can update the state.Wait, perhaps another approach is to model the state as (current_city, stops_so_far, time_so_far), and for each such state, track the minimum cost. Then, when processing a state, if the cost is higher than a previously recorded cost for the same state, we can skip processing it.So, the steps would be:- Initialize a priority queue with the starting state: (0, src, 0 stops, 0 time).- For each state in the queue, extract the one with the minimum cost.- If current_city is dst, check if time_so_far <= T and stops_so_far <=k. If yes, update the answer if this is the cheapest so far.- For each flight from current_city to next_city: - new_stops = stops_so_far + 1 - new_time = time_so_far + flight_time - new_cost = current_cost + flight_price - If new_stops >k or new_time > T: skip. - Check if for the state (next_city, new_stops, new_time), the new_cost is less than the current known cost. If yes, update and add to the priority queue.But how do we track the minimum cost for each (city, stops, time)? We can have a dictionary or a 3D array where for each city, stops, time, we store the minimum cost.Wait, but with n=100, k=100, and T=10,000, the 3D array would be 100 * 100 * 10,000 = 100,000,000 entries. That's a lot, but perhaps manageable.In Python, initializing a 3D list of that size might be memory-intensive, but perhaps we can use a dictionary for each city and stops, mapping time to cost. But that might complicate things.Alternatively, for each city, we can have a 2D array where for each stops, we track the minimum time and cost. Wait, but that might not capture all possibilities because for a given stops, there could be multiple times with different costs.Hmm, perhaps the priority queue approach is manageable. Let's outline the steps:1. Create a priority queue (min-heap) that orders states by their current cost. Each state is a tuple (current_cost, current_city, stops, time).2. Initialize the queue with the starting state: cost 0, city src, stops 0, time 0.3. Create a 3D array (or a dictionary) to keep track of the minimum cost for each (city, stops, time). Initialize all to infinity except for (src, 0, 0) which is 0.4. While the queue is not empty: a. Extract the state with the minimum cost. b. If current_city is dst, check if time <= T and stops <=k. If yes, update the result if this is the minimum cost found so far. c. For each flight from current_city to next_city: i. Calculate new_stops = stops + 1. ii. Calculate new_time = time + flight_time. iii. Calculate new_cost = current_cost + flight_price. iv. If new_stops >k or new_time > T: skip. v. Check if new_cost is less than the recorded cost for (next_city, new_stops, new_time). If yes, update and add to the queue.5. After processing all possible states, if the minimum cost to reach dst is found, return it. Else, return -1.But wait, the problem is that for each state, we might have multiple entries in the priority queue with different costs. So, when we extract a state, if the cost is higher than the recorded minimum for that state, we can skip processing it.Yes, that's an important optimization. So, in the code, when we extract a state (cost, city, stops, time), we first check if the recorded cost for (city, stops, time) is less than the current cost. If it is, we skip processing this state.This way, we avoid processing outdated and more expensive paths.Now, how to represent the 3D array? Since n is up to 100, k up to 99, and T up to 10,000, perhaps using a list of lists of dictionaries. For each city, a list of stops, and for each stop, a dictionary mapping time to cost.But in Python, initializing such a structure might be a bit involved. Alternatively, for each city, we can have a list of (stops, time) pairs, each with their minimum cost.Wait, perhaps a better way is to represent it as a dictionary where the key is (city, stops, time), and the value is the minimum cost. But for efficiency, perhaps using a list of lists of dictionaries is better.Alternatively, for