What is the time complexity of Minimum Number of Food Buckets to Feed the Hamsters?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Minimum Number of Food Buckets to Feed the Hamsters?

This problem uses String, Dynamic Programming, Greedy. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Minimum Number of Food Buckets to Feed the Hamsters?

Insight 1: Greedy approach: Place the bucket to the right of the hamster whenever possible. This maximizes the chance of feeding another hamster with the same bucket. Insight 2: Local optimality: The problem can be solved by iterating through the string and making locally optimal decisions at each hamster position. This leads to a globally optimal solution.

Which companies ask LeetCode 2086. Minimum Number of Food Buckets to Feed the Hamsters in interviews?

This problem is frequently asked at Geico, Grab, Sprinklr.

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Minimum Number of Food Buckets to Feed the Hamsters - LeetCode 2086 Solution

Minimum Number of Food Buckets to Feed the Hamsters - Complete Solution Guide

Minimum Number of Food Buckets to Feed the Hamsters is LeetCode problem 2086, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given a 0-indexed string hamsters where hamsters[i] is either: 'H' indicating that there is a hamster at index i , or '.' indicating that index i is empty. You will add some number of food buckets at the empty indices in order to feed the hamsters. A hamster can be fed if there is at least one food bucket to its left or to its right. More formally, a hamster at index i can be fed if you place a food bucket at index i - 1 and/or at index i + 1 . Return the minimum number of food buckets y

Detailed Explanation

The problem asks us to find the minimum number of food buckets needed to feed all hamsters in a line, given a string representing the line where 'H' denotes a hamster and '.' denotes an empty space. A hamster can be fed if there's a food bucket either to its left or to its right. The goal is to place buckets only in empty spaces such that all hamsters are fed. If it's impossible to feed all hamsters, return -1. The input is a string `hamsters` consisting of 'H' and '.' characters. The output is an integer representing the minimum number of buckets or -1 if it's impossible.

Solution Approach

The provided solution uses a greedy approach. It iterates through the string `hamsters`. When it encounters a hamster ('H'), it first tries to place a bucket to its right (if possible). If that's not possible, it tries to place a bucket to its left (if possible). If neither is possible, it means the hamster cannot be fed, so the solution returns -1. If the current character is an empty space ('.'), the algorithm simply moves to the next character. The number of buckets placed is counted and returned at the end.

Step-by-Step Algorithm

Step 1: Initialize `buckets` to 0 and `i` to 0.
Step 2: Iterate through the `hamsters` string using a `while` loop as long as `i` is less than the length of the string.
Step 3: If the character at index `i` is 'H':
Step 4: Check if placing a bucket to the right is possible (i.e., `i + 1` is within the string bounds and `hamsters[i+1]` is '.'). If it is, increment `buckets` by 1, and advance `i` by 3 to skip the next hamster fed by this bucket (the next empty space and next hamster if they exist).
Step 5: If placing a bucket to the right is not possible, check if placing a bucket to the left is possible (i.e., `i > 0` and `hamsters[i-1]` is '.'). If it is, increment `buckets` by 1 and advance `i` by 1.
Step 6: If neither placing a bucket to the right nor to the left is possible, return -1 (impossible to feed this hamster).
Step 7: Else (if the character at index `i` is '.'), increment `i` by 1.
Step 8: After the loop finishes, return the value of `buckets`.

Key Insights

Insight 1: Greedy approach: Place the bucket to the right of the hamster whenever possible. This maximizes the chance of feeding another hamster with the same bucket.
Insight 2: Local optimality: The problem can be solved by iterating through the string and making locally optimal decisions at each hamster position. This leads to a globally optimal solution.
Insight 3: Edge cases: Consider scenarios where a hamster is surrounded by other hamsters ('HHH'), which makes feeding it impossible. Also, handle hamsters at the beginning and end of the line.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: String, Dynamic Programming, Greedy.

Companies

Asked at: Geico, Grab, Sprinklr.

Minimum Number of Food Buckets to Feed the Hamsters | LeetCode 2086

Medium

String Dynamic Programming Greedy

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public int minimumBuckets(String hamsters) {
        int n = hamsters.length();
        int buckets = 0;
        int i = 0;
        while (i < n) {
            if (hamsters.charAt(i) == 'H') {
                // Greedy choice: place bucket to the right to potentially feed another hamster
                if (i + 1 < n && hamsters.charAt(i+1) == '.') {
                    buckets += 1;
                    i += 3;
                // If right is not possible, must place left
                } else if (i > 0 && hamsters.charAt(i-1) == '.') {
                    buckets += 1;
                    i += 1;
                // Impossible to feed this hamster
                } else {
                    return -1;
                }
            } else {  // hamsters[i] == '.'
                i += 1;
            }
        }
        return buckets;
    }
}

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Problem Info

Description

Problem 2086: Minimum Number of Food Buckets to Feed the Hamsters - Detailed explanation and solution approaches.

