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Rabbits in Forest

Difficulty: Medium

Problem Description

There is a forest with an unknown number of rabbits. We asked n rabbits "How many rabbits have the same color as you?" and collected the answers in an integer array answers where answers[i] is the answer of the i<sup>th</sup> rabbit. Given the array answers, return the minimum number of rabbits that could be in the forest.

Key Insights

  • Each rabbit's answer indicates how many other rabbits share its color.
  • If a rabbit answers x, it implies there are x + 1 rabbits of that color (including itself).
  • To minimize the total number of rabbits, we can group rabbits with the same answer together.
  • Use a counting approach to determine how many rabbits share each possible answer.

Space and Time Complexity

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

Solution

To solve this problem, we can use a hash map to count the occurrences of each answer provided by the rabbits. For each unique answer x, the minimum number of rabbits required is calculated as the ceiling of the count of rabbits giving that answer divided by x + 1, multiplied by x + 1. This accounts for the fact that if multiple rabbits give the same answer, they can share the same color. The total minimum rabbits will be the sum of the calculated values for all unique answers.

Code Solutions

def numRabbits(answers):
    count = {}
    for answer in answers:
        if answer in count:
            count[answer] += 1
        else:
            count[answer] = 1
            
    total_rabbits = 0
    for answer, freq in count.items():
        # Calculate the number of groups of rabbits for the current answer
        total_rabbits += ((freq + answer) // (answer + 1)) * (answer + 1)
    
    return total_rabbits
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