916. Word Subsets - Explanation

Prerequisites

Before attempting this problem, you should be comfortable with:

Character Frequency Counting - Using arrays or hash maps to count occurrences of each character in a string
Hash Maps - For efficient frequency lookups and comparisons
Greedy Optimization - Combining multiple constraints into a single merged requirement to reduce comparisons

1. Brute Force

Intuition

A word from words1 is "universal" if every word in words2 is a subset of it. For a word to be a subset of another, every character must appear at least as many times in the target word. The straightforward approach is to check each word in words1 against all words in words2, comparing character frequencies to determine if all words2 words are subsets of words1.

Algorithm

Iterate through each word w1 in words1.
Count the frequency of each character in w1.
For each word w2 in words2, count its character frequencies.
Compare the counts: if any character in w2 appears more times than in w1, mark w1 as not universal and break.
If w1 passes all subset checks, add it to the res list.
Return the list of universal words.

class Solution:
    def wordSubsets(self, words1: List[str], words2: List[str]) -> List[str]:
        res = []
        for w1 in words1:
            count1 = Counter(w1)
            is_subset = True

            for w2 in words2:
                count2 = Counter(w2)
                for c in count2:
                    if count2[c] > count1[c]:
                        is_subset = False
                        break

                if not is_subset: break

            if is_subset:
                res.append(w1)

        return res

public class Solution {
    public List<String> wordSubsets(String[] words1, String[] words2) {
        List<String> res = new ArrayList<>();

        for (String w1 : words1) {
            int[] count1 = new int[26];
            for (char c : w1.toCharArray()) count1[c - 'a']++;

            boolean isSubset = true;
            for (String w2 : words2) {
                int[] count2 = new int[26];
                for (char c : w2.toCharArray()) count2[c - 'a']++;

                for (int i = 0; i < 26; i++) {
                    if (count2[i] > count1[i]) {
                        isSubset = false;
                        break;
                    }
                }

                if (!isSubset) break;
            }

            if (isSubset) res.add(w1);
        }

        return res;
    }
}

class Solution {
public:
    vector<string> wordSubsets(vector<string>& words1, vector<string>& words2) {
        vector<string> res;

        for (const string& w1 : words1) {
            vector<int> count1(26, 0);
            for (char c : w1) count1[c - 'a']++;

            bool isSubset = true;
            for (const string& w2 : words2) {
                vector<int> count2(26, 0);
                for (char c : w2) count2[c - 'a']++;

                for (int i = 0; i < 26; i++) {
                    if (count2[i] > count1[i]) {
                        isSubset = false;
                        break;
                    }
                }

                if (!isSubset) break;
            }

            if (isSubset) res.push_back(w1);
        }

        return res;
    }
};

class Solution {
    /**
     * @param {string[]} words1
     * @param {string[]} words2
     * @return {string[]}
     */
    wordSubsets(words1, words2) {
        const res = [];

        for (const w1 of words1) {
            const count1 = Array(26).fill(0);
            for (const c of w1) count1[c.charCodeAt(0) - 97]++;

            let isSubset = true;
            for (const w2 of words2) {
                const count2 = Array(26).fill(0);
                for (const c of w2) count2[c.charCodeAt(0) - 97]++;

                for (let i = 0; i < 26; i++) {
                    if (count2[i] > count1[i]) {
                        isSubset = false;
                        break;
                    }
                }

                if (!isSubset) break;
            }

            if (isSubset) res.push(w1);
        }

        return res;
    }
}

public class Solution {
    public IList<string> WordSubsets(string[] words1, string[] words2) {
        List<string> res = new List<string>();

        foreach (string w1 in words1) {
            int[] count1 = new int[26];
            foreach (char c in w1) count1[c - 'a']++;

            bool isSubset = true;
            foreach (string w2 in words2) {
                int[] count2 = new int[26];
                foreach (char c in w2) count2[c - 'a']++;

                for (int i = 0; i < 26; i++) {
                    if (count2[i] > count1[i]) {
                        isSubset = false;
                        break;
                    }
                }

                if (!isSubset) break;
            }

            if (isSubset) res.Add(w1);
        }

        return res;
    }
}

func wordSubsets(words1 []string, words2 []string) []string {
    res := []string{}

    for _, w1 := range words1 {
        count1 := [26]int{}
        for _, c := range w1 {
            count1[c-'a']++
        }

        isSubset := true
        for _, w2 := range words2 {
            count2 := [26]int{}
            for _, c := range w2 {
                count2[c-'a']++
            }

            for i := 0; i < 26; i++ {
                if count2[i] > count1[i] {
                    isSubset = false
                    break
                }
            }

            if !isSubset {
                break
            }
        }

        if isSubset {
            res = append(res, w1)
        }
    }

    return res
}

class Solution {
    fun wordSubsets(words1: Array<String>, words2: Array<String>): List<String> {
        val res = mutableListOf<String>()

        for (w1 in words1) {
            val count1 = IntArray(26)
            for (c in w1) count1[c - 'a']++

            var isSubset = true
            for (w2 in words2) {
                val count2 = IntArray(26)
                for (c in w2) count2[c - 'a']++

