Question

677. 键值映射

English Version

题目描述

设计一个 map ，满足以下几点:

• 字符串表示键，整数表示值
• 返回具有前缀等于给定字符串的键的值的总和

实现一个 MapSum 类：

• MapSum() 初始化 MapSum 对象
• void insert(String key, int val) 插入 key-val 键值对，字符串表示键 key ，整数表示值 val 。如果键 key 已经存在，那么原来的键值对 key-value 将被替代成新的键值对。
• int sum(string prefix) 返回所有以该前缀 prefix 开头的键 key 的值的总和。

 

示例 1：

输入：
["MapSum", "insert", "sum", "insert", "sum"]
[[], ["apple", 3], ["ap"], ["app", 2], ["ap"]]
输出：
[null, null, 3, null, 5]

解释：
MapSum mapSum = new MapSum();
mapSum.insert("apple", 3);  
mapSum.sum("ap");       // 返回 3 (apple = 3)
mapSum.insert("app", 2);  
mapSum.sum("ap");       // 返回 5 (apple + app = 3 + 2 = 5)

 

提示：

• 1 <= key.length, prefix.length <= 50
• key 和 prefix 仅由小写英文字母组成
• 1 <= val <= 1000
• 最多调用 50 次 insert 和 sum

解法

方法一：哈希表 + 前缀树

我们用哈希表 $d$ 存放键值对，用前缀树 $t$ 存放键值对的前缀和。前缀树的每个节点包含两个信息：

• val：以该节点为前缀的键值对的值的总和
• children：长度为 $26$ 的数组，存放该节点的子节点

插入键值对 $(key, val)$ 时，我们先判断哈希表是否存在该键，如果存在，那么前缀树每个节点的 val 都要减去该键原来的值，然后再加上新的值。如果不存在，那么前缀树每个节点的 val 都要加上新的值。

查询前缀和时，我们从前缀树的根节点开始，遍历前缀字符串，如果当前节点的子节点中不存在该字符，那么说明前缀树中不存在该前缀，返回 $0$。否则，继续遍历下一个字符，直到遍历完前缀字符串，返回当前节点的 val。

时间复杂度方面，插入键值对的时间复杂度为 $O(n)$，其中 $n$ 为键的长度。查询前缀和的时间复杂度为 $O(m)$，其中 $m$ 为前缀的长度。

空间复杂度 $O(n \times m \times C)$，其中 $n$ 和 $m$ 分别是键的数量以及键的最大长度；而 $C$ 是字符集的大小，本题中 $C = 26$。

class Trie:
  def __init__(self):
    self.children: List[Trie | None] = [None] * 26
    self.val: int = 0

  def insert(self, w: str, x: int):
    node = self
    for c in w:
      idx = ord(c) - ord('a')
      if node.children[idx] is None:
        node.children[idx] = Trie()
      node = node.children[idx]
      node.val += x

  def search(self, w: str) -> int:
    node = self
    for c in w:
      idx = ord(c) - ord('a')
      if node.children[idx] is None:
        return 0
      node = node.children[idx]
    return node.val


class MapSum:
  def __init__(self):
    self.d = defaultdict(int)
    self.tree = Trie()

  def insert(self, key: str, val: int) -> None:
    x = val - self.d[key]
    self.d[key] = val
    self.tree.insert(key, x)

  def sum(self, prefix: str) -> int:
    return self.tree.search(prefix)


# Your MapSum object will be instantiated and called as such:
# obj = MapSum()
# obj.insert(key,val)
# param_2 = obj.sum(prefix)

class Trie {
  private Trie[] children = new Trie[26];
  private int val;

  public void insert(String w, int x) {
    Trie node = this;
    for (int i = 0; i < w.length(); ++i) {
      int idx = w.charAt(i) - 'a';
      if (node.children[idx] == null) {
        node.children[idx] = new Trie();
      }
      node = node.children[idx];
      node.val += x;
    }
  }

  public int search(String w) {
    Trie node = this;
    for (int i = 0; i < w.length(); ++i) {
      int idx = w.charAt(i) - 'a';
      if (node.children[idx] == null) {
        return 0;
      }
      node = node.children[idx];
    }
    return node.val;
  }
}

