You are given two string arrays words1 and words2.
A string b is a subset of string a if every letter in b occurs in a including multiplicity.
"wrr" is a subset of "warrior" but is not a subset of "world".A string a from words1 is universal if for every string b in words2, b is a subset of a.
Return an array of all the universal strings in words1. You may return the answer in any order.
Example 1:
Input: words1 = ["amazon","apple","facebook","google","leetcode"], words2 = ["e","o"]
Output: ["facebook","google","leetcode"]
Example 2:
Input: words1 = ["amazon","apple","facebook","google","leetcode"], words2 = ["lc","eo"]
Output: ["leetcode"]
Example 3:
Input: words1 = ["acaac","cccbb","aacbb","caacc","bcbbb"], words2 = ["c","cc","b"]
Output: ["cccbb"]
Constraints:
1 <= words1.length, words2.length <= 1041 <= words1[i].length, words2[i].length <= 10words1[i] and words2[i] consist only of lowercase English letters.words1 are unique.When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:
The brute-force strategy for the 'Word Subsets' problem involves checking every word in the first list to see if it contains all the letters and counts found in every word from the second list. We essentially go through each word in the first list and compare it to every word in the second list.
Here's how the algorithm would work step-by-step:
def word_subsets_brute_force(words1, words2):
result = []
for word1 in words1:
is_subset = True
# Iterate through each word in the second list
for word2 in words2:
word1_counts = {}
word2_counts = {}
for char in word1:
word1_counts[char] = word1_counts.get(char, 0) + 1
for char in word2:
word2_counts[char] = word2_counts.get(char, 0) + 1
# Check if word1 contains all letters of word2 with sufficient counts
for char, count in word2_counts.items():
if char not in word1_counts or word1_counts[char] < count:
is_subset = False
break
# Only add to result if word1 is a subset of all words2
if is_subset:
result.append(word1)
return resultThe goal is to find words that contain all the letters from each word in a given list. Instead of checking every word combination, we create a profile of required letters and then filter our words based on this profile. This avoids redundant checks and focuses on essential letter requirements.
Here's how the algorithm would work step-by-step:
def word_subsets(words1, words2):
master_letter_requirements = [0] * 26
# Find maximum letter frequencies required across all words2
for word2 in words2:
word_letter_frequency = [0] * 26
for letter in word2:
word_letter_frequency[ord(letter) - ord('a')] += 1
for i in range(26):
master_letter_requirements[i] = max(master_letter_requirements[i], word_letter_frequency[i])
result = []
# Iterate through words1 to check for subset property
for word1 in words1:
word1_letter_frequency = [0] * 26
# Count frequencies for each letter
for letter in word1:
word1_letter_frequency[ord(letter) - ord('a')] += 1
is_subset = True
# Check if all letters meet min. requirements
for i in range(26):
if word1_letter_frequency[i] < master_letter_requirements[i]:
is_subset = False
break
# Add to result if the word meets frequency requirements.
if is_subset:
result.append(word1)
return result| Case | How to Handle |
|---|---|
| words1 or words2 is null or empty | Return an empty list if either input array is null or empty as no subsets can be formed. |
| words1 or words2 contains empty strings | Treat empty strings as strings with no characters; frequency counts will be all zeros, and handle accordingly based on the algorithm used. |
| words1 or words2 contains very long strings exceeding reasonable memory limits | Consider handling large strings in chunks or using a more memory-efficient data structure for character counting to avoid out-of-memory errors. |
| words1 and words2 contain same words | The algorithm should correctly identify these words as subsets if the frequency criteria are met. |
| words2 contains words that are permutations of each other, but not subsets | Character frequency analysis must ensure that the subsets are based on minimum occurrences of characters, not just presence of characters. |
| words2 has some very large frequencies of certain characters such that no words1 satisfy subset requirements | The solution should return an empty result, as no words in words1 meet the subset condition defined by the high character frequencies of words2. |
| Unicode characters present in words1 or words2 | Ensure character frequency counting handles extended ASCII or Unicode characters correctly, possibly using a wider character representation. |
| Words contain characters with mixed cases (upper and lower) | Consider converting all words to lowercase or uppercase uniformly to ensure case-insensitive comparison if that is desired. |