each city, we can have a list of size k+1, and each element is a dictionary mapping time to the minimum cost for that number of stops.So, for example, for city u, stops s, time t, the cost is stored in dp[u][s][t].But in Python, initializing this as a list of lists of dictionaries would be something like:dp = [ [ {} for _ in range(k+1) ] for _ in range(n) ]But for each city, for each stop, the dictionary starts empty. Then, when we process a state, we check if the time is in the dictionary for that stop and city. If not, or if the new cost is lower, we update it.This approach could be memory-efficient because for each city and stop, only the times that are reachable are stored.So, the steps in code would be:- Read the input: n, edges, src, dst, k, T.- Build the adjacency list for the flights. Each flight is from u to v, with price w and time t.- Initialize the dp structure: a list of n elements, each is a list of k+1 elements, each is a dictionary.- For each city u in 0..n-1: for s in 0..k: dp[u][s] is a dictionary mapping time to cost. Initially, all are empty except for dp[src][0][0] = 0.- Initialize the priority queue with (0, src, 0, 0).- result = infinity- while queue not empty: extract (current_cost, u, s, t) from the queue. if u is dst: if t <= T and s <=k: if current_cost < result: result = current_cost if current_cost > dp[u][s].get(t, infinity): continue for each flight from u to v: new_s = s + 1 new_t = t + flight_time new_cost = current_cost + flight_price if new_s >k or new_t > T: continue if new_cost < dp[v][new_s].get(new_t, infinity): dp[v][new_s][new_t] = new_cost heappush(queue, (new_cost, v, new_s, new_t))- After processing all, if result is still infinity, return -1 else return result.Wait, but in the initial state, dp[src][0][0] is 0. So, when we process it, we check if src is dst. If so, we can return 0 if T is >=0 and k >=0.But in the code, the initial state is (0, src, 0, 0). So, if src == dst, then the cost is 0, time is 0, which is within T and k. So, that's handled.But what about when the flight is directly from src to dst with 0 stops? Like in example 2.Yes, because in that case, the initial state is processed, and since src is dst, it's considered.Wait, but in the code, the initial state is (0, src, 0, 0). So, when src == dst, the code will immediately check and update the result.But in the code, after extracting the state, it first checks if u is dst. So, that's correct.Now, let's test this approach against the examples.Example 1:n=3, edges=[[0,1,100,1],[1,2,100,1],[0,2,500,2]]src=0, dst=2, k=1, T=2.The initial state is (0,0,0,0). Since 0 is not dst, proceed.Flights from 0: to 1 (cost 100, time 1), and to 2 (cost 500, time 2).So, for flight to 1: new_s=1, new_t=1, new_cost=100.Check if 100 < dp[1][1][1] (which is infinity). So, add (100,1,1,1) to the queue.For flight to 2: new_s=0, new_t=2, new_cost=500.Check if 500 < dp[2][0][2] (infinity). So, add (500,2,0,2) to the queue.Now, the queue has (100,1,1,1) and (500,2,0,2). The next state to process is (100,1,1,1).Now, current_city is 1. It's not dst. So, process its flights: to 2.Flight to 2: new_s=2, which is >k=1. So, skip.So, no new states added.Next, process (500,2,0,2). current_city is 2, which is dst. Check if t=2 <= T=2 and s=0 <=k=1. Yes. So, update result to 500.But wait, is there a cheaper path? Let's see.Wait, after processing (100,1,1,1), there are no more flights from 1 except to 2, which is beyond k=1.So, the queue now has nothing else. So, the result is 500, but that's not correct because the correct answer is 200.Wait, what's wrong here.Ah, because in the code, when processing (100,1,1,1), it's not the destination, so it processes the flight to 2, which would be new_s=2, which is beyond k=1. So, it's skipped.But wait, the flight from 1 to 2 is allowed because the total stops would be 1 (from 0->1 is 1 stop, then 1->2 is another stop, making total stops 2, which is more than k=1. So, that's why it's skipped.But in the example, the correct path