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Solution
def solve(n, plants, C):
ans = 0
i = 0
l = len(plants)
// ... rest of solution available after purchaseExplanation
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To approach the watering plants problem, begin by visualizing the setup and the constraints clearly. You are tasked with watering N plants, each located at a consecutive position on a straight path, starting from position 0 and ending at position N - 1. Each plant requires a certain amount of water, which is specified in an array. You start at position -1, which is where the water source is located, and you must use this source to refill your watering can whenever it runs out.
Now, the main constraint here is that the can has a fixed capacity C. You must water the plants in left-to-right order, and you can only refill the can when it does not have enough water for the next plant. Preemptive refilling is not allowed. Also, each step you take, either forward or backward along the x-axis, counts as a movement step, and the goal is to compute the total number of such steps needed to water all the plants.
Your approach to solving this problem should start by simulating the process logically and step-by-step, taking into account both water usage and physical movement. You begin at -1, and your task is to move from there to each plant in order, water it if you have enough water, and, if not, go back to -1 to refill before continuing. Every movement from one x-coordinate to another incurs a step cost of 1 per unit distance.
To think through this, imagine a loop from the first to the last plant. At each plant, you evaluate whether your current water supply is enough to water that plant. If it is, you water it and subtract the required amount from your current water level. You then move on to the next plant, adding to your step counter the distance between the previous plant (or -1 if you just started) and the current plant.
However, if your current water is not sufficient for the next plant, you are forced to walk back to -1 to refill. This results in extra steps: the distance from your current position to -1, then again the distance from -1 to the plant you were trying to water. You also reset your water to full capacity after the refill. Importantly, this refill can only happen once the water in your can is insufficient for the current plant.
To simulate this process accurately, you should maintain a few key variables during your traversal:
1. A step counter to keep track of all your movements.
2. A current position tracker so you know where you are at each point.
3. A water tracker that records how much water remains in the can.
Each plant you visit will either result in:
- A forward step and water deduction, or
- A backtrack to the water source, a refill, and another forward movement to reach the same plant again.
An efficient way to think about this is to simulate each plant step-by-step. For each plant:
- Check whether the water left in your can is enough.
- If yes, move to that plant, water it, deduct the water amount, and add the step count from your current position to the plant's position.
- If no, you must walk all the way back to the water source, which is at position -1, and then come back to the plant. This round trip adds twice the distance from the plant to the water source to your step counter, and you reset your water capacity.
Another aspect to carefully consider is the initial movement from the starting point at -1 to plant 0. This is always required and adds 1 step. From there, if you never need to refill, you just move from plant to plant in linear order, each step adding 1 to the counter as you move to the next plant. But the complexity comes from the possibility of having to backtrack multiple times whenever the can runs out.
Think also about edge cases. If the first plant requires more water than the capacity of the can, the problem is invalid, since you can’t water that plant at all. In general, all plant water requirements must be less than or equal to C, otherwise it’s impossible to water them with the given can.
In summary, your mental model should simulate walking along the line of plants, watering each as long as the can allows, and returning to refill only when necessary. Track steps precisely and maintain a logical order of actions to ensure all plants are watered with the fewest necessary moves under the given rules.
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