# 1858. Longest Word With All Prefixes

## Description

Given an array of strings words, find the longest string in words such that every prefix of it is also in words.

• For example, let words = ["a", "app", "ap"]. The string "app" has prefixes "ap" and "a", all of which are in words.

Return the string described above. If there is more than one string with the same length, return the lexicographically smallest one, and if no string exists, return "".

Example 1:

Input: words = ["k","ki","kir","kira", "kiran"]
Output: "kiran"
Explanation: "kiran" has prefixes "kira", "kir", "ki", and "k", and all of them appear in words.


Example 2:

Input: words = ["a", "banana", "app", "appl", "ap", "apply", "apple"]
Output: "apple"
Explanation: Both "apple" and "apply" have all their prefixes in words.
However, "apple" is lexicographically smaller, so we return that.


Example 3:

Input: words = ["abc", "bc", "ab", "qwe"]
Output: ""


Constraints:

• 1 <= words.length <= 105
• 1 <= words[i].length <= 105
• 1 <= sum(words[i].length) <= 105

## Solutions

Solution 1: Trie

We define a trie, each node of the trie has two attributes, one is a children array of length $26$, and the other is a isEnd flag indicating whether it is the end of a word.

We traverse words, for each word w, we start traversing from the root node. If the current node’s children array does not contain the first character of w, we create a new node, then continue to traverse the next character of w, until we finish traversing w, we mark the isEnd of the current node as true.

Next, we traverse words, for each word w, we start traversing from the root node. If the isEnd field of the current node’s children array is false, it means that some prefix of w is not in words, we return false. Otherwise, we continue to traverse the next character of w, until we finish traversing w, we return true.

 The time complexity is $O(\sum_{w \in words} w )$, and the space complexity is $O(\sum_{w \in words} w )$.
• class Trie {
private Trie[] children = new Trie[26];
private boolean isEnd;

public Trie() {
}

public void insert(String w) {
Trie node = this;
for (char c : w.toCharArray()) {
int idx = c - 'a';
if (node.children[idx] == null) {
node.children[idx] = new Trie();
}
node = node.children[idx];
}
node.isEnd = true;
}

public boolean search(String w) {
Trie node = this;
for (char c : w.toCharArray()) {
int idx = c - 'a';
node = node.children[idx];
if (!node.isEnd) {
return false;
}
}
return true;
}
}

class Solution {
public String longestWord(String[] words) {
Trie trie = new Trie();
for (String w : words) {
trie.insert(w);
}
String ans = "";
for (String w : words) {
if ((w.length() > ans.length() || (w.length() == ans.length() && w.compareTo(ans) < 0))
&& trie.search(w)) {
ans = w;
}
}
return ans;
}
}

• class Trie {
private:
Trie* children[26];
bool isEnd = false;

public:
Trie() {
fill(begin(children), end(children), nullptr);
}

void insert(const string& w) {
Trie* node = this;
for (char c : w) {
int idx = c - 'a';
if (!node->children[idx]) {
node->children[idx] = new Trie();
}
node = node->children[idx];
}
node->isEnd = true;
}

bool search(const string& w) {
Trie* node = this;
for (char c : w) {
int idx = c - 'a';
node = node->children[idx];
if (!node->isEnd) {
return false;
}
}
return true;
}
};

class Solution {
public:
string longestWord(vector<string>& words) {
Trie trie;
for (const string& w : words) {
trie.insert(w);
}
string ans = "";
for (const string& w : words) {
if ((w.size() > ans.size() || (w.size() == ans.size() && w < ans)) && trie.search(w)) {
ans = w;
}
}
return ans;
}
};

• class Trie:
__slots__ = ["children", "is_end"]

def __init__(self):
self.children: List[Trie | None] = [None] * 26
self.is_end: bool = False

def insert(self, w: str) -> None:
node = self
for c in w:
idx = ord(c) - ord("a")
if not node.children[idx]:
node.children[idx] = Trie()
node = node.children[idx]
node.is_end = True

def search(self, w: str) -> bool:
node = self
for c in w:
idx = ord(c) - ord("a")
node = node.children[idx]
if not node.is_end:
return False
return True

class Solution:
def longestWord(self, words: List[str]) -> str:
trie = Trie()
for w in words:
trie.insert(w)
ans = ""
for w in words:
if (len(w) > len(ans) or len(w) == len(ans) and w < ans) and trie.search(w):
ans = w
return ans


