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Rabbits in Forest

Number: 797

Difficulty: Medium

Paid? No

Companies: Amazon, Apple, Wish

Problem Description

In this problem, we are given an array of answers from rabbits in a forest. Each rabbit is asked how many other rabbits share his/her color. Using these responses, we want to determine the minimum total number of rabbits in the forest, accounting for rabbits that did not answer.

Key Insights

  • Use a hash table (or dictionary) to count the frequency of each answer.
  • For an answer x (meaning the rabbit sees x other rabbits of the same color), the group size is (x + 1) because the rabbit himself/herself is included.
  • For each unique answer, calculate the number of groups needed as the ceiling of (frequency / (x + 1)).
  • Multiply the number of groups by the group size (x + 1) and sum this value for all unique answers to obtain the minimum total number of rabbits.

Space and Time Complexity

Time Complexity: O(n), where n is the number of elements in the answers array. Space Complexity: O(n) in the worst case due to the hash table storing counts for each distinct answer.

Solution

The solution leverages a greedy approach:

  1. Traverse the answers array once to count the occurrences of each answer using a hash table.
  2. For each distinct answer x with frequency count, compute the number of groups required as:
    • groups = ceil(count / (x + 1))
  3. The contribution of each distinct answer to the total count is groups multiplied by the group size (x + 1).
  4. Sum these contributions to get the minimum total number of rabbits.

The essential trick is understanding that if a rabbit says x, there must be a full group size of (x + 1), and even if not all rabbits in a potential group answered, we still must account for the full group.

Code Solutions

# Python solution for Rabbits in Forest

import math

def numRabbits(answers):
    # Step 1: Count frequency of each answer using a dictionary
    count_map = {}
    for answer in answers:
        count_map[answer] = count_map.get(answer, 0) + 1
    
    # Variable to accumulate total rabbits
    total_rabbits = 0
    
    # Step 2: Compute minimal rabbits needed based on frequency counts
    for answer, count in count_map.items():
        group_size = answer + 1  # total rabbits of that color in a group
        # Calculate number of groups required using ceiling division
        groups = math.ceil(count / group_size)
        # Total rabbits is groups multiplied by the group size
        total_rabbits += groups * group_size
    
    return total_rabbits

# Example usage:
print(numRabbits([1,1,2]))  # Output: 5
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