                for (i in 0 until 26) {
                    if (count2[i] > count1[i]) {
                        isSubset = false
                        break
                    }
                }

                if (!isSubset) break
            }

            if (isSubset) res.add(w1)
        }

        return res
    }
}

class Solution {
    func wordSubsets(_ words1: [String], _ words2: [String]) -> [String] {
        var res = [String]()

        for w1 in words1 {
            var count1 = [Int](repeating: 0, count: 26)
            for c in w1 {
                count1[Int(c.asciiValue! - Character("a").asciiValue!)] += 1
            }

            var isSubset = true
            for w2 in words2 {
                var count2 = [Int](repeating: 0, count: 26)
                for c in w2 {
                    count2[Int(c.asciiValue! - Character("a").asciiValue!)] += 1
                }

                for i in 0..<26 {
                    if count2[i] > count1[i] {
                        isSubset = false
                        break
                    }
                }

                if !isSubset { break }
            }

            if isSubset {
                res.append(w1)
            }
        }

        return res
    }
}

impl Solution {
    pub fn word_subsets(words1: Vec<String>, words2: Vec<String>) -> Vec<String> {
        let mut res = Vec::new();

        for w1 in &words1 {
            let mut count1 = [0i32; 26];
            for &b in w1.as_bytes() {
                count1[(b - b'a') as usize] += 1;
            }

            let mut is_subset = true;
            for w2 in &words2 {
                let mut count2 = [0i32; 26];
                for &b in w2.as_bytes() {
                    count2[(b - b'a') as usize] += 1;
                }

                for i in 0..26 {
                    if count2[i] > count1[i] {
                        is_subset = false;
                        break;
                    }
                }

                if !is_subset {
                    break;
                }
            }

            if is_subset {
                res.push(w1.clone());
            }
        }

        res
    }
}

Time & Space Complexity

Time complexity: $O(N * n + N * M * m)$
Space complexity:
- $O(1)$ extra space, since we have at most $26$ different characters.
- $O(N * n)$ space for the output list.

Where $N$ is the size of the array $words1$ , $n$ is the length of the longest word in $words1$ , $M$ is the size of the array $words2$ , and $m$ is the length of the longest word in $words2$ .

2. Greedy + Hash Map

Intuition

Instead of checking every word in words2 for each candidate, we can precompute a single "maximum requirement" array. The key insight is that if a word is universal, it must satisfy all words in words2 simultaneously. This means for each character, we only need the maximum count required across all words in words2. By merging all requirements into one frequency map, we reduce the problem to a single comparison per candidate word.

Algorithm

Build a combined frequency map for words2: for each character, store the maximum count needed across all words.
Iterate through each word w in words1.
Count the frequency of each character in w.
Compare against the combined requirement: if any character count in w is less than required, skip this word.
If w meets all requirements, add it to the res list.
Return the list of universal words.

class Solution:
    def wordSubsets(self, words1: List[str], words2: List[str]) -> List[str]:
        count_2 = defaultdict(int)
        for w in words2:
            count_w = Counter(w)
            for c, cnt in count_w.items():
                count_2[c] = max(count_2[c], cnt)

        res = []
        for w in words1:
            count_w = Counter(w)
            flag = True
            for c, cnt in count_2.items():
                if count_w[c] < cnt:
                    flag = False
                    break
            if flag:
                res.append(w)

        return res

public class Solution {
    public List<String> wordSubsets(String[] words1, String[] words2) {
        int[] count2 = new int[26];
        for (String w : words2) {
            int[] countW = new int[26];
            for (char c : w.toCharArray()) {
                countW[c - 'a']++;
            }
            for (int i = 0; i < 26; i++) {
                count2[i] = Math.max(count2[i], countW[i]);
            }
        }

        List<String> res = new ArrayList<>();
        for (String w : words1) {
            int[] countW = new int[26];
            for (char c : w.toCharArray()) {
                countW[c - 'a']++;
            }

            boolean flag = true;
            for (int i = 0; i < 26; i++) {
                if (countW[i] < count2[i]) {
                    flag = false;
                    break;
                }
            }

            if (flag) {
                res.add(w);
            }
        }

        return res;
    }
}

class Solution {
public:
    vector<string> wordSubsets(vector<string>& words1, vector<string>& words2) {
        vector<int> count2(26, 0);
        for (string& w : words2) {
            vector<int> countW(26, 0);
            for (char c : w) countW[c - 'a']++;
            for (int i = 0; i < 26; ++i)
                count2[i] = max(count2[i], countW[i]);
        }

        vector<string> res;
        for (string& w : words1) {
            vector<int> countW(26, 0);
            for (char c : w) countW[c - 'a']++;

            bool flag = true;
            for (int i = 0; i < 26; ++i) {
                if (countW[i] < count2[i]) {
                    flag = false;
                    break;
                }
            }

            if (flag) res.push_back(w);
        }

        return res;
    }
};

