#2079

Medium

LeetCode Problem Workspace

Watering Plants

Simulate watering plants while managing a watering can's capacity, considering distance and refills.

Problem Statement

You are given an array of integers representing the amount of water each plant needs. The plants are placed in a row with each one having a specific location. Initially, you are at the river with a full watering can. Each plant needs a certain amount of water, and it takes one step to move one unit along the x-axis to water the plants. You must determine the total number of steps to water all the plants in the garden.

At the start, you begin at the river (located at x = -1), and you refill the watering can at the river. If the watering can does not have enough water for the next plant, you need to return to the river to refill it. You must calculate the total number of steps to water all the plants.

Examples

Example 1

Input: plants = [2,2,3,3], capacity = 5

Output: 14

Start at the river with a full watering can:

Walk to plant 0 (1 step) and water it. Watering can has 3 units of water.
Walk to plant 1 (1 step) and water it. Watering can has 1 unit of water.
Since you cannot completely water plant 2, walk back to the river to refill (2 steps).
Walk to plant 2 (3 steps) and water it. Watering can has 2 units of water.
Since you cannot completely water plant 3, walk back to the river to refill (3 steps).
Walk to plant 3 (4 steps) and water it. Steps needed = 1 + 1 + 2 + 3 + 3 + 4 = 14.

Example 2

Input: plants = [1,1,1,4,2,3], capacity = 4

Output: 30

Start at the river with a full watering can:

Water plants 0, 1, and 2 (3 steps). Return to river (3 steps).
Water plant 3 (4 steps). Return to river (4 steps).
Water plant 4 (5 steps). Return to river (5 steps).
Water plant 5 (6 steps). Steps needed = 3 + 3 + 4 + 4 + 5 + 5 + 6 = 30.

Example 3

Input: plants = [7,7,7,7,7,7,7], capacity = 8

Output: 49

You have to refill before watering each plant. Steps needed = 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 = 49.

Constraints

n == plants.length
1 <= n <= 1000
1 <= plants[i] <= 106
max(plants[i]) <= capacity <= 109

Solution Approach

Simulate the process

Start by simulating the process of watering each plant. Move along the row of plants and check if the current water can fully water the plant. If it can, water the plant and move to the next. If not, return to the river to refill the can and then continue watering. Keep track of the steps taken.

Track water usage and refills

For each plant, check if the remaining water in the can is sufficient. If not, simulate walking back to the river, refilling, and walking back to the plant. Accumulate the steps taken for each plant watering.

Account for distances

Consider the distances between the plants and ensure that each step is counted as the can is either used up or refilled. Pay close attention to the total distance covered when returning to the river for refills.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on how efficiently you simulate the watering process, considering that you may need to walk back to the river multiple times. The space complexity depends on how the state (water level and steps) is stored and updated for each plant during the simulation.

What Interviewers Usually Probe

Tests understanding of array manipulation and simulation techniques.
Checks the ability to manage state transitions and distance calculations in a real-world scenario.
Assesses problem-solving skills related to edge cases, such as large plant water requirements and multiple refills.

Common Pitfalls or Variants

Common pitfalls

Failing to correctly simulate refilling the watering can after running out of water for a plant.
Overlooking the distance when walking back to the river for refills.
Not managing the steps effectively, especially when dealing with large water requirements or plant quantities.

Follow-up variants

The array length may vary, increasing the complexity as more plants are added.
The capacity of the watering can may differ, altering the refill frequency.
Consider different walking patterns (e.g., skipping certain plants) to optimize the process.

FAQ

How can I optimize the solution for this problem?

Optimizing the solution involves carefully managing the refills and minimizing unnecessary walks back to the river. You can try to group plants based on their water needs to reduce refilling trips.

What happens if the plants array contains very large values?

If the water requirements are large, you will need to simulate multiple trips to the river. The challenge becomes managing these refills efficiently.

How do I handle situations where I must refill the watering can frequently?

Frequent refills require careful tracking of the water usage and efficient walking back to the river to minimize unnecessary steps.

What is the key pattern to solving the Watering Plants problem?

The key pattern is simulation, where you track the water usage and simulate walking back to the river when the can is empty, ensuring that each step is counted correctly.

How can GhostInterview help me with this problem?

GhostInterview provides a structured approach to break down the problem, helps you simulate the watering process, and ensures you account for all edge cases and steps required.

terminal

Solution

Solution 1: Simulation

We can simulate the process of watering the plants. We use a variable $\textit{water}$ to represent the current amount of water in the watering can, initially $\textit{water} = \textit{capacity}$.

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class Solution:
    def wateringPlants(self, plants: List[int], capacity: int) -> int:
        ans, water = 0, capacity
        for i, p in enumerate(plants):
            if water >= p:
                water -= p
                ans += 1
            else:
                water = capacity - p
                ans += i * 2 + 1
        return ans

Continue Practicing

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