To solve the "Boats to Save People" problem, you should focus on pairing the lightest and heaviest individuals using a two-pointer technique. This method ensures that the number of boats used is minimized. After sorting the array of people, you can scan through the array, pairing the lightest and heaviest individuals until all are accounted for.
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 boat can carry a maximum weight of limit, and each boat can hold at most two people at once. The goal is to find the minimum number of boats required to carry all people, where the sum of the weights of the two individuals in each boat does not exceed the limit.
Return the minimum number of boats needed to transport everyone. If it's not possible to pair people optimally, you may need to carry them in separate boats.
Examples
Example 1
Input: people = [1,2], limit = 3
Output: 1
1 boat (1, 2)
Example 2
Input: people = [3,2,2,1], limit = 3
Output: 3
3 boats (1, 2), (2) and (3)
Example 3
Input: people = [3,5,3,4], limit = 5
Output: 4
4 boats (3), (3), (4), (5)
Constraints
- 1 <= people.length <= 5 * 104
- 1 <= people[i] <= limit <= 3 * 104
Solution Approach
Sorting and Two-pointer Technique
Start by sorting the people array. Then use two pointers: one at the beginning (lightest person) and one at the end (heaviest person). Try to pair the lightest and heaviest individuals; if their combined weight exceeds the limit, the heavier person will need their own boat. If they fit together, move both pointers inward and assign them to a boat.
Greedy Pairing
The greedy approach ensures that we are always attempting to use the available boat capacity as efficiently as possible. By pairing the heaviest person with the lightest available person, we minimize wasted boat capacity, which directly reduces the total number of boats needed.
Time and Space Optimization
Sorting the array takes O(n log n) time, and the two-pointer scan runs in O(n). This leads to an overall time complexity of O(n log n). The space complexity is O(1) if we modify the array in place, or O(n) if we use extra space for sorting.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity is dominated by the sorting step, O(n log n), followed by the O(n) two-pointer scan. The space complexity is O(1) if the array is sorted in place, or O(n) for additional space usage during sorting.
What Interviewers Usually Probe
- The candidate shows understanding of greedy algorithms by selecting optimal pairs.
- The candidate efficiently uses a two-pointer approach to minimize boats used.
- The candidate handles edge cases such as when all people exceed the boat limit by themselves.
Common Pitfalls or Variants
Common pitfalls
- Failing to handle the case where no one can be paired due to extreme weight differences.
- Incorrectly using a brute force approach, which results in higher time complexity than necessary.
- Not properly managing edge cases where the number of people is small or where everyone has the same weight.
Follow-up variants
- What if the boat can carry more than two people at a time?
- How would the problem change if there is a weight range restriction for pairing?
- What if some boats can carry additional weight but with a cost?
How GhostInterview Helps
- GhostInterview helps by ensuring you practice the two-pointer technique effectively, allowing you to handle pairing challenges in real-time interviews.
- It provides personalized feedback to improve the way you apply greedy strategies in boat pairing problems.
- GhostInterview's interactive guidance ensures you optimize your solution with time complexity considerations, perfect for a fast-paced interview environment.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the best approach for the "Boats to Save People" problem?
The best approach is a greedy algorithm using two-pointer scanning, which efficiently minimizes the number of boats required.
How do I pair people effectively in the Boats to Save People problem?
After sorting the array, use two pointers: one at the beginning and one at the end, pairing the lightest and heaviest people together as long as their total weight doesn't exceed the limit.
What is the time complexity of the solution?
The time complexity is O(n log n) due to the sorting step, followed by an O(n) two-pointer scan.
Can I solve the problem with a brute force approach?
A brute force approach would result in higher time complexity, making it less efficient. The two-pointer method is the optimal solution.
What happens if no people can be paired due to their weights?
In cases where people cannot be paired, each individual will need their own boat, increasing the total number of boats.
Need direct help with Boats to Save People instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Boats to Save People from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
Maximize the advantage of nums1 over nums2 using a two-pointer greedy strategy, carefully tracking which elements beat others.
Open problem page#826 Most Profit Assigning WorkAssign workers to jobs maximizing total profit using difficulty, profit, and worker arrays efficiently with binary search pattern.
Open problem page#948 Bag of TokensMaximize your score in the Bag of Tokens problem by strategically playing tokens with two-pointer scanning and greedy techniques.
Open problem page