is 0->1->2, which is 2 stops, but k is 1. Wait, wait, no. Wait, the number of stops is the number of intermediate cities. So, 0->1 is 1 stop, 1->2 is another stop, making total stops 2. But k is 1, which is the maximum allowed. So, that path is not allowed.Wait, wait, the problem says up to k stops. So, in the first example, k=1. So, the path 0->1->2 has 1 stop (the flight from 0 to 1 is the first stop, then 1 to 2 is the second stop? Or is it the number of flights minus one?Wait, I think the number of stops is the number of intermediate cities. So, 0->1->2 has 1 stop (city 1). So, the number of stops is 1, which is <=k=1.Wait, that's a crucial point. So, the number of stops is the number of flights minus one. So, 0->1 is 1 flight, 0 stops. 0->1->2 is 2 flights, 1 stop.So, in the code, the new_s is s+1, which is correct.So, in the first example, the path 0->1->2 has s=1, which is <=k=1.So, in the code, when processing (100,1,1,1), the flight to 2 would be new_s=2, which is >k=1. So, it's skipped. But that's incorrect because the number of stops is 1 (the flight from 1 to 2 is the second flight, but the number of stops is 1 (only city 1 is a stop)).Wait, no. The number of stops is the number of intermediate cities. So, 0->1 is 0 stops, 0->1->2 is 1 stop. So, in the code, when processing the flight from 1 to 2, the new_s is s+1, which is 1+1=2. But k is 1, so it's allowed? No, because 2>1.Wait, that's the problem. So, the code is incorrectly counting the number of stops.Ah, I see. So, the issue is that the code is incrementing the stops by 1 for each flight, which counts the number of flights, not the number of stops. So, the number of stops is the number of flights minus one.So, in the code, for each flight, the number of stops increases by 1. So, for the initial state, s=0, which is 0 flights. Then, each flight adds 1 to s. So, the number of stops is s.Wait, no. Because the initial state is s=0, which represents 0 stops. Then, each flight increases s by 1, which represents the number of stops. So, for the flight 0->1, s becomes 1, which is 1 stop. Then, flight 1->2 would make s=2, which is 2 stops, which is more than k=1.But in the example, the correct path is 0->1->2, which is 1 stop. So, the code is counting the number of flights as the number of stops, which is incorrect.So, the mistake is in how the stops are being counted. The number of stops is the number of intermediate cities, which is the number of flights minus one.So, the code should track the number of flights, and the number of stops is flights -1.But in the code, the variable 's' is the number of stops, so for each flight, s increases by 1. So, for the initial state, s=0 (0 stops, 0 flights). Then, each flight adds 1 to s, which is the number of stops.Wait, no. Because the initial state is s=0, which is 0 stops. Then, each flight increases s by 1, so the number of stops is s.But in reality, the number of stops is the number of flights minus one. So, for 0->1->2, it's 2 flights, 1 stop.So, the code is incorrectly counting s as the number of flights, not the number of stops.So, the code needs to be adjusted. Instead of s being the number of stops, it should be the number of flights. Or, perhaps, the initial state should have s=0 (0 flights), and each flight increases s by 1. Then, the number of stops is s-1.Wait, that makes more sense. Because the number of stops is the number of flights minus one.So, in the code, the variable 's' should represent the number of flights taken so far. Then, the number of stops is s-1.So, when processing a flight, new_s = s + 1. The number of stops is new_s -1.So, the condition is: new_s -1 <=k.So, in the code, the condition should be:if (new_s -1) >k or new_time > T: skip.Wait, that's a crucial correction.So, in the code, for each flight, new_s is s +1. Then, the number of stops is new_s -1. So, the condition is:if (new_s -1) >k or new_time > T: skip.So, in the example:Initial state: s=0 (0 flights, 0 stops).Flight 0->1: new_s=1 (1 flight, 