acwing 字典树/前缀树(Trie)

• 树中为每个节点编号，每条路径表示一个原始元素，
• 如：节点为字符，原始元素为字符串，
• 或：节点为比特位，原始元素为一个数
• 因为会使用节点编号查询存储矩阵的行位置
• 所以存储矩阵的行数开可能的最多的节点个数

AcWing 835. Trie字符串统计

#include 
#include 
#include 

using namespace std;

const int maxn = 1e5 + 10;
int trie[maxn][26], count[maxn];
int index = 0;


void insert(const string& str)
{
    int cur = 0;
    for(int i = 0; i < str.size(); ++i)
    {
        int col_idx = str[i] - 'a';
        // 当前字符在字典树路径中未出现，插入并指定序号
        if(trie[cur][col_idx] == 0)
            trie[cur][col_idx] = ++index;
        // 沿着树中路径向下查询
        cur = trie[cur][col_idx];
    }
    // 当前路径结尾处标记累加已出现次数
    count[cur]++;
}

int query(const string& str)
{
    int cur = 0;
    for(int i = 0; i < str.size(); ++i)
    {
        int col_idx = str[i] - 'a';
        if(trie[cur][col_idx] == 0)
            return 0;
        cur = trie[cur][col_idx];
    }
    return count[cur];
}

int main()
{
    int N;
    cin >> N;
    char op;
    string str;
    for(int i = 0; i < N; ++i)
    {
        cin >> op >> str;
        if(op == 'I')
            insert(str);
        else
            cout << query(str) << endl;
    }   
    
    return 0;    
}

AcWing 143. 最大异或对

#include 
#include 

using namespace std;

const int N = 1e5 + 10, M = 31e5 + 10;
int n = 0, index = 0;
int nums[N], trie[M][2];
// int re[M];

// 构建树
void insert(int num)
{
    int cur = 0;
    for(int i = 31; i >= 0; --i)
    {
        int col_idx = (num >> i) & 1;
        if(trie[cur][col_idx] == 0)
            trie[cur][col_idx] = ++index;
        cur = trie[cur][col_idx];
    }
    // re[cur] = num;
}

// 查询树中与当前元素异或值最大的节点
// 根据对应比特位上是否相异确定查询路径
int query(int num)
{
    int ret = 0, cur = 0;
    for(int i = 31; i >=0; --i)
    {
        int col_idx = (num >> i) & 1;
        if(trie[cur][!col_idx] != 0)
        {
            ret += 1 << i;
            cur = trie[cur][!col_idx];
        }
        else
            cur = trie[cur][col_idx];
    }
    // return num ^ re[cur];
    return ret;
}

int main()
{
    cin >> n;
    for(int i = 0; i < n; ++i)
    {
        cin >> nums[i];
        insert(nums[i]);
    }
    int ret = 0;
    for(int i = 0; i < n; ++i)
        ret = max(ret, query(nums[i]));
    cout << ret;
    return 0;
}

lc上前缀树实现（节点型）

208. 实现 Trie (前缀树)

class Trie {
private:
    vector<Trie*> next;
    bool isEnd;
public:
    Trie() 
        :next(26), isEnd(false)
    { }
    
    void insert(string word) {
        Trie *cur = this;
        for(auto &a : word)
        {
            int idx = a - 'a';
            if(cur->next[idx] == nullptr)
                cur->next[idx] = new Trie;
            cur = cur->next[idx];
        }
        cur->isEnd = true;
    }
    
    bool search(string word) {
        Trie *cur = this;
        for(auto &a : word)
        {
            int idx = a - 'a';
            if(cur->next[idx] == nullptr)
                return false;
            cur = cur->next[idx];
        }
        return cur->isEnd;
    }
    
    bool startsWith(string prefix) {
        Trie *cur = this;
        for(auto &a : prefix)
        {
            int idx = a - 'a';
            if(cur->next[idx] == nullptr)
                return false;
            cur = cur->next[idx];
        }
        return true;
    }
};