Can HashMap have null keys and null values?

HashMap allows one null key and any number of null values. The null key is stored at bucket 0 with a hash of 0.

The hash function for null

The very first line of HashMap.hash short-circuits null:

static final int hash(Object key) {
    int h;
    return (key == null) ? 0 : (h = key.hashCode()) ^ (h >>> 16);
}

So the null key always hashes to 0, and (n - 1) & 0 == 0, meaning it always lives at index 0.

Null values are unrestricted

There's nothing special about a null value — it's just a reference stored in Node.value. You can have many entries with null values, no problem.

Map<String, String> m = new HashMap<>();
m.put(null, "first");
m.put(null, "second");       // overwrites; one null key only
m.put("a", null);
m.put("b", null);

System.out.println(m.size());     // 3 (null, a, b)
System.out.println(m.get(null));  // second
System.out.println(m.get("a"));   // null

The containsKey trap

Because get returns null both when the key is absent and when its value is null, you cannot distinguish those cases by inspecting the return value:

m.put("present", null);
m.get("present"); // null
m.get("missing"); // null

m.containsKey("present"); // true  -- the right way to check
m.containsKey("missing"); // false

Use containsKey or getOrDefault to disambiguate, or just avoid null values entirely (often better — Optional makes intent explicit).

How other maps compare

TreeMap rejects null keys because it has to call compareTo on them. ConcurrentHashMap rejects both nulls because get returning null would otherwise be ambiguous in concurrent code (you can't safely containsKey-then-get).