The size of the hash table is not determinate at the very beginning. If the total size of keys is too large (e.g. size >= capacity / 10), we should double the size of the hash table and rehash every keys. Say you have a hash table looks like below:

size=3, capacity=4

[null, 21, 14, null]
       ↓    ↓
       9   null
       ↓
      null

The hash function is:

int hashcode(int key, int capacity) {
    return key % capacity;
}

Here we have three numbers, 9, 14 and 21, where 21 and 9 share the same position as they all have the same hashcode 1 (21 % 4 = 9 % 4 = 1). We store them in the hash table by linked list.

Rehashing this hash table, double the capacity, you will get:

size=3, capacity=8

index:   0    1    2    3     4    5    6   7
hash : [null, 9, null, null, null, 21, 14, null]

For this problem, given the original hash table, return the new hash table after rehashing.

Notice

For negative integer in hash table, the position can be calculated as follow:

C++/Java: if you directly calculate -4 % 3 you will get -1. You can use function: a % b = (a % b + b) % b to make it is a non negative integer. Python: you can directly use -1 % 3, you will get 2 automatically.

Example

Original Table:

[null, 21, 14, null]
       ↓    ↓
       9   null
       ↓
      null


Rehashed Table: 

[null, 9, null, null, null, 21, 14, null]
       ↓                    ↓    ↓
      null                 null null

public class Solution {   
    public ListNode[] rehashing(ListNode[] hashTable) {
        ListNode[] table = new ListNode[hashTable.length * 2];
        
        for (ListNode head : hashTable) {
            if (head == null)
                continue;
            for (ListNode p = head; p != null; p = p.next)
                insert(table, p);
        }
        
        return table;
    }
    
    void insert(ListNode[] table, ListNode node) {
        int code = hash(node.val, table.length);
        if (table[code] == null)
            table[code] = new ListNode(node.val);
        else {
            ListNode p = table[code];
            while (p.next != null)
                p = p.next;
            p.next = new ListNode(node.val);
        }
    }
    
    int hash(int key, int cap) {
        return (key % cap + cap) % cap;
    }
}
public class ListNode {
    int val;
    ListNode next;
    ListNode(int x) {
        val = x;
        next = null;
    }
}