0 stops). So, 0 <=k=1.Flight 1->2: new_s=2 (2 flights, 1 stop). So, 1 <=k=1.So, in the code, the condition should be:if (new_s -1) >k or new_time > T: skip.So, the code needs to be adjusted to reflect this.So, the steps are:For each flight, new_s = s +1.if (new_s -1) >k or new_time > T: skip.Else, proceed.In the first example, when processing the flight from 1 to 2:new_s = 1+1=2.new_s -1 =1 <=k=1.new_time =1+1=2 <=T=2.So, this flight is allowed.So, the code would add the state (200, 2, 2, 2) to the queue.Then, when processing this state, since current_city is dst, it's considered. The cost is 200, which is better than the 500.So, the result is updated to 200.So, the code needs to be modified to account for the correct number of stops.So, in the code:When processing a flight, new_s = s +1.if (new_s -1) >k: skip.Similarly, the initial state is s=0 (0 flights, 0 stops).So, the code should be adjusted as follows:In the code, the condition is:if (new_s -1) > k or new_time > T: continue.So, in the code:for each flight from u to v: new_s = s +1 new_t = t + flight_time new_cost = current_cost + flight_price if (new_s -1) >k or new_t > T: continue if new_cost < dp[v][new_s].get(new_t, infinity): dp[v][new_s][new_t] = new_cost heappush(queue, (new_cost, v, new_s, new_t))So, that's the correction.Now, let's see how this affects the first example.Initial state: (0,0,0,0). s=0.Flight 0->1: new_s=1, new_s-1=0 <=k=1.So, add (100,1,1,1) to the queue.Flight 0->2: new_s=1, new_s-1=0 <=k=1. So, add (500,2,1,2) to the queue.Now, the queue has (100,1,1,1) and (500,2,1,2).Processing (100,1,1,1):current_city is 1, not dst.Flights from 1: to 2.new_s=2, new_s-1=1 <=k=1.new_t=1+1=2 <=T=2.new_cost=200.So, add (200,2,2,2) to the queue.Then, process (500,2,1,2):current_city is 2, which is dst.s=1, new_s-1=0 <=k=1.t=2 <=T=2.So, update result to 500.Then, process (200,2,2,2):current_city is 2.s=2, new_s-1=1 <=k=1.t=2 <=T=2.So, update result to 200.So, the correct answer is 200.So, the code now correctly handles the number of stops.Another test case: example 2.n=3, edges same as before.src=0, dst=2, k=0, T=2.So, the initial state is (0,0,0,0).Flights from 0:0->1: new_s=1, new_s-1=0 <=k=0? No, because 0 is allowed. Wait, k=0.Wait, new_s-1 =0, which is <=k=0. So, allowed.Wait, but k=0 means the maximum number of stops is 0. So, the number of flights can be 1 (since stops = flights -1).So, for k=0, the maximum number of flights is 1.So, in the initial state, s=0.Flight 0->1: new_s=1, new_s-1=0 <=k=0. So, allowed.Flight 0->2: new_s=1, new_s-1=0 <=k=0. So, allowed.So, the code would process both.But in the example, the correct answer is 500, which is the direct flight.So, in the code:After processing (0,0,0,0), it adds (100,1,1,1) and (500,2,1,2).Then, the next state is (100,1,1,1). current_city is 1, not dst.Flights from 1: to 2.new_s=2, new_s-1=1 >k=0. So, skip.So, no new states added.Then, process (500,2,1,2). current_city is dst.s=1, new_s-1=0 <=k=0. So, allowed.t=2 <=T=2.So, update result to 500.So, the code returns 500, which is correct.So, the correction in the code is crucial.Now, the code needs to be written with this correction.Another thing to consider is that the priority queue can have multiple entries for the same (city, s, t) with different costs. So, when a state is extracted from the queue, we need to check if the current cost is the minimum known for that state. If not, we skip processing it.So, in the code, after extracting (current_cost, u, s, t), we check if current_cost is greater than dp[u][s].get(t, infinity). If yes, skip.This is important because the priority queue can have older, more expensive paths that are no longer relevant.So, the code outline is:- Read input.- Build adjacency list.- Initialize dp as a list of lists of dictionaries.- Initialize the priority queue.- Process each state in the queue, updating dp and adding new states as needed.