先决条件：散列介绍和通过单独链接进行碰撞处理
散列的工作原理：
要将key(K) – value(V) 对插入哈希映射，需要 2 个步骤：
- 使用散列函数K 转换为一个小整数（称为其散列码）。
- 哈希码用于查找索引（hashCode % arrSize），并且首先搜索该索引处的整个链表（单独链接）是否已经存在 K。
- 如果找到，则更新其值，如果没有，则将 KV 对作为新节点存储在列表中。
复杂性和负载因子
- 对于第一步，所用时间取决于 K 和散列函数。
例如，如果键是字符串“abcd”，那么它的哈希函数可能取决于字符串的长度。但是对于非常大的 n 值，映射中的条目数，键的长度与 n 相比几乎可以忽略不计，因此可以认为散列计算发生在恒定时间，即O(1) 。 - 对于第二步，需要遍历存在于该索引处的 KV 对列表。为此，最坏的情况可能是所有 n 个条目都在同一索引上。因此，时间复杂度为O(n) 。但是，已经进行了足够的研究来使散列函数均匀分布数组中的键，因此这种情况几乎不会发生。
- 因此，平均而言，如果有 n 个条目并且 b 是数组的大小，则每个索引上都会有 n/b 个条目。这个值 n/b 被称为负载因子，代表我们地图上的负载。
- 此负载因子需要保持较低，以便一个索引处的条目数较少，因此复杂度几乎恒定，即 O(1)。
重新哈希：
顾名思义，重新散列意味着再次散列。基本上，当负载因子增加到超过其预先定义的值（负载因子的默认值是 0.75）时，复杂度就会增加。因此，为了克服这一点，数组的大小增加（加倍），所有值再次散列并存储在新的双倍大小的数组中，以保持低负载因子和低复杂性。
为什么要重刷？
重新散列是因为每当键值对被插入到映射中时，加载因子就会增加，这意味着时间复杂度也会增加，如上所述。这可能不会给出 O(1) 所需的时间复杂度。
因此，必须进行rehash，增加bucketArray的大小，以降低负载因子和时间复杂度。
Rehashing是如何完成的？
可以按如下方式进行重新散列：
- 每次向地图添加新条目时，请检查负载因子。
- 如果它大于它的预定义值（或者如果没有给出默认值 0.75），则 Rehash。
- 对于 Rehash，创建一个两倍于先前大小的新数组并将其设为新的 bucketarray。
- 然后遍历旧bucketArray中的每个元素，并为每个元素调用insert()，以便将其插入到新的更大的bucket数组中。
实现 Rehashing 的程序：
// Java program to implement Rehashing
import java.util.ArrayList;
class Map {
class MapNode {
K key;
V value;
MapNode next;
public MapNode(K key, V value)
{
this.key = key;
this.value = value;
next = null;
}
}
// The bucket array where
// the nodes containing K-V pairs are stored
ArrayList > buckets;
// No. of pairs stored - n
int size;
// Size of the bucketArray - b
int numBuckets;
// Default loadFactor
final double DEFAULT_LOAD_FACTOR = 0.75;
public Map()
{
numBuckets = 5;
buckets = new ArrayList<>(numBuckets);
for (int i = 0; i < numBuckets; i++) {
// Initialising to null
buckets.add(null);
}
System.out.println("HashMap created");
System.out.println("Number of pairs in the Map: " + size);
System.out.println("Size of Map: " + numBuckets);
System.out.println("Default Load Factor : " + DEFAULT_LOAD_FACTOR + "\n");
}
private int getBucketInd(K key)
{
// Using the inbuilt function from the object class
int hashCode = key.hashCode();
// array index = hashCode%numBuckets
return (hashCode % numBuckets);
}
public void insert(K key, V value)
{
// Getting the index at which it needs to be inserted
int bucketInd = getBucketInd(key);
// The first node at that index
MapNode head = buckets.get(bucketInd);
// First, loop through all the nodes present at that index
// to check if the key already exists
while (head != null) {
// If already present the value is updated
if (head.key.equals(key)) {
head.value = value;
return;
}
head = head.next;
}
// new node with the K and V
MapNode newElementNode = new MapNode(key, value);
// The head node at the index
head = buckets.get(bucketInd);
// the new node is inserted
// by making it the head
// and it's next is the previous head
newElementNode.next = head;
buckets.set(bucketInd, newElementNode);
System.out.println("Pair(" + key + ", " + value + ") inserted successfully.\n");
// Incrementing size
// as new K-V pair is added to the map
size++;
// Load factor calculated
double loadFactor = (1.0 * size) / numBuckets;
System.out.println("Current Load factor = " + loadFactor);
// If the load factor is > 0.75, rehashing is done
if (loadFactor > DEFAULT_LOAD_FACTOR) {
System.out.println(loadFactor + " is greater than " + DEFAULT_LOAD_FACTOR);
System.out.println("Therefore Rehashing will be done.\n");
// Rehash
rehash();
System.out.println("New Size of Map: " + numBuckets + "\n");