class MapSum {
  private Map<String, Integer> d = new HashMap<>();
  private Trie trie = new Trie();

  public MapSum() {
  }

  public void insert(String key, int val) {
    int x = val - d.getOrDefault(key, 0);
    d.put(key, val);
    trie.insert(key, x);
  }

  public int sum(String prefix) {
    return trie.search(prefix);
  }
}

/**
 * Your MapSum object will be instantiated and called as such:
 * MapSum obj = new MapSum();
 * obj.insert(key,val);
 * int param_2 = obj.sum(prefix);
 */

class Trie {
public:
  Trie()
    : children(26, nullptr) {
  }

  void insert(string& w, int x) {
    Trie* node = this;
    for (char c : w) {
      c -= 'a';
      if (!node->children[c]) {
        node->children[c] = new Trie();
      }
      node = node->children[c];
      node->val += x;
    }
  }

  int search(string& w) {
    Trie* node = this;
    for (char c : w) {
      c -= 'a';
      if (!node->children[c]) {
        return 0;
      }
      node = node->children[c];
    }
    return node->val;
  }

private:
  vector<Trie*> children;
  int val = 0;
};

class MapSum {
public:
  MapSum() {
  }

  void insert(string key, int val) {
    int x = val - d[key];
    d[key] = val;
    trie->insert(key, x);
  }

  int sum(string prefix) {
    return trie->search(prefix);
  }

private:
  unordered_map<string, int> d;
  Trie* trie = new Trie();
};

/**
 * Your MapSum object will be instantiated and called as such:
 * MapSum* obj = new MapSum();
 * obj->insert(key,val);
 * int param_2 = obj->sum(prefix);
 */

type trie struct {
  children [26]*trie
  val    int
}

func (t *trie) insert(w string, x int) {
  for _, c := range w {
    c -= 'a'
    if t.children[c] == nil {
      t.children[c] = &trie{}
    }
    t = t.children[c]
    t.val += x
  }
}

func (t *trie) search(w string) int {
  for _, c := range w {
    c -= 'a'
    if t.children[c] == nil {
      return 0
    }
    t = t.children[c]
  }
  return t.val
}

type MapSum struct {
  d map[string]int
  t *trie
}

func Constructor() MapSum {
  return MapSum{make(map[string]int), &trie{}}
}

func (this *MapSum) Insert(key string, val int) {
  x := val - this.d[key]
  this.d[key] = val
  this.t.insert(key, x)
}

func (this *MapSum) Sum(prefix string) int {
  return this.t.search(prefix)
}

/**
 * Your MapSum object will be instantiated and called as such:
 * obj := Constructor();
 * obj.Insert(key,val);
 * param_2 := obj.Sum(prefix);
 */

class Trie {
  children: Trie[];
  val: number;

  constructor() {
    this.children = new Array(26);
    this.val = 0;
  }

  insert(w: string, x: number) {
    let node: Trie = this;
    for (const c of w) {
      const i = c.charCodeAt(0) - 97;
      if (!node.children[i]) {
        node.children[i] = new Trie();
      }
      node = node.children[i];
      node.val += x;
    }
  }

  search(w: string): number {
    let node: Trie = this;
    for (const c of w) {
      const i = c.charCodeAt(0) - 97;
      if (!node.children[i]) {
        return 0;
      }
      node = node.children[i];
    }
    return node.val;
  }
}

class MapSum {
  d: Map<string, number>;
  t: Trie;
  constructor() {
    this.d = new Map();
    this.t = new Trie();
  }

  insert(key: string, val: number): void {
    const x = val - (this.d.get(key) ?? 0);
    this.d.set(key, val);
    this.t.insert(key, x);
  }

  sum(prefix: string): number {
    return this.t.search(prefix);
  }
}

/**
 * Your MapSum object will be instantiated and called as such:
 * var obj = new MapSum()
 * obj.insert(key,val)
 * var param_2 = obj.sum(prefix)
 */