- Keep track of the minimum cost to reach dst.Now, let's think about the data structures.In Python, for the adjacency list, we can represent it as a list of lists. Each index represents a city, and each element is a list of tuples (v, w, t), representing flights from u to v with price w and time t.For the dp, since n is up to 100, k up to 99, and T up to 10,000, using a list of lists of dictionaries is manageable.So, in code:import heapqn = ... edges = ... src = ... dst = ... k = ... T = ... # Build adjacency listadj = [[] for _ in range(n)]for u, v, w, t in edges: adj[u].append( (v, w, t) )# Initialize dpINF = float('inf')dp = [ [ dict() for _ in range(k+2) ] for _ in range(n) ]# dp[u][s][t] = min_costfor u in range(n): for s in range(k+2): dp[u][s] = dict()dp[src][0][0] = 0heap = []heapq.heappush(heap, (0, src, 0, 0))result = INFwhile heap: current_cost, u, s, t = heapq.heappop(heap) if u == dst: if (s-1) <=k and t <= T: if current_cost < result: result = current_cost # Check if current state is outdated if current_cost > dp[u][s].get(t, INF): continue for flight in adj[u]: v, w, flight_t = flight new_s = s + 1 new_t = t + flight_t new_cost = current_cost + w # Check constraints if (new_s -1) > k or new_t > T: continue # Check if this state is better than existing if new_cost < dp[v][new_s].get(new_t, INF): dp[v][new_s][new_t] = new_cost heapq.heappush(heap, (new_cost, v, new_s, new_t))if result != INF: print(result)else: print(-1)Wait, but in the code, the initial state is (0, src, 0, 0). So, s=0, which is 0 flights, 0 stops.When processing flights, new_s is s+1, which is 1 flight, 0 stops.So, the condition is (new_s -1) <=k.Yes.But wait, in the code, the condition is:if (new_s -1) >k or new_t > T: continue.Which is correct.So, this should handle the cases correctly.Now, let's test this code with the examples.In example 1:After processing the initial state, the queue has (100,1,1,1) and (500,2,1,2).Processing (100,1,1,1):Flights to 2: new_s=2, new_s-1=1 <=k=1.new_t=2 <=T=2.So, new_cost=200.dp[2][2][2] =200.Add to queue.Processing (500,2,1,2):u is dst, s=1, new_s-1=0 <=k=1.t=2 <=T=2.So, result is 500.Then, process (200,2,2,2):u is dst, s=2, new_s-1=1 <=k=1.t=2 <=T=2.So, result is updated to 200.So, correct.In example 2:After processing initial state, queue has (100,1,1,1) and (500,2,1,2).Processing (100,1,1,1):Flights to 2: new_s=2, new_s-1=1 >k=0. So, skip.Processing (500,2,1,2):u is dst, s=1, new_s-1=0 <=k=0.t=2 <=T=2.So, result is 500.So, correct.Another test case: what if there are multiple paths with varying stops and times.For example, n=2, edges=[[0,1,100,5], [0,1,200,3]].src=0, dst=1, k=0, T=4.So, the direct flight with time 3 is allowed. So, the cost is 200.Another flight has time 5, which is over T=4.So, the code should return 200.Let's see.Initial state: (0,0,0,0).Flights:0->1 (100,5): new_s=1, new_s-1=0 <=k=0.new_t=5 >T=4. So, skip.0->1 (200,3): new_s=1, new_s-1=0 <=k=0.new_t=3 <=4.So, add (200,1,1,3) to queue.Processing (200,1,1,3):u is dst.s=1, new_s-1=0 <=k=0.t=3 <=4.So, result is 200.So, correct.Another test case: what if a flight's time is exactly T.Yes, it's allowed.So, the code should handle that.Another edge case: src == dst.In this case, the initial state is (0, src, 0, 0). Since src == dst, the code will immediately check and set result=0, provided that s-1 <=k and t <=T.But s=0, s-1 =-1, which is <=k (since k is >=0). And t=0 <=T.So, the code returns 0.Another edge case: no flights.If src != dst, then no path exists. So, return -1.So, the code should handle that.Now, considering the constraints:n is up to 100, k up to 99, T up to 10,000.The code's time complexity depends on the number of states processed. Each state is (u, s, t), with u up to 100, s up to k+1=100, t up to T=10,000.So, the maximum number of states is 100 * 100 * 10,000 = 100,000,000. But in practice, it's much less because not all combinations are reachable.But in Python, with a priority queue, this might be manageable, but could be slow for large inputs.But given the constraints, it's acceptable.So, the code should handle all cases correctly.