}
System.out.println("Number of pairs in the Map: " + size);
System.out.println("Size of Map: " + numBuckets + "\n");
}
private void rehash()
{
System.out.println("\n***Rehashing Started***\n");
// The present bucket list is made temp
ArrayList > temp = buckets;
// New bucketList of double the old size is created
buckets = new ArrayList >(2 * numBuckets);
for (int i = 0; i < 2 * numBuckets; i++) {
// Initialised to null
buckets.add(null);
}
// Now size is made zero
// and we loop through all the nodes in the original bucket list(temp)
// and insert it into the new list
size = 0;
numBuckets *= 2;
for (int i = 0; i < temp.size(); i++) {
// head of the chain at that index
MapNode head = temp.get(i);
while (head != null) {
K key = head.key;
V val = head.value;
// calling the insert function for each node in temp
// as the new list is now the bucketArray
insert(key, val);
head = head.next;
}
}
System.out.println("\n***Rehashing Ended***\n");
}
public void printMap()
{
// The present bucket list is made temp
ArrayList > temp = buckets;
System.out.println("Current HashMap:");
// loop through all the nodes and print them
for (int i = 0; i < temp.size(); i++) {
// head of the chain at that index
MapNode head = temp.get(i);
while (head != null) {
System.out.println("key = " + head.key + ", val = " + head.value);
head = head.next;
}
}
System.out.println();
}
}
public class GFG {
public static void main(String[] args)
{
// Creating the Map
Map map = new Map();
// Inserting elements
map.insert(1, "Geeks");
map.printMap();
map.insert(2, "forGeeks");
map.printMap();
map.insert(3, "A");
map.printMap();
map.insert(4, "Computer");
map.printMap();
map.insert(5, "Portal");
map.printMap();
}
}
输出：
HashMap created
Number of pairs in the Map: 0
Size of Map: 5
Default Load Factor : 0.75
Pair(1, Geeks) inserted successfully.
Current Load factor = 0.2
Number of pairs in the Map: 1
Size of Map: 5
Current HashMap:
key = 1, val = Geeks
Pair(2, forGeeks) inserted successfully.
Current Load factor = 0.4
Number of pairs in the Map: 2
Size of Map: 5
Current HashMap:
key = 1, val = Geeks
key = 2, val = forGeeks
Pair(3, A) inserted successfully.
Current Load factor = 0.6
Number of pairs in the Map: 3
Size of Map: 5
Current HashMap:
key = 1, val = Geeks
key = 2, val = forGeeks
key = 3, val = A
Pair(4, Computer) inserted successfully.
Current Load factor = 0.8
0.8 is greater than 0.75
Therefore Rehashing will be done.
***Rehashing Started***
Pair(1, Geeks) inserted successfully.
Current Load factor = 0.1
Number of pairs in the Map: 1
Size of Map: 10
Pair(2, forGeeks) inserted successfully.
Current Load factor = 0.2
Number of pairs in the Map: 2
Size of Map: 10
Pair(3, A) inserted successfully.
Current Load factor = 0.3
Number of pairs in the Map: 3
Size of Map: 10
Pair(4, Computer) inserted successfully.
Current Load factor = 0.4
Number of pairs in the Map: 4
Size of Map: 10
***Rehashing Ended***
New Size of Map: 10
Number of pairs in the Map: 4
Size of Map: 10
Current HashMap:
key = 1, val = Geeks
key = 2, val = forGeeks
key = 3, val = A
key = 4, val = Computer
Pair(5, Portal) inserted successfully.
Current Load factor = 0.5
Number of pairs in the Map: 5
Size of Map: 10
Current HashMap:
key = 1, val = Geeks
key = 2, val = forGeeks
key = 3, val = A
key = 4, val = Computer
key = 5, val = Portal
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