Topics

String Dynamic Programming Greedy

Companies

GeicoGrabSprinklr

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:2086

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

8 steps

1
Step 1: Initialize `buckets` to 0 and `i` to 0.
2
Step 2: Iterate through the `hamsters` string using a `while` loop as long as `i` is less than the length of the string.
3
Step 3: If the character at index `i` is 'H':
4
Step 4: Check if placing a bucket to the right is possible (i.e., `i + 1` is within the string bounds and `hamsters[i+1]` is '.'). If it is, increment `buckets` by 1, and advance `i` by 3 to skip the next hamster fed by this bucket (the next empty space and next hamster if they exist).
5
Step 5: If placing a bucket to the right is not possible, check if placing a bucket to the left is possible (i.e., `i > 0` and `hamsters[i-1]` is '.'). If it is, increment `buckets` by 1 and advance `i` by 1.
6
Step 6: If neither placing a bucket to the right nor to the left is possible, return -1 (impossible to feed this hamster).
7
Step 7: Else (if the character at index `i` is '.'), increment `i` by 1.
8
Step 8: After the loop finishes, return the value of `buckets`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(n) because the while loop iterates through the string at most once. The space complexity is O(1) because the algorithm uses a fixed number of variables regardless of the input size.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Dynamic Programming

A dynamic programming approach could be used to solve this problem by maintaining a table of minimum buckets needed up to a certain index. This is typically overkill for this problem.

Time: O(n)Space: O(n)

Trade-offs: The DP approach has the same time complexity but higher space complexity than the greedy approach. It's generally not preferred due to the increased space usage and added complexity of implementation. Greedy algorithm suffices in this case.

✨

Key Insights

1Insight 1: Greedy approach: Place the bucket to the right of the hamster whenever possible. This maximizes the chance of feeding another hamster with the same bucket.
2Insight 2: Local optimality: The problem can be solved by iterating through the string and making locally optimal decisions at each hamster position. This leads to a globally optimal solution.
3Insight 3: Edge cases: Consider scenarios where a hamster is surrounded by other hamsters ('HHH'), which makes feeding it impossible. Also, handle hamsters at the beginning and end of the line.

📚

Key Terms Explained

For Students

Dynamic Programming

Breaking complex problems into smaller subproblems and storing results.

Greedy Algorithm

Making the best choice at each step without looking ahead.

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: String like "HHH". The algorithm correctly identifies that it's impossible to feed the middle hamster and returns -1.
Edge case 2: String like "H". If a hamster exists at the start or end with no possible adjacent bucket position, the code returns -1.
Edge case 3: Empty string. The code will return 0 since it won't enter the loop. While the problem statement indicates the length is greater than 0, this is a reasonable default.
Edge case 4: String starting with 'H' and the next element is also H, such as 'HH...' The solution will correctly find that placing the bucket on the left or right is impossible

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the case where a hamster is surrounded by other hamsters, resulting in not returning -1 when it's impossible to feed all hamsters.

✗Common mistake 2: Incorrectly updating the index `i` after placing a bucket, potentially causing the algorithm to revisit already processed characters. For example, if placing the bucket to the right and not incrementing by 3. Incrementing by less than 3 or more than 3 can cause a wrong answer.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Resource allocation along a linear path. For example, placing charging stations along a road such that all electric vehicles can access a charging station within a certain range. Here, vehicles are like hamsters, and charging stations are the buckets.

🏦Real-world scenario 2: Optimizing server placement in a data center to ensure that all users can access a server with minimal latency. Users can be treated as hamsters and servers as food buckets. The goal is to minimize the number of servers required while guaranteeing that all users can connect to a server with low latency.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

String problems often involve sliding windows or two pointers. Consider if the character set is limited (lowercase letters = only 26 possibilities).

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Mutating strings directly in languages where strings are immutable. Use StringBuilder or arrays.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: September 15, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 14

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 7

❓

Frequently Asked Questions

How do I handle string manipulation efficiently?

In languages with immutable strings (Java, Python, C#), use StringBuilder/list to avoid O(n) concatenation cost. Consider using character arrays for in-place modifications. For pattern matching, consider KMP or Rabin-Karp for O(n+m) complexity.

How do I identify if a problem needs dynamic programming?

DP problems typically have: 1) Overlapping subproblems (same calculation repeated), 2) Optimal substructure (optimal solution uses optimal solutions to subproblems). Look for keywords like "minimum/maximum," "count ways," "is it possible," or "longest/shortest."

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Minimum Number of Food Buckets to Feed the Hamsters"?

For this medium-level String problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether dynamic programming techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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