answer：Okay, so I'm trying to understand this question about resolution theorem proving and its attributes. The question mentions three main attributes: soundness, completeness, and succinctness. I need to figure out which combination of these accurately reflects the essence of resolution theorem proving.First, let me recall what each of these terms means in the context of logic and theorem proving.Soundness: This means that if a theorem prover proves something, it's actually true. In other words, it doesn't produce false positives. So, for resolution theorem proving, if it proves that a formula is unsatisfiable, then that formula is indeed unsatisfiable. This is important because it prevents the prover from incorrectly declaring something as unsatisfiable when it's actually satisfiable.Completeness: This means that if something is true (or in this case, unsatisfiable), the theorem prover will eventually find a proof for it. So, resolution is complete if every unsatisfiable formula has a resolution proof. That means there are no cases where the formula is unsatisfiable, but the prover can't find a proof. This is crucial because it ensures that the prover doesn't miss any valid proofs.Succinctness: This refers to the length of the proof. If a formula has a resolution proof, then the length of that proof is polynomial in relation to the original formula. This is about efficiency—ensuring that the proofs aren't excessively long, which is important for practical applications because longer proofs take more time and resources to compute.Now, the question is asking which combination of these attributes accurately mirrors the essence of resolution theorem proving. So, I need to think about whether all three attributes are correct or if one of them isn't.I remember that resolution is both sound and complete for propositional logic. That means it will correctly identify all unsatisfiable formulas and nothing else. So, soundness and completeness are definitely attributes of resolution theorem proving.But what about succinctness? I think that's a bit trickier. Resolution can sometimes produce proofs that are exponentially long in the worst case, even if the formula is unsatisfiable. However, the question mentions that succinctness offers a proof whose length is polynomial in relation to the original expression if it possesses a resolution proof. Wait, that might not be entirely accurate because while there are cases where resolution proofs are polynomial, in general, resolution isn't always succinct. There are formulas where the shortest resolution proof is exponential in size relative to the formula.So, does resolution theorem proving guarantee a polynomial-length proof whenever a resolution proof exists? Or is that a different property? I think it's more that resolution can sometimes be succinct, but it's not guaranteed. The succinctness here might be referring to the fact that if a resolution proof exists, it's possible to have a proof that's polynomial in size, but in practice, it might not always be the case.Wait, maybe I'm conflating resolution with other proof systems. Some proof systems are known for their succinctness, like cutting planes or Frege systems, but resolution is not necessarily known for that. In fact, resolution is often used as a base system, and other systems are built on top of it to improve succinctness.So, putting it all together, resolution is sound and complete, but it's not necessarily always succinct. Therefore, the combination of soundness and completeness accurately mirrors the essence of resolution theorem proving, while succinctness might not always hold.But the question says, "if it possesses a resolution proof, succinctness offers a proof whose length is polynomial in relation to the original expression." So, if a resolution proof exists, then there exists a polynomial-length proof. Is that true? I think that's not necessarily the case because the existence of a resolution proof doesn't guarantee that it's polynomial in size. It could still be exponential.Therefore, succinctness as described might not be an accurate attribute of resolution theorem proving in general. So, the correct combination would be soundness and completeness.Wait, but I'm a bit confused because I remember that resolution is not always succinct, but it's sound and complete. So, the answer should be that soundness and completeness accurately mirror the essence, but succinctness isn't guaranteed.But the question is phrased as which amalgamation of these attributes accurately mirrors the essence. So, it's not saying that all three are correct, but which combination is accurate.So, the correct answer would be that resolution is sound and complete, but not necessarily succinct. Therefore, the combination of soundness and completeness is accurate, while succinctness isn't always a given.Wait, but the question mentions that succinctness offers a proof whose length is polynomial in relation to the original expression if it possesses a resolution proof. So, perhaps in the context of the question, they are considering that if a resolution proof exists, then it can be succinct. But in reality, that's not always the case. So, maybe the question is trying to say that succinctness is an attribute, but in reality, it's not always true.Therefore, the correct answer is that resolution is sound and complete, but not necessarily succinct. So, the combination of soundness and completeness accurately mirrors the essence, while succinctness isn't always present.But I'm not entirely sure. Maybe I should double-check.Looking up, resolution is indeed sound and complete. However, the size of resolution proofs can be exponential in the worst case. So, succinctness isn't guaranteed. Therefore, the correct combination is soundness and completeness.

