Bulls and Cows

Updated on 13 May, 2025
Bulls and Cows header image

Problem Statement

In the "Bulls and Cows" game, you have a hidden number called the 'secret' and your friend tries to guess this number. After each guess, your responsibility is to provide feedback in the form of hints about how close their guess was to the secret. The feedback comprises two types of hints: "bulls" and "cows." Bulls indicate the number of digits in the guess that are both correct in value and positioned correctly in relation to the secret. On the other hand, cows represent the number of digits that are correct in value but positioned incorrectly. The challenge lies not just in counting these bulls and cows but also ensuring that a digit from the guess can only be used once, which becomes non-trivial when duplicates are involved. The expected output is a format of "xAyB" where x represents the bulls and y represents the cows.

Examples

Example 1

Input:

secret = "1807", guess = "7810"

Output:

"1A3B"

Explanation:

Bulls are connected with a '|' and cows are underlined:
"1807"
|
"7810"

Example 2

Input:

secret = "1123", guess = "0111"

Output:

"1A1B"

Explanation:

Bulls are connected with a '|' and cows are underlined:
"1123" "1123"
| or |
"0111" "0111"
Note that only one of the two unmatched 1s is counted as a cow since the non-bull digits can only be rearranged to allow one 1 to be a bull.

Constraints

  • 1 <= secret.length, guess.length <= 1000
  • secret.length == guess.length
  • secret and guess consist of digits only.

Approach and Intuition

The task involves string manipulation and a clear understanding of how to compare positions of characters in two strings (the secret and the guess). Below is a step-by-step breakdown on how to derive the solution:

  1. Initialize counters for bulls and cows to zero.

  2. First, iterate through the secret and guess at the same index. If a character in secret is the same as in guess at the same index, increase the bull counter and record this index as checked so that these characters aren't reconsidered for cows.

  3. Use a hash map or array to keep track of the frequencies of each character in secret that wasn't a bull. This helps in efficiently checking which characters in guess (that aren't bulls) can actually be considered as cows.

  4. For each character in guess that wasn't already counted as a bull, check if it can be a cow by looking it up in the hash map or array. If it's a non-bull character and exists in the map, it means this character is in the wrong position but is indeed in secret, so increase the cow counter and decrease the count in the map.

  5. Iterate through to check all characters, adjust counts in each step to ensure no character is double-counted as both bull and cow.

This method overall checks direct matches first (bulls) and then leverages frequency counts to correctly allocate cows, ensuring to handle duplicates accurately by managing counters for each digit. The use of a tracking counter for bulls and a map for managing potential cows provides a robust way to handle the game's constraints and provide accurate feedback.

Solutions

  • Java
  • Python
java
class Solution {
    public String calculateHint(String secret, String guess) {
        HashMap<Character, Integer> mapCounter = new HashMap<>();
        
        int bullsCount = 0, cowsCount = 0;
        int length = guess.length();
        for (int i = 0; i < length; ++i) {
            char charSecret = secret.charAt(i);
            char charGuess = guess.charAt(i);
            if (charSecret == charGuess) {
                bullsCount++;    
            } else {
                if (mapCounter.getOrDefault(charSecret, 0) < 0) 
                    cowsCount++;
                if (mapCounter.getOrDefault(charGuess, 0) > 0)
                    cowsCount++;
                mapCounter.put(charSecret, mapCounter.getOrDefault(charSecret, 0) + 1);
                mapCounter.put(charGuess, mapCounter.getOrDefault(charGuess, 0) - 1);
            }
        } 
                
        return Integer.toString(bullsCount) + "A" + Integer.toString(cowsCount) + "B";
    }
}

The provided solution in Java aims to solve the "Bulls and Cows" game by determining how many bulls (correct digits in the correct position) and cows (correct digits but in the wrong position) a guess has relative to a secret number.

Here's a breakdown of the approach:

  • A HashMap named mapCounter is introduced to store the frequency of characters that are not bulls, helping track the characters in both secret and guess.

  • Two integer counters, bullsCount and cowsCount, are initialized to zero. They count the number of bulls and cows respectively.

  • The algorithm iterates over each character of the secret and guess strings. If characters at the same index in both strings match, it increments the bullsCount.

  • If they don't match, it uses the mapCounter to:

    • Decrement the count for characters from guess (indicating these characters need matches from secret).
    • Increment the count for characters from secret (indicating these characters need matches from guess).

    If after modifying the map:

    • A previously recorded character from secret now matches a character in guess (i.e., map value becomes less than zero), it increments the cowsCount.
    • A previously recorded character from guess now matches a character in secret (i.e., map value becomes positive), it also increments the cowsCount.
  • Finally, the method returns the counts as a formatted string "{bullsCount}A{cowsCount}B", where A signifies the number of bulls and B signifies the number of cows.

By utilizing the HashMap to efficiently track the mismatches and later matches, this approach ensures the game logic is handled in a clear and concise manner without repetitively scanning arrays or strings. This makes the solution both efficient and straightforward to understand.

python
class Solution:
    def calculateHint(self, secret: str, guess: str) -> str:
        counts = defaultdict(int)
        bull_count = cow_count = 0

        for index, sec in enumerate(secret):
            gue = guess[index]
            if sec == gue:
                bull_count += 1
            else:
                cow_count += int(counts[sec] < 0) + int(counts[gue] > 0)
                counts[sec] += 1
                counts[gue] -= 1

        return f"{bull_count}A{cow_count}B"

This solution addresses the "Bulls and Cows" game using Python. In the game, you need to guess a secret string, where Bulls indicate correct characters in the right position, and Cows represent correct characters but in the wrong position.

  • Initialize a dictionary counts to track the appearance of characters.
  • Initialize two counters, bull_count and cow_count, to zero for tracking the number of Bulls and Cows respectively.
  • Loop through the characters of both secret and guess strings simultaneously. Use enumerate for indexing.
  • Compare each character of secret with the corresponding character in guess:
    • If they match, increment bull_count.
    • If they don't, update cow_count based on the conditions in the dictionary and adjust the dictionary counts accordingly:
      • Increment the count for the current secret character.
      • Decrement the count for the guessed character.
  • Construct and return the result string formatted as "{bull_count}A{cow_count}B".

This approach effectively counts both Bulls directly and uses the appearance dictionary to determine Cows by considering character frequencies across different indices. Ensure understanding and utilizing collections such as defaultdict to handle the counting logic efficiently.

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