class Solution {
    /**
     * @param {string[]} words1
     * @param {string[]} words2
     * @return {string[]}
     */
    wordSubsets(words1, words2) {
        const count2 = new Array(26).fill(0);
        for (let w of words2) {
            const countW = new Array(26).fill(0);
            for (let c of w) {
                countW[c.charCodeAt(0) - 97]++;
            }
            for (let i = 0; i < 26; i++) {
                count2[i] = Math.max(count2[i], countW[i]);
            }
        }

        const res = [];
        for (let w of words1) {
            const countW = new Array(26).fill(0);
            for (let c of w) {
                countW[c.charCodeAt(0) - 97]++;
            }

            let flag = true;
            for (let i = 0; i < 26; i++) {
                if (countW[i] < count2[i]) {
                    flag = false;
                    break;
                }
            }

            if (flag) res.push(w);
        }

        return res;
    }
}

public class Solution {
    public IList<string> WordSubsets(string[] words1, string[] words2) {
        int[] count2 = new int[26];
        foreach (string w in words2) {
            int[] countW = new int[26];
            foreach (char c in w) {
                countW[c - 'a']++;
            }
            for (int i = 0; i < 26; i++) {
                count2[i] = Math.Max(count2[i], countW[i]);
            }
        }

        List<string> res = new List<string>();
        foreach (string w in words1) {
            int[] countW = new int[26];
            foreach (char c in w) {
                countW[c - 'a']++;
            }

            bool flag = true;
            for (int i = 0; i < 26; i++) {
                if (countW[i] < count2[i]) {
                    flag = false;
                    break;
                }
            }

            if (flag) {
                res.Add(w);
            }
        }

        return res;
    }
}

func wordSubsets(words1 []string, words2 []string) []string {
    count2 := [26]int{}
    for _, w := range words2 {
        countW := [26]int{}
        for _, c := range w {
            countW[c-'a']++
        }
        for i := 0; i < 26; i++ {
            if countW[i] > count2[i] {
                count2[i] = countW[i]
            }
        }
    }

    res := []string{}
    for _, w := range words1 {
        countW := [26]int{}
        for _, c := range w {
            countW[c-'a']++
        }

        flag := true
        for i := 0; i < 26; i++ {
            if countW[i] < count2[i] {
                flag = false
                break
            }
        }

        if flag {
            res = append(res, w)
        }
    }

    return res
}

class Solution {
    fun wordSubsets(words1: Array<String>, words2: Array<String>): List<String> {
        val count2 = IntArray(26)
        for (w in words2) {
            val countW = IntArray(26)
            for (c in w) {
                countW[c - 'a']++
            }
            for (i in 0 until 26) {
                count2[i] = maxOf(count2[i], countW[i])
            }
        }

        val res = mutableListOf<String>()
        for (w in words1) {
            val countW = IntArray(26)
            for (c in w) {
                countW[c - 'a']++
            }

            var flag = true
            for (i in 0 until 26) {
                if (countW[i] < count2[i]) {
                    flag = false
                    break
                }
            }

            if (flag) {
                res.add(w)
            }
        }

        return res
    }
}

class Solution {
    func wordSubsets(_ words1: [String], _ words2: [String]) -> [String] {
        var count2 = [Int](repeating: 0, count: 26)
        for w in words2 {
            var countW = [Int](repeating: 0, count: 26)
            for c in w {
                countW[Int(c.asciiValue! - Character("a").asciiValue!)] += 1
            }
            for i in 0..<26 {
                count2[i] = max(count2[i], countW[i])
            }
        }

        var res = [String]()
        for w in words1 {
            var countW = [Int](repeating: 0, count: 26)
            for c in w {
                countW[Int(c.asciiValue! - Character("a").asciiValue!)] += 1
            }

            var flag = true
            for i in 0..<26 {
                if countW[i] < count2[i] {
                    flag = false
                    break
                }
            }

            if flag {
                res.append(w)
            }
        }

        return res
    }
}

impl Solution {
    pub fn word_subsets(words1: Vec<String>, words2: Vec<String>) -> Vec<String> {
        let mut count2 = [0i32; 26];
        for w in &words2 {
            let mut count_w = [0i32; 26];
            for &b in w.as_bytes() {
                count_w[(b - b'a') as usize] += 1;
            }
            for i in 0..26 {
                count2[i] = count2[i].max(count_w[i]);
            }
        }

        let mut res = Vec::new();
        for w in &words1 {
            let mut count_w = [0i32; 26];
            for &b in w.as_bytes() {
                count_w[(b - b'a') as usize] += 1;
            }

            let mut flag = true;
            for i in 0..26 {
                if count_w[i] < count2[i] {
                    flag = false;
                    break;
                }
            }

            if flag {
                res.push(w.clone());
            }
        }

        res
    }
}

Time & Space Complexity

Time complexity: $O(N * n + M * m)$
Space complexity:
- $O(1)$ extra space, since we have at most $26$ different characters.
- $O(N * n)$ space for the output list.

Where $N$ is the size of the array $words1$ , $n$ is the length of the longest word in $words1$ , $M$ is the size of the array $words2$ , and $m$ is the length of the longest word in $words2$ .