【哈希表】(一) 设计哈希表
2024-06-08 21:19:35
目录
一、设计哈希表
二、设计哈希表的关键
三、设计哈希集合
3.1 题目要求
3.2 解决过程
四、设计哈希映射
4.1 题目要求
4.2 解决过程
五、设计哈希表 - 解决方案
六、复杂度分析 - 哈希表
参考文献：https://leetcode-cn.com/leetbook/read/hash-table/x6sast/
一、设计哈希表
参考文献：https://leetcode-cn.com/leetbook/read/hash-table/xht3is/
二、设计哈希表的关键
参考文献：https://leetcode-cn.com/leetbook/read/hash-table/xh8uld/
三、设计哈希集合
3.1 题目要求
3.2 解决过程
测试用例
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法一：数组哈希表 + 数组桶。
一方面，为降低删除成本，使用 None 代替被删除 key，但不会降低线性搜索查找 key 的成本。
另一方面，其实也可用数组哈希表实现桶，实现最大可能的空间换时间，此处将不做尝试。
2020/08/16 - 91.62% (180ms) - 最简单但并非最佳实现
class MyHashSet:def __init__(self):""" Initialize your data structure here. """self.hashtable = [[] for _ in range(1001)] # 数组哈希表 + 数组桶def add(self, key: int) -> None:hash_key = key % 1000 # 通过哈希函数计算哈希值bucket = self.hashtable[hash_key] # 通过哈希值找到相应桶bucket.append(key)def remove(self, key: int) -> None:hash_key = key % 1000 # 通过哈希函数计算哈希值bucket = self.hashtable[hash_key] # 通过哈希值找到相应桶for i in range(len(bucket)):if bucket[i] == key:# 不显式删除, 而是用 None 代替, 从而降低删除成本, 但并未降低查找成本bucket[i] = None def contains(self, key: int) -> bool:"""Returns true if this set contains the specified element"""hash_key = key % 1000 # 通过哈希函数计算哈希值bucket = self.hashtable[hash_key] # 通过哈希值找到相应桶for i in range(len(bucket)):if bucket[i] == key:return Truereturn False# Your MyHashSet object will be instantiated and called as such:
# obj = MyHashSet()
# obj.add(key)
# obj.remove(key)
# param_3 = obj.contains(key)法二：数组哈希表 + 单链表桶。
2020/08/15 - 66.83% (248ms)
class Node:def __init__(self, val=None, next=None):self.val = valself.next = nextclass SingleLinkedList:def __init__(self):self.dummy = Node() # 哑结点/伪头部/哨兵节点self.end = self.dummy # 尾结点def append(self, val):if not self.search(val):self.end.next = Node(val)self.end = self.end.nextdef delete(self, val):cur = self.dummywhile cur.next:if cur.next.val == val:if self.end.val == val:self.end = cur # 重设尾结点cur.next = cur.next.nextbreakcur = cur.nextreturndef search(self, val):cur = self.dummy.nextwhile cur:if cur.val == val:return Truecur = cur.nextreturn Falseclass MyHashSet:def __init__(self):""" Initialize your data structure here. """self.hashtable = [SingleLinkedList() for _ in range(1001)] # 数组哈希表 + 数组桶def add(self, key: int) -> None:hash_key = key % 1000 # 通过哈希函数计算哈希值 # 单链表实现桶self.hashtable[hash_key].append(key)def remove(self, key: int) -> None:hash_key = key % 1000 # 通过哈希函数计算哈希值self.hashtable[hash_key].delete(key)def contains(self, key: int) -> bool:""" Returns true if this set contains the specified element. """hash_key = key % 1000 # 通过哈希函数计算哈希值return self.hashtable[hash_key].search(key) 法三：链表哈希表 + 单链表桶。暂不实现。
法四：数组哈希表 + 二叉搜索树。暂不实现。
官方实现与说明
class MyHashSet(object):def __init__(self):self.keyRange = 769self.bucketArray = [Bucket() for i in range(self.keyRange)]def _hash(self, key):return key % self.keyRangedef add(self, key):bucketIndex = self._hash(key)self.bucketArray[bucketIndex].insert(key)def remove(self, key):bucketIndex = self._hash(key)self.bucketArray[bucketIndex].delete(key)def contains(self, key):bucketIndex = self._hash(key)return self.bucketArray[bucketIndex].exists(key)class Node:def __init__(self, value, nextNode=None):self.value = valueself.next = nextNodeclass Bucket:def __init__(self):# a pseudo headself.head = Node(0)def insert(self, newValue):# if not existed, add the new element to the head.if not self.exists(newValue):newNode = Node(newValue, self.head.next)# set the new head.self.head.next = newNodedef delete(self, value):prev = self.headcurr = self.head.nextwhile curr is not None:if curr.value == value:# remove the current nodeprev.next = curr.nextreturnprev = currcurr = curr.nextdef exists(self, value):curr = self.head.nextwhile curr is not None:if curr.value == value:# value existed already, do nothingreturn Truecurr = curr.nextreturn False
