Boats To Save People Leetcode Problem 881 [Python Solution]

If you're looking to tackle the Boats To Save People problem on LeetCode, you've come to the right place.

This blog post will guide you through the problem, providing a step-by-step solution in Python.

By the end, you'll have a clear understanding of how to approach and solve this problem efficiently.

Problem Overview

Problem Statement: You are given an array people where people[i] represents the weight of the ith person, and an infinite number of boats, each with a maximum weight limit called limit.

Each boat can carry at most two people at the same time, provided that the sum of the weights of those people does not exceed the boat's weight limit.

Your task is to determine the minimum number of boats required to carry all the given people.

To illustrate, consider the following example:

Example 1:

Input: people = [1, 2], limit = 3
Output: 1
Explanation: 1 boat (1, 2)

In this case, we can use a single boat to carry both people since their total weight (1 + 2) does not exceed the limit of 3. Now, let's dive deeper into this problem.

Understanding the Constraints

Before we jump into the solution, it's crucial to understand the problem constraints.

This helps us define the boundaries within which our solution must operate.

• The length of the people array is between 1 and 5 * 10^4.
• The weight of each person (people[i]) falls within the range of 1 to limit, where limit is between 1 and 3 * 10^4.

Efficient Python Code Solution

Now, let's implement an efficient solution to this problem in Python.

We'll use a two-pointer approach and sort the people array to optimize our solution.

Here's the Python code to solve the Boats To Save People problem:

class Solution(object):
    def numRescueBoats(self, people, limit):
        # Sort the people array in ascending order.

people.sort()

        # Initialize pointers for the heaviest and lightest persons.

right = len(people) - 1
        left = 0

        # Initialize the result to count the number of boats used.

res = 0

        while left <= right:
            # Check if the sum of weights of the lightest and heaviest persons
            # does not exceed the boat's weight limit.

if people[left] + people[right] <= limit:
                left += 1
            right -= 1

            # Increment the boat count.

res += 1

        return res

This code implements a two-pointer approach to efficiently pair people and count the number of boats needed.

The time complexity of this solution is primarily determined by the sorting step, which is O(n log n).

Reasoning Behind Our Approach

The key insight behind this solution is to be greedy in our approach.

We start with the heaviest person and try to pair them with the lightest person, as this maximizes the boat's capacity usage.

If they can be paired without exceeding the weight limit, we use one boat for both.

We continue this process until we have accounted for all the people.

Additionally, we sort the people array to simplify the pairing process.

By sorting in ascending order, we ensure that we are dealing with the heaviest and lightest persons as we iterate through the array.

This simplifies the logic and helps us achieve an optimal solution.

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Conclusion

In this blog post, we tackled the Boats To Save People problem on LeetCode.

We provided a detailed Python solution using a two-pointer approach and explained the reasoning behind our approach.

By understanding the problem constraints and leveraging a greedy strategy, we were able to efficiently solve the problem.

If you have any questions, suggestions, or comments, please feel free to share them.

This guide is designed for beginners, and we encourage you to explore and experiment with the code.

Happy coding!

Question Link on LeetCode