• type Trie struct {
children [26]*Trie
isEnd    bool
}

func newTrie() *Trie {
return &Trie{}
}

func (t *Trie) insert(w string) {
node := t
for _, c := range w {
idx := c - 'a'
if node.children[idx] == nil {
node.children[idx] = newTrie()
}
node = node.children[idx]
}
node.isEnd = true
}

func (t *Trie) search(w string) bool {
node := t
for _, c := range w {
idx := c - 'a'
node = node.children[idx]
if !node.isEnd {
return false
}
}
return true
}

func longestWord(words []string) string {
trie := newTrie()
for _, w := range words {
trie.insert(w)
}
ans := ""
for _, w := range words {
if (len(w) > len(ans) || (len(w) == len(ans) && w < ans)) && trie.search(w) {
ans = w
}
}
return ans
}

• class Trie {
private children: (Trie | null)[] = Array(26).fill(null);
private isEnd: boolean = false;

insert(w: string): void {
let node: Trie = this;
for (const c of w) {
const idx: number = c.charCodeAt(0) - 'a'.charCodeAt(0);
if (!node.children[idx]) {
node.children[idx] = new Trie();
}
node = node.children[idx] as Trie;
}
node.isEnd = true;
}

search(w: string): boolean {
let node: Trie = this;
for (const c of w) {
const idx: number = c.charCodeAt(0) - 'a'.charCodeAt(0);
node = node.children[idx] as Trie;
if (!node.isEnd) {
return false;
}
}
return true;
}
}

function longestWord(words: string[]): string {
const trie: Trie = new Trie();
for (const w of words) {
trie.insert(w);
}
let ans: string = '';
for (const w of words) {
if ((w.length > ans.length || (w.length === ans.length && w < ans)) && trie.search(w)) {
ans = w;
}
}
return ans;
}


• public class Trie {
private Trie[] children = new Trie[26];
private bool isEnd;

public Trie() { }

public void Insert(string w) {
Trie node = this;
foreach (char c in w.ToCharArray()) {
int idx = c - 'a';
if (node.children[idx] == null) {
node.children[idx] = new Trie();
}
node = node.children[idx];
}
node.isEnd = true;
}

public bool Search(string w) {
Trie node = this;
foreach (char c in w.ToCharArray()) {
int idx = c - 'a';
node = node.children[idx];
if (!node.isEnd) {
return false;
}
}
return true;
}
}

public class Solution {
public string LongestWord(string[] words) {
Trie trie = new Trie();
foreach (string w in words) {
trie.Insert(w);
}

string ans = "";
foreach (string w in words) {
if ((w.Length > ans.Length || (w.Length == ans.Length && string.Compare(w, ans) < 0)) && trie.Search(w)) {
ans = w;
}
}
return ans;
}
}


• struct Trie {
children: [Option<Box<Trie>>; 26],
is_end: bool,
}

impl Trie {
fn new() -> Self {
Trie {
children: Default::default(),
is_end: false,
}
}

fn insert(&mut self, w: &str) {
let mut node = self;
for c in w.chars() {
let idx = (c as usize) - ('a' as usize);
node = node.children[idx].get_or_insert_with(|| Box::new(Trie::new()));
}
node.is_end = true;
}

fn search(&self, w: &str) -> bool {
let mut node = self;
for c in w.chars() {
let idx = (c as usize) - ('a' as usize);
if let Some(next_node) = &node.children[idx] {
node = next_node.as_ref();
if !node.is_end {
return false;
}
}
}
true
}
}

impl Solution {
pub fn longest_word(words: Vec<String>) -> String {
let mut trie = Trie::new();
for w in &words {
trie.insert(w);
}
let mut ans = String::new();
for w in &words {
if (w.len() > ans.len() || (w.len() == ans.len() && w < &ans)) && trie.search(w) {
ans = w.clone();
}
}
ans
}
}