## 该实现集成了大量 BST 操作, 值得观摩
class MyHashSet:def __init__(self):self.keyRange = 769self.bucketArray = [Bucket() for i in range(self.keyRange)]def _hash(self, key) -> int:return key % self.keyRangedef add(self, key: int) -> None:bucketIndex = self._hash(key)self.bucketArray[bucketIndex].insert(key)def remove(self, key: int) -> None:bucketIndex = self._hash(key)self.bucketArray[bucketIndex].delete(key)def contains(self, key: int) -> bool:bucketIndex = self._hash(key)return self.bucketArray[bucketIndex].exists(key)class Bucket:def __init__(self):self.tree = BSTree()def insert(self, value):self.tree.root = self.tree.insertIntoBST(self.tree.root, value)def delete(self, value):self.tree.root = self.tree.deleteNode(self.tree.root, value)def exists(self, value):return (self.tree.searchBST(self.tree.root, value) is not None)class TreeNode:def __init__(self, value):self.val = valueself.left = Noneself.right = Noneclass BSTree:def __init__(self):self.root = Nonedef searchBST(self, root: TreeNode, val: int) -> TreeNode:if root is None or val == root.val:return rootreturn self.searchBST(root.left, val) if val < root.val else self.searchBST(root.right, val)def insertIntoBST(self, root: TreeNode, val: int) -> TreeNode:if not root:return TreeNode(val)if val > root.val:root.right = self.insertIntoBST(root.right, val) # insert into the right subtreeelif val == root.val:return rootelse:root.left = self.insertIntoBST(root.left, val) # insert into the left subtreereturn rootdef successor(self, root):"""One step right and then always left"""root = root.rightwhile root.left:root = root.leftreturn root.valdef predecessor(self, root):"""One step left and then always right"""root = root.leftwhile root.right:root = root.rightreturn root.valdef deleteNode(self, root: TreeNode, key: int) -> TreeNode:if not root:return None# delete from the right subtreeif key > root.val:root.right = self.deleteNode(root.right, key)# delete from the left subtreeelif key < root.val:root.left = self.deleteNode(root.left, key)# delete the current nodeelse:# the node is a leafif not (root.left or root.right):root = None# the node is not a leaf and has a right childelif root.right:root.val = self.successor(root)root.right = self.deleteNode(root.right, root.val)# the node is not a leaf, has no right child, and has a left childelse:root.val = self.predecessor(root)root.left = self.deleteNode(root.left, root.val)return root2020/08/16 - 53.27% (276ms)
参考文献
https://leetcode-cn.com/leetbook/read/hash-table/xh377h/
https://leetcode-cn.com/problems/design-hashset/solution/she-ji-ha-xi-ji-he-by-leetcode/
四、设计哈希映射
4.1 题目要求
4.2 解决过程
个人实现
法一：数组。
2020/08/23 - 6.11% (1364ms)
class MyHashMap:def __init__(self):"""Initialize your data structure here."""self.hashmap = [None for _ in range(1000000)] # 哈希映射, 数组实现def put(self, key: int, value: int) -> None:"""value will always be non-negative."""self.hashmap[key] = valuedef get(self, key: int) -> int:"""Returns the value to which the specified key is mapped, or -1 if this map contains no mapping for the key"""return self.hashmap[key] if self.hashmap[key] is not None else -1def remove(self, key: int) -> None:"""Removes the mapping of the specified value key if this map contains a mapping for the key"""self.hashmap[key] = None# Your MyHashMap object will be instantiated and called as such:
# obj = MyHashMap()
# obj.put(key,value)
# param_2 = obj.get(key)
# obj.remove(key)法二：数组实现哈希表。
2020/08/23 - 77.88% (256ms)
class MyHashMap(object):def __init__(self):# better to be a prime number, less collisionself.keyspace = 2069self.hashmap = [[] for i in range(self.keyspace)]def put(self, key, value):hashkey = key % self.keyspacebucket = self.hashmap[hashkey]for i in range(len(bucket)):if bucket[i][0] == key:bucket[i][1] = valuebucket.append([key, value])def get(self, key):hashkey = key % self.keyspacebucket = self.hashmap[hashkey]for i in range(len(bucket)):if bucket[i][0] == key:return bucket[i][1]return -1def remove(self, key):hashkey = key % self.keyspacebucket = self.hashmap[hashkey]for i in range(len(bucket)):if bucket[i][0] == key:bucket[i][0] = None # 把该键置为 None 表示删除官方实现与说明
