#2086

Medium

auto_awesomeState transition dynamic programming

LeetCode Problem Workspace

Minimum Number of Food Buckets to Feed the Hamsters

Find the minimum number of food buckets required to feed all hamsters, using dynamic programming and greedy techniques.

Problem Statement

You are given a string, hamsters, where each character represents either a hamster ('H') or an empty space ('.'). You need to place food buckets in the empty spaces such that each hamster is fed. A hamster is fed if there is a food bucket directly to its left or right. The goal is to return the minimum number of food buckets needed, or -1 if it is impossible to feed all hamsters.

To feed all hamsters, we must place food buckets in specific locations. Consider the feasibility when placing food buckets, especially in cases where hamsters are grouped together with no empty space between them. If feeding all hamsters is impossible, return -1. Otherwise, return the number of food buckets required.

Examples

Example 1

Input: hamsters = "H..H"

Output: 2

We place two food buckets at indices 1 and 2. It can be shown that if we place only one food bucket, one of the hamsters will not be fed.

Example 2

Input: hamsters = ".H.H."

Output: 1

We place one food bucket at index 2.

Example 3

Input: hamsters = ".HHH."

Output: -1

If we place a food bucket at every empty index as shown, the hamster at index 2 will not be able to eat.

Constraints

1 <= hamsters.length <= 105
hamsters[i] is either'H' or '.'.

Solution Approach

Dynamic Programming Approach

We can use dynamic programming to determine the optimal positions for food buckets. Track the state of the solution at each empty position and decide whether placing a bucket will help feed the hamsters. Transition through the states based on the conditions of whether adjacent hamsters are fed or not.

Greedy Strategy

Use a greedy approach to place food buckets at optimal positions, starting from the leftmost empty space. Make the decision to place a bucket wherever it's most beneficial, ensuring that all hamsters are fed with the least number of buckets.

State Transition Analysis

The problem can be reduced to analyzing the state transitions of empty spaces and hamsters. For each empty space, evaluate whether placing a food bucket satisfies the feeding condition for adjacent hamsters, ensuring all conditions are met with the minimum number of placements.

Complexity Analysis

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

The time and space complexity depend on the final approach. The dynamic programming approach may involve linear iteration over the string with additional states, while the greedy method may require a linear pass with constant space usage. Both approaches should work efficiently within the problem's constraints.

What Interviewers Usually Probe

Can the candidate apply dynamic programming to solve state transition problems?
Is the candidate able to use greedy methods for optimization problems?
How does the candidate handle edge cases where feeding hamsters is impossible?

Common Pitfalls or Variants

Common pitfalls

Overlooking cases where hamsters are grouped together with no adjacent empty space.
Failing to account for all possible placements of food buckets in a greedy solution.
Misunderstanding the conditions under which feeding all hamsters is impossible.

Follow-up variants

Modify the problem to allow placing food buckets at non-adjacent positions only.
Consider different variations where hamsters need to be fed in specific sequences.
Extend the problem by adding constraints on the number of buckets that can be placed.

FAQ

What is the minimum number of food buckets needed to feed all hamsters?

The minimum number of food buckets is calculated by placing them at empty positions adjacent to hamsters, using dynamic programming or a greedy approach.

When is it impossible to feed all the hamsters?

It is impossible when hamsters are grouped together without any empty space between them, and no placement of food buckets can feed them all.

How does dynamic programming help in solving this problem?

Dynamic programming helps by evaluating the optimal positions for food buckets based on the state transitions of adjacent hamsters and empty spaces.

Can a greedy approach work for this problem?

Yes, a greedy approach works by placing food buckets in the most beneficial positions, starting from the leftmost empty space.

What are the edge cases to consider in this problem?

Edge cases include consecutive hamsters without any empty space, hamsters at the start or end of the string, and strings with only one hamster or one empty space.

terminal

Solution

Solution 1

#### Python3

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

class Solution:
    def minimumBuckets(self, street: str) -> int:
        ans = 0
        i, n = 0, len(street)
        while i < n:
            if street[i] == 'H':
                if i + 1 < n and street[i + 1] == '.':
                    i += 2
                    ans += 1
                elif i and street[i - 1] == '.':
                    ans += 1
                else:
                    return -1
            i += 1
        return ans

Continue Practicing

#2311 longest binary subsequence less than or equal to k #2472 maximum number of non overlapping palindrome substrings #2522 partition string into substrings with values at most k