answer：Okay, I need to edit the given Python code to calculate the standard deviation, median, mode, and interquartile range (IQR) of a list of numbers. Let me think about how to approach each part step by step.First, the standard deviation. I remember that standard deviation measures the spread of the data. To calculate it, I need to find the mean of the list, then for each number, subtract the mean and square the result. The average of these squared differences is the variance, and the square root of the variance is the standard deviation. I should make sure to handle cases where the list is empty or has only one element, returning 0 in those cases to avoid division by zero errors.Next, the median. The median is the middle value when the data is ordered. If the list has an odd number of elements, it's the middle one. If even, it's the average of the two middle numbers. I'll need to sort the list first. Again, handle empty or single-element lists by returning 0 or the single element, respectively.For the mode, it's the most frequently occurring number. If all numbers appear the same number of times, there's no mode, so return None. If there are multiple modes (like in a tie), return all of them. I'll use a dictionary to count frequencies and then find the maximum frequency. Then collect all numbers that have this maximum frequency.The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). To find Q1 and Q3, I need to split the sorted data into two halves. For Q1, it's the median of the first half, and for Q3, the median of the second half. I'll write a helper function to find the median of a sublist. This function will handle both odd and even lengths, similar to the main median function.I should also consider edge cases throughout. For example, if the list is empty, all functions should return 0 or handle it gracefully. If the list has only one element, the standard deviation is 0, the median is that element, and there's no mode. For the IQR, if the list has less than two elements, return 0.Let me outline the steps for each function:1. **Standard Deviation**: - Check if the list is empty or has one element: return 0. - Calculate the mean. - Compute the squared differences from the mean. - Find the average of these squared differences (variance). - Take the square root of the variance.2. **Median**: - Sort the list. - Check the length: if even, average the two middle numbers; if odd, take the middle one.3. **Mode**: - Count the frequency of each number. - Find the maximum frequency. - Collect all numbers with this frequency. - If all frequencies are 1, return None.4. **IQR**: - Sort the list. - Find Q1 as the median of the first half. - Find Q3 as the median of the second half. - Subtract Q1 from Q3.I'll also need to handle cases where the list has repeated modes, ensuring all modes are returned in a list.Now, let me think about the helper functions. The median function can be reused for Q1 and Q3. So, I'll create a helper function, maybe called `get_median`, which takes a list and returns its median.Testing each function with sample data is important. For example, for the mode, a list like [1, 2, 2, 3, 3] should return [2, 3]. For the IQR, a list like [1, 2, 3, 4, 5, 6, 7, 8] should have Q1=2.5 and Q3=6.5, so IQR=4.I should also consider performance, but since the functions are straightforward and the input size isn't specified, it's probably acceptable.Putting it all together, I'll structure the code with each function handling its part, ensuring that edge cases are properly addressed to avoid errors.

answer：Alright, I need to help the user implement a CSS code for a button with specific requirements. Let me break down what they're asking for.First, the button needs rounded corners with a 3-pixel radius. I know that's done using the border-radius property. So I'll set border-radius: 3px; in the button's style.Next, they want a hover effect that changes the color and increases the radius to 5 pixels. So I'll use the :hover pseudo-class. I'll change the background-color and border-radius properties there. I should choose a different color, maybe from a standard palette, so I'll pick blue for the hover state.They also mentioned a transition effect when hovering. Transitions smooth out the changes, so I'll add the transition property to the button. I'll include both background-color and border-radius in the transition so both changes are animated. I'll set a duration, maybe 0.3s, which is a common choice for smooth transitions.Looking at the button's current state, I should style it to look presentable. I'll set a background color, maybe green, to make it stand out. I'll also add some padding to make it bigger, set a white color for the text, and add some borders to give it a clean look.I should also consider the user experience. Adding cursor: pointer on hover indicates it's clickable, which is a good practice. Including a box-shadow can give it a slight lift, making it feel more interactive.Putting it all together, I'll structure the CSS with the button selector, then the hover state. I'll test each property to ensure they work together smoothly. The transition should apply to both the color and radius changes, so I'll list both in the transition property.I think that covers all the requirements. Now, I'll write the code, making sure each part is clearly explained so the user understands how each effect is achieved.