class Bucket:def __init__(self):self.bucket = []def get(self, key):for (k, v) in self.bucket:if k == key:return vreturn -1def update(self, key, value):found = Falsefor i, kv in enumerate(self.bucket):if key == kv[0]:self.bucket[i] = (key, value)found = Truebreakif not found:self.bucket.append((key, value))def remove(self, key):for i, kv in enumerate(self.bucket):if key == kv[0]:del self.bucket[i] # 直接删除, 复杂度 O(n-i), 没有下一节的 O(1) 删除好class MyHashMap(object):def __init__(self):# better to be a prime number, less collisionself.key_space = 2069self.hash_table = [Bucket() for i in range(self.key_space)]def put(self, key, value):hash_key = key % self.key_spaceself.hash_table[hash_key].update(key, value)def get(self, key):hash_key = key % self.key_spacereturn self.hash_table[hash_key].get(key)def remove(self, key):hash_key = key % self.key_spaceself.hash_table[hash_key].remove(key)2020/08/23 - 69.60% (276ms)
参考文献
https://leetcode-cn.com/leetbook/read/hash-table/xhqwd3/
https://leetcode-cn.com/problems/design-hashmap/solution/she-ji-ha-xi-biao-by-leetcode/
五、设计哈希表 - 解决方案
#define MAX_LEN 100000 // the amount of buckets
class MyHashSet {
private:vector<int> set[MAX_LEN]; // hash set implemented by array/** Returns the corresponding bucket index. */int getIndex(int key) {return key % MAX_LEN;}/** Search the key in a specific bucket. Returns -1 if the key does not existed. */int getPos(int key, int index) {// Each bucket contains a list. Iterate all the elements in the bucket to find the target key.for (int i = 0; i < set[index].size(); ++i) {if (set[index][i] == key) {return i;}}return -1;}
public:/** Initialize your data structure here. */MyHashSet() {}void add(int key) {int index = getIndex(key);int pos = getPos(key, index);if (pos < 0) {// Add new key if key does not exist.set[index].push_back(key);}}void remove(int key) {int index = getIndex(key);int pos = getPos(key, index);if (pos >= 0) {// Remove the key if key exists.set[index].erase(set[index].begin() + pos);}}/** Returns true if this set did not already contain the specified element */bool contains(int key) {int index = getIndex(key);int pos = getPos(key, index);return pos >= 0;}
};/*** Your MyHashSet object will be instantiated and called as such:* MyHashSet obj = new MyHashSet();* obj.add(key);* obj.remove(key);* bool param_3 = obj.contains(key);*/
#define MAX_LEN 100000 // the amount of bucketsclass MyHashMap {
private:vector<pair<int, int>> map[MAX_LEN]; // hash map implemented by array/** Returns the corresponding bucket index. */int getIndex(int key) {return key % MAX_LEN;}/** Search the key in a specific bucket. Returns -1 if the key does not existed. */int getPos(int key, int index) {// Each bucket contains a vector. Iterate all the elements in the bucket to find the target key.for (int i = 0; i < map[index].size(); ++i) {if (map[index][i].first == key) {return i;}}return -1;}public:/** Initialize your data structure here. */MyHashMap() {}/** value will always be positive. */void put(int key, int value) {int index = getIndex(key);int pos = getPos(key, index);if (pos < 0) {map[index].push_back(make_pair(key, value));} else {map[index][pos].second = value;}}/** Returns the value to which the specified key is mapped, or -1 if this map contains no mapping for the key */int get(int key) {int index = getIndex(key);int pos = getPos(key, index);if (pos < 0) {return -1;} else {return map[index][pos].second;}}/** Removes the mapping of the specified value key if this map contains a mapping for the key */void remove(int key) {int index = getIndex(key);int pos = getPos(key, index);if (pos >= 0) {map[index].erase(map[index].begin() + pos);}}
};/*** Your MyHashMap object will be instantiated and called as such:* MyHashMap obj = new MyHashMap();* obj.put(key,value);* int param_2 = obj.get(key);* obj.remove(key);*/
参考文献：https://leetcode-cn.com/leetbook/read/hash-table/xh62wm/
六、复杂度分析 - 哈希表
参考文献：https://leetcode-cn.com/leetbook/read/hash